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Office: Durand Building, 496 Lomita Mall
Mail Code: 94305-4035
Phone: (650) 723-3317
Web Site: http://aa.stanford.edu

Courses offered by the Department of Aeronautics and Astronautics are listed under the subject code AA on the Stanford Bulletin's ExploreCourses web site.

The Department of Aeronautics and Astronautics prepares students for professional positions in industry, government, and academia by offering a comprehensive program of graduate teaching and research. In this broad program, students have the opportunity to learn and integrate multiple engineering disciplines. The program emphasizes structural, aerodynamic, guidance and control, and propulsion problems of aircraft and spacecraft. Courses in the teaching program lead to the degrees of Master of Science, Engineer, and Doctor of Philosophy. Undergraduates and doctoral students in other departments may also elect a minor in Aeronautics and Astronautics.

Requirements for all degrees include courses on basic topics in Aeronautics and Astronautics, as well as in mathematics, and related fields in engineering and the sciences.

The current research and teaching activities cover a number of advanced fields, with emphasis on:

  • Aeroelasticity and Flow Simulation
  • Aircraft Design, Performance, and Control
  • Applied Aerodynamics
  • Autonomy
  • Computational Aero-Acoustics
  • Computational Fluid Dynamics
  • Computational Mechanics and Dynamical Systems
  • Control of Robots, including Space and Deep-Underwater Robots
  • Conventional and Composite Materials and Structures
  • Decision Making under Uncertainty
  • Direct and Large-Eddy Simulation of Turbulence
  • High-Lift Aerodynamics
  • Hybrid Propulsion
  • Hypersonic and Supersonic Flow
  • Micro and Nano Systems and Materials
  • Multidisciplinary Design Optimization
  • Navigation Systems (especially GPS)
  • Optimal Control, Estimation, System Identification
  • Sensors for Harsh Environments
  • Space Debris Characterization
  • Space Environment Effects on Spacecraft
  • Space Plasmas
  • Spacecraft Design and Satellite Engineering
  • Turbulent Flow and Combustion

Mission of the Undergraduate Program in Aeronautics and Astronautics

The mission of the undergraduate program in Aeronautics and Astronautics Engineering is to provide students with the fundamental principles and techniques necessary for success and leadership in the conception, design, implementation, and operation of aerospace and related engineering systems. Courses in the major introduce students to engineering principles. Students learn to apply this fundamental knowledge to conduct laboratory experiments and aerospace system design problems. Courses in the major include engineering fundamentals, mathematics, and the sciences, as well as in-depth courses in aeronautics and astronautics, dynamics, mechanics of materials, fluids engineering, and heat transfer. The major prepares students for careers in aircraft and spacecraft engineering, space exploration, air and space-based telecommunication industries, teaching, research, military service, and many related technology-intensive fields.

Learning Outcomes (Graduate)

The purpose of the master’s program is to provide students with the knowledge and skills necessary for a professional career or doctoral studies. This is done through course work which provides a solid grounding in the basic disciplines, including fluid mechanics, dynamics and control, propulsion, structural mechanics, and applied or computational mathematics, and course work or supervised research which provides depth and breadth in the student’s area of specialization.

The Ph.D. is conferred upon candidates who have demonstrated substantial scholarship and the ability to conduct independent research. Through course work and guided research, the program prepares students to make original contributions in Aeronautics and Astronautics and related fields.

Graduate Programs in Aeronautics and Astronautics

Admission

To be eligible to apply for admission to the department, a student must have a bachelor’s degree in engineering, physical science, mathematics, or an acceptable equivalent. Students who have not yet received a master’s degree in a closely allied discipline will be considered for admission to the master’s program; eligibility for the Ph.D. program is considered after the master’s year (see “Doctor of Philosophy”). Applications for admission with financial aid (fellowships or assistantships) or without financial aid must be received and completed by December 6 for the next Autumn Quarter.

Information about admission to the Honors Cooperative Program is included in the “School of Engineering” section of this bulletin. The department considers HCP applications for Winter or Spring quarters as well as for Autumn Quarter; prospective applicants may contact the department’s student services office with questions.

Further information and application forms for all graduate degree programs may be obtained from Graduate Admissions, the Registrar’s Office, http://gradadmissions.stanford.edu.

Transfer Credits

The number of transfer credits allowed for each degree (Engineer and Ph.D.) is delineated in the “Graduate Degrees” section of this bulletin; transfer credit is not accepted for the master's degree. Transfer credit is allowed only for courses taken as a graduate student, after receiving a bachelor’s degree, in which equivalence to Stanford courses is established and for which a grade of ‘B’ or better has been awarded. Transfer credits, if approved, reduce the total number of Stanford units required for a degree.

Fellowships and Assistantships

Fellowships and course or research assistantships are available to qualified graduate students. Fellowships sponsored by Gift Funds, Stanford University, and Industrial Affiliates of Stanford University in Aeronautics and Astronautics provide grants to several first-year students for up to five quarters to cover tuition and living expenses. Stanford Graduate Fellowships, sponsored by the University, provide grants for up to three full years of study and research; each year, the department is invited to nominate several outstanding doctoral or predoctoral students for these prestigious awards. Students who have excelled in their master’s-level course work at Stanford are eligible for course assistantships in the department; those who have demonstrated research capability are eligible for research assistantships from individual faculty members. Students may also hold assistantships in other departments if the work is related to their academic progress; the criteria for selecting course or research assistants are determined by each hiring department. A standard, 20 hours/week course or research assistantship provides a semi-monthly salary and an 8-10 unit tuition grant per quarter. Research assistants may be given the opportunity of additional summer employment. They may use their work as the basis for a dissertation or Engineer’s thesis.

Aeronautics and Astronautics Facilities

The work of the department is centered in the William F. Durand Building for Space Engineering and Science. This 120,000 square foot building houses advanced research and teaching facilities and concentrates in one complex the Department of Aeronautics and Astronautics. The Durand Building also houses faculty and staff offices and several conference rooms.

Through the department’s close relations with nearby NASA-Ames Research Center, students and faculty have access to one of the best and most extensive collections of experimental aeronautical research facilities in the world, as well as the latest generation of supercomputers.

General Information

Further information about the facilities and programs of the department is available at http://aa.stanford.edu, or from the department’s student services office.

The department has a student branch of the American Institute of Aeronautics and Astronautics, which sponsors programs and speakers covering aerospace topics and social events. It also conducts visits to nearby research, government, and industrial facilities, and sponsors a Young Astronauts Program in the local schools.

Bachelor of Science in Engineering (Aeronautics and Astronautics)

Although primarily a graduate-level department, the program offers an undergraduate major in Aeronautics and Astronautics (AA) leading to the B.S. degree in Engineering. For further information, see the Handbook for Undergraduate Engineering Programs at http://ughb.stanford.edu.

Undergraduates interested in aerospace are encouraged to combine either a minor or a coterminal M.S. in Aeronautics and Astronautics with a major in a related discipline (such as Mechanical or Electrical Engineering). Students considering these options are encouraged to contact the department’s student services office.

Aeronautics and Astronautics (AA)

Mission of the Undergraduate Program in Aeronautics and Astronautics

The mission of the undergraduate program in Aeronautics and Astronautics Engineering is to provide students with the fundamental principles and techniques necessary for success and leadership in the conception, design, implementation, and operation of aerospace and related engineering systems. Courses in the major introduce students to engineering principles. Students learn to apply this fundamental knowledge to conduct laboratory experiments and aerospace system design problems. Courses in the major include engineering fundamentals, mathematics, and the sciences, as well as in-depth courses in aeronautics and astronautics, dynamics, mechanics of materials, fluids engineering, and heat transfer. The major prepares students for careers in aircraft and spacecraft engineering, space exploration, air and space-based telecommunication industries, teaching, research, military service, and many related technology-intensive fields.

Completion of the undergraduate program in Aeronautics and Astronautics leads to the conferral of the Bachelor of Science in Engineering. The subplan "Aeronautics and Astronautics" appears on the transcript and on the diploma.

Requirements

Units
Mathematics
24 units minimum 1
Select one sequence; may also be satisfied with AP Calculus.
MATH 19
MATH 20
MATH 21
Calculus
and Calculus
and Calculus
10
or
MATH 41
MATH 42
Calculus
and Calculus
10
CME 100/ENGR 154Vector Calculus for Engineers5
or MATH 51 Linear Algebra and Differential Calculus of Several Variables
CME 102/ENGR 155AOrdinary Differential Equations for Engineers5
or MATH 53 Ordinary Differential Equations with Linear Algebra
CME 106/ENGR 155CIntroduction to Probability and Statistics for Engineers4-5
or STATS 110 Statistical Methods in Engineering and the Physical Sciences
or STATS 116 Theory of Probability
or CS 109 Introduction to Probability for Computer Scientists
Science
19 units minimum
PHYSICS 41Mechanics (or AP Physics)4
PHYSICS 43Electricity and Magnetism (or AP Physics)4
PHYSICS 45Light and Heat4
CHEM 31XChemical Principles Accelerated ( or CHEM 31A and CHEM 31B, AP Chemistry)5
Science elective 23-5
Technology in Society (one course required)
3 units minimum; course chosen must be on the SoE Approved Courses list at <ughb.stanford.edu> the year taken. 33-5
Engineering Fundamentals (three courses required)
11 units minimum
ENGR 30Engineering Thermodynamics3
ENGR 70AProgramming Methodology5
Fundamentals Elective 43-5
Engineering Depth
28 units minimum
AA 100Introduction to Aeronautics and Astronautics3
AA 190Directed Research and Writing in Aero/Astro3-5
ME 70Introductory Fluids Engineering4
ENGR 14Intro to Solid Mechanics4
ENGR 15Dynamics4
ME 131AHeat Transfer3
ME 161Dynamic Systems, Vibrations and Control3-4
or PHYSICS 110 Advanced Mechanics
CEE 101AMechanics of Materials4
or ME 80 Mechanics of Materials
Aero/Astro Depth
18 units minimum
Engineering Electives (two courses required) 56-10
See Course List AA-1 below for a list of options
Depth Area I (two courses required) 66-10
See Course List AA-2 below for a list of options
Depth Area II (two courses required) 66-10
See Course List AA-2 below for a list of options
Total Units114-136

For additional information and sample programs see the Handbook for Undergraduate Engineering Programs.

1

It is recommended that the CME series (100, 102) be taken rather than the MATH series (51, 53). If students take the MATH series, it is recommended to take CME 192 Introduction to MATLAB, offered in the autumn, winter and spring. Finally, CME 104 Linear Algebra and Partial Differential Equations for Engineers (or Math 52) is recommended, but not required.

2

Courses that satisfy the Science Requirement are listed in Figure 4-2 in the Handbook for Undergraduate Engineering Programs at http://ughb.stanford.edu.

3

Courses that satisfy the Technology in Society Requirement are listed in Figure 4-3 in the Handbook for Undergraduate Engineering Programs at http://ughb.stanford.edu.

4

Courses that satisfy the Engineering Fundamentals Requirement are listed in Figure 4-4 in the Handbook for Undergraduate Engineering Programs at http://ughb.stanford.edu.  ENGR 70B or X (same as CS 106B or X) is not allowed to fulfill the third fundamentals requirement.

5

Courses that satisfy the Engineering Electives are listed in Figure AA-1 in the Handbook for Undergraduate Engineering Programs at http://ughb.stanford.edu, as well as Course List AA-1 below.

6

Courses that satisfy the Depth Area choices are listed in Figure AA-2 in the Handbook for Undergraduate Engineering Programs at http://ughb.stanford.edu, as well as Course List AA-2 below.

Units
AA-1. Engineering Electives: Two Courses Required
AA 250Nanomaterials for Aerospace3
ENGR 240Introduction to Micro and Nano Electromechanical Systems3
ME 210Introduction to Mechatronics4
ME 220Introduction to Sensors3-4
ME 227Vehicle Dynamics and Control3
ME 250Internal Combustion Engines3-5
ME 257Turbine and Internal Combustion Engines3
ME 260Fuel Cell Science and Technology3
ME 324Precision Engineering4
ME 331AAdvanced Dynamics & Computation3
ME 331BAdvanced Dynamics, Simulation & Control3
ME 345Fatigue Design and Analysis3
ME 348Experimental Stress Analysis3
ME 351AFluid Mechanics3
ME 351BFluid Mechanics3
CHEMENG 140Micro and Nanoscale Fabrication Engineering3
CS 107Computer Organization and Systems3-5
CS 110Principles of Computer Systems3-5
CS 140Operating Systems and Systems Programming3-4
CS 161Design and Analysis of Algorithms3-5
EE 102ASignal Processing and Linear Systems I4
EE 102BSignal Processing and Linear Systems II4
EE 101ACircuits I4
EE 101BCircuits II4
EE 108Digital System Design4
EE 180Digital Systems Architecture4
ENERGY 121Fundamentals of Multiphase Flow3
ENERGY 191Optimization of Energy Systems3-4
ENERGY 226Thermal Recovery Methods3
MATSCI 155Nanomaterials Synthesis4
MATSCI 156Solar Cells, Fuel Cells, and Batteries: Materials for the Energy Solution3-4
MATSCI 197Rate Processes in Materials3-4
MATSCI 198Mechanical Properties of Materials3-4
PHYSICS 100Introduction to Observational Astrophysics4
It is recommended that students review prerequisites for all courses.
Units
AA-2. Depth Area: Four Courses Required, Two From Each of Two Areas
Dynamics and Controls
ENGR 105Feedback Control Design3
ENGR 205Introduction to Control Design Techniques3
AA 203Introduction to Optimal Control and Dynamic Optimization3
AA 222Introduction to Multidisciplinary Design Optimization3-4
AA 242AClassical Dynamics3
AA 271ADynamics and Control of Spacecraft and Aircraft3
Systems Design
AA 236ASpacecraft Design3-5
AA 236BSpacecraft Design Laboratory3-5
AA 241AIntroduction to Aircraft Design, Synthesis, and Analysis3
AA 241BIntroduction to Aircraft Design, Synthesis, and Analysis3
AA 284BPropulsion System Design Laboratory3
Fluids and CFD
AA 200Applied Aerodynamics3
AA 201AFundamentals of Acoustics3
AA 210AFundamentals of Compressible Flow3
AA 214A/CME 207Numerical Methods in Engineering and Applied Sciences3
AA 283Aircraft and Rocket Propulsion3
ME 131BFluid Mechanics: Compressible Flow and Turbomachinery4
ME 140Advanced Thermal Systems5
Structures
AA 240AAnalysis of Structures3
AA 240BAnalysis of Structures3
AA 256Mechanics of Composites3
AA 280Smart Structures3
ME 335AFinite Element Analysis3
It is recommended that students review prerequisites for all courses.

Aeronautics and Astronautics (AA) Minor

The Aero/Astro minor introduces undergraduates to the key elements of modern aerospace systems. Within the minor, students may focus on aircraft, spacecraft, or disciplines relevant to both. The course requirements for the minor are described in detail below. Courses cannot be double-counted within a major and a minor, or within multiple minors; if necessary, the Aero/Astro adviser can help select substitute courses to fulfill the AA minor core.

The following core courses fulfill the minor requirements:

Units
AA 100Introduction to Aeronautics and Astronautics3
ENGR 14Intro to Solid Mechanics *4
ENGR 15Dynamics *4
ENGR 30Engineering Thermodynamics *3
ME 70Introductory Fluids Engineering4
ME 131AHeat Transfer 13
Two courses from one of the upper-division elective areas below (min. 6 units)
Plus one course from a second area below (min. 3 units)9-15
Aerospace Systems Synthesis/Design
Spacecraft Design
Spacecraft Design Laboratory
Introduction to Aircraft Design, Synthesis, and Analysis
Introduction to Aircraft Design, Synthesis, and Analysis
Propulsion System Design Laboratory
Dynamics and Controls
Feedback Control Design
Introduction to Control Design Techniques
Introduction to Optimal Control and Dynamic Optimization
Introduction to Multidisciplinary Design Optimization
Classical Dynamics
Dynamics and Control of Spacecraft and Aircraft
Fluids
Applied Aerodynamics
Fundamentals of Acoustics
Fundamentals of Compressible Flow
Numerical Methods in Engineering and Applied Sciences
Aircraft and Rocket Propulsion
Fluid Mechanics: Compressible Flow and Turbomachinery
Advanced Thermal Systems
Structures
Analysis of Structures
Analysis of Structures
Mechanics of Composites
Smart Structures
Finite Element Analysis
Total Units30-36
*

ENGR 14 Intro to Solid Mechanics, ENGR 15 Dynamics, or ENGR 30 Engineering Thermodynamics are waived as minor requirements if already taken as part of the major.

1

 AA minors that are not ME majors should take ME 131A for 3 units.

Master of Science in Aeronautics and Astronautics

The University’s basic requirements for the master’s degree are outlined in the "Graduate Degrees" section of this bulletin.

Students with an aeronautical engineering background should be able to complete the master’s degree in five quarters; note that many courses are not taught during the summer. Students with a bachelor’s degree in Physical Science, Mathematics, or other areas of Engineering may find it necessary to take certain prerequisite courses, which may lengthen the time required to obtain the master’s degree.

The Master of Science (M.S.) program is a terminal degree program. It is based on the completion of lecture courses focused on a theme within the discipline of Aeronautics and Astronautics engineering. No thesis is required. No research is required.

Grade Point Averages

A minimum grade point average (GPA) of 2.75 is required to fulfill the department's master's degree requirements. A minimum GPA of 3.5 is required for eligibility to attempt the Ph.D. qualifying examination. Students must also meet the University's quarterly academic requirements for graduate students as described in the "Degree Progress" section of this bulletin and in the "Satisfactory Progress" section of the Guide to Graduate Studies in Aeronautics and Astronautics. All courses (excluding seminars) used to satisfy the requirements for basic courses, mathematics and technical electives must be taken for a letter grade. Insufficient grade points on which to base the GPA may delay expected degree conferral or result in refusal of permission to take the qualifying examinations.

Course Requirements

The master's degree program requires 45 quarter units of course work, which must be taken at Stanford. The course work is divided into four categories:

  • Basic Courses
  • Mathematics Courses
  • Technical Electives
  • Other Electives

Basic Courses

Master's degree candidates must select eight courses as follows:

Units
(I) Five courses in the basic areas of Aeronautics and Astronautics (one in each area):
Fluids
AA 200Applied Aerodynamics3
AA 210AFundamentals of Compressible Flow3
Structures
AA 240AAnalysis of Structures3
Guidance and Control
ENGR 105Feedback Control Design3
ENGR 205Introduction to Control Design Techniques3
Propulsion
AA 283Aircraft and Rocket Propulsion3
Experimentation/Design Requirements (see courses under Related Courses tab above)
(II) Three courses (one each from three of the four areas below)
Fluids
AA 200Applied Aerodynamics3
AA 210AFundamentals of Compressible Flow3
AA 244AIntroduction to Plasma Physics and Engineering3
Structures
AA 240BAnalysis of Structures3
AA 242BMechanical Vibrations3
AA 256Mechanics of Composites3
AA 280Smart Structures3
Guidance and Control
AA 242AClassical Dynamics3
AA 242BMechanical Vibrations3
AA 251Introduction to the Space Environment3
AA 271ADynamics and Control of Spacecraft and Aircraft3
AA 272CGlobal Positioning Systems3
AA 279ASpace Mechanics3
One course selected from AA courses numbered 200 and above, excluding seminars and independent research

Course Waivers

Waivers of the basic courses required for the M.S. degree in Aeronautics and Astronautics can only be granted by the instructor of that course. Students who believe that they have had a substantially equivalent course at another institution should consult with the course instructor to determine if they are eligible for a waiver, and with their adviser to judge the effect on their overall program plans. To request a waiver, students should fill out a Petition for Waiver form (reverse side of the department's program proposal) and have it approved by the instructor and their adviser. One additional technical elective must be added for each basic course that is waived.

Mathematics Courses

M.S. candidates are expected to exhibit competence in applied mathematics. Students meet this requirement by taking two courses, for a minimum of 6 units, of either advanced mathematics offered by the Mathematics Department or technical electives that strongly emphasize applied mathematics.  Common choices include:

  • AA 212 Advanced Feedback Control Design
  • AA 214A Numerical Methods in Engineering and Applied Sciences
  • AA 214B Numerical Methods for Compressible Flows
  • AA 214C Numerical Computation of Viscous Flow
  • AA 215A Advanced Computational Fluid Dynamics
  • AA 215B Advanced Computational Fluid Dynamics
  • AA 218 Introduction to Symmetry Analysis
  • AA 222 Introduction to Multidisciplinary Design Optimization
  • AA 228 Decision Making under Uncertainty
  • AA 229 Advanced Topics in Sequential Decision Making
  • AA 242B Mechanical Vibrations

See the list of mathematics courses under Related Courses tab for additional suggestions, which includes all courses in the Mathematics Department numbered 200 or above.

A maximum of three independent study/research units (AA 290 or independent study in another department) may count toward your M.S. program.  If you fulfill your experimentation/design requirement with a course other than AA 290 (or equivalent from another department), it is possible to count AA 290 as a technical or free elective.

Technical Electives

Students, in consultation with their adviser, select at least four courses* from among the graduate-level courses, totaling at least 12 units, from departments in the School of Engineering and related science departments. These courses should be taken for a letter grade; the student should not elect the credit/no-credit option for any course except free elective.

*Up to three seminar units may count toward an M.S. program, and is counted as one technical elective. At least three additional graduate courses offered in Engineering or related math/science departments should be taken to meet the technical elective section requirement.

Other Electives

It is recommended that all candidates enroll in a humanities or social sciences course to complete the 45-unit requirement. Practicing courses in, for example, art, music, and physical education do not qualify in this category.  Language courses may qualify.

Coterminal Master's Program in Aeronautics and Astronautics

This program allows Stanford undergraduates an opportunity to work simultaneously toward a B.S. degree and an M.S. in Aeronautics and Astronautics. Stanford undergraduates who wish to continue their studies for the master of science degree in the coterminal program must have earned a minimum of 120 units towards graduation. This includes allowable Advanced Placement (AP) and transfer credit.

The department-specific AA coterminal program application, which includes information and deadlines, can be obtained from the AA student services office. A completed application (including letters of recommendation, transcripts and GRE scores) must be received no later than the quarter prior to the expected completion of the undergraduate degree. Admission is granted or denied through the departmental faculty admissions committee. Stanford undergraduates interested in learning more about receiving an AA master's degree as a coterm student should review the information on the University Registrar's web site and visit the AA student services office.

University Coterminal Requirements

Coterminal master’s degree candidates are expected to complete all master’s degree requirements as described in this bulletin. University requirements for the coterminal master’s degree are described in the “Coterminal Master’s Program” section. University requirements for the master’s degree are described in the "Graduate Degrees" section of this bulletin.

After accepting admission to this coterminal master’s degree program, students may request transfer of courses from the undergraduate to the graduate career to satisfy requirements for the master’s degree. Transfer of courses to the graduate career requires review and approval of both the undergraduate and graduate programs on a case by case basis.

In this master’s program, courses taken three quarters prior to the first graduate quarter, or later, are eligible for consideration for transfer to the graduate career. No courses taken prior to the first quarter of the sophomore year may be used to meet master’s degree requirements.

Course transfers are not possible after the bachelor’s degree has been conferred.

The University requires that the graduate adviser be assigned in the student’s first graduate quarter even though the undergraduate career may still be open. The University also requires that the Master’s Degree Program Proposal be completed by the student and approved by the department by the end of the student’s first graduate quarter.

The Honors Cooperative Program

The Honors Cooperative Program (HCP) makes it possible for academically qualified engineers and scientists in nearby companies to be part-time master's students in Aeronautics and Astronautics while continuing nearly full-time professional employment. Prospective HCP students follow the same admission process and must meet the same admission requirements as full-time master's students. For more information regarding the Honors Cooperative Program, see the “School of Engineering” section of this bulletin.

Master of Science in Engineering (AA)

Students whose career objectives require a more interdepartmental or narrowly focused program than is possible in the M.S. program in Aeronautics and Astronautics (AA) may pursue a program for an M.S. degree in Engineering (45 units). This program is described in the “Graduate Programs in the School of Engineering” section of this bulletin.

Sponsorship by the Department of Aeronautics and Astronautics in this more general program requires that the student file a proposal before completing 18 units of the proposed graduate program. The proposal must be accompanied by a statement explaining the objectives of the program and how the program is coherent, contains depth, and fulfills a well-defined career objective. The proposed program must include at least 12 units of graduate-level work in the department and meet rigorous standards of technical breadth and depth comparable to the regular AA Master of Science program. The grade and unit requirements are the same as for the M.S. degree in Aeronautics and Astronautics.

Engineer in Aeronautics and Astronautics

The degree of Engineer represents an additional year (or more) of study beyond the M.S. degree and includes a research thesis. The program is designed for students who wish to do professional engineering work upon graduation and who want to engage in more specialized study than is afforded by the master’s degree alone. It is expected that full-time students will be able to complete the degree within two years of study after the master’s degree.

The University’s basic requirements for the degree of Engineer are outlined in the “Graduate Degrees” section of this bulletin. The following are department requirements.

The candidate’s prior study program should have fulfilled the department’s requirements for the master’s degree or a substantial equivalent. Beyond the master’s degree, a total of 45 units of work is required, including a thesis and a minimum of 21 units of courses chosen as follows:

  1. 21 units of approved technical electives, of which 6 are in mathematics or applied mathematics. See the list of mathematics courses under Related Courses tab above. All courses in the Mathematics Department numbered 200 or above are included. The remaining 15 units are chosen in consultation with the adviser, and represent a coherent field of study related to the thesis topic. Suggested fields include: (a) acoustics, (b) aerospace structures, (c) aerospace systems synthesis and design, (d) analytical and experimental methods in solid and fluid mechanics, (e) computational fluid dynamics, and (f) guidance and control.
  2. The remaining 24 units may be thesis, research, technical courses, or free electives.

Candidates for the degree of Engineer are expected to have a minimum grade point average (GPA) of 3.0 for work in courses beyond those required for the master’s degree. All courses except seminars and directed research should be taken for a letter grade.

Engineer's thesis

For specific information on the format and deadlines for submission of theses, please check with the Graduate Degree Progress Office. The department recommends that students follow the format defined in the handbook Directions for Preparing Doctoral Dissertations, available in the Graduate Degree Progress Office. Note: the advisor must sign the thesis before the filing deadline, which is generally the last day of classes during the graduation quarter.

Doctor of Philosophy in Aeronautics and Astronautics

The University’s basic requirements for the Ph.D. degree are outlined in the “Graduate Degrees” section of this bulletin.

Department requirements are stated below. Applicants who have received their M.S. from other institutions may apply directly to the Ph.D. program. Students who are currently pursuing the M.S. in our department and wish to continue for the Ph.D. should submit a graduate program authorization petition form online through Axess at the beginning of their last quarter in the master's program.

Before beginning dissertation research for the Ph.D. degree, a student must pass the departmental qualifying examination. A student must meet the following conditions by the appropriate deadline to be able to take the qualifying examination:

  1. 30 units of master's course work completed in our department. A student who has completed fewer than 30 units may petition to take the qualifying examination.
  2. Stanford graduate GPA of 3.5 or higher.
  3. Investigation of a research problem, under the direction of a faculty member who evaluates this work as evidence of the potential for doctoral research. The minimum requirement for taking the qualifying examination is to complete 3 units of AA 290 before the qualifying examination quarter.

Additional information about the deadlines, nature, and scope of the Ph.D. qualifying examination can be obtained from the department. Recommended courses to prepare for the qualifying examination are listed on the AA web site. After passing the exam, the student must submit an approved program of Ph.D. course work on an Application for Candidacy for Doctoral Degree to the department's student services office.

Course Requirements

Each individual Ph.D. program in Aeronautics and Astronautics, designed by the student in consultation with the adviser, should represent a strong and cohesive program reflecting the student's major field of interest. A total of 90 units of credit is required beyond the M.S. Of these 90 units, a minimum of 27 must be formal course work (excluding research, directed study and seminars), consisting primarily of graduate courses in engineering and the pertinent sciences. The remainder of the 90 units may be in the form of either Ph.D. dissertation units or free electives. For students who elect a minor in another department, a maximum of 9 units from the minor program may be included in the 27 units of formal course work; the remaining minor units may be considered free electives and are included in the 90 unit total required for the AA Ph.D. degree.

Ph.D. students in Aeronautics and Astronautics must take 9 units of mathematics courses, with at least 6 of these units from courses with numbers over 200. The AA department and other engineering departments offer many courses that have sufficient mathematical content that they may be used to satisfy the mathematics requirement. See the list of mathematics courses under Related Courses tab for suggestions. Others may be acceptable if approved by the adviser and the AA Student Services Office.  University requirements for continuous registration apply to doctoral students for the duration of the degree.

Grade Point Average

A minimum grade point average (GPA) of 3.0 is required to fulfill the department’s Ph.D. It is incumbent upon Ph.D. students to request letter grades in all courses listed on the Application for Candidacy form.

Candidacy

Ph.D. students must complete the candidacy process and be admitted to candidacy by their second year of doctoral study. There are two requirements for admission to Ph.D candidacy in Aeronautics and Astronautics: students must first pass the departmental qualifying exam and must then submit an application for candidacy. The candidacy form lists the courses the student will take to fulfill the requirements for the degree. The form must include the 90 non-MS units required for the Ph.D.; it should be signed by the adviser and submitted to the AA student services office for the candidacy chairman's signature. AA has a department-specific candidacy form, which may be obtained in the AA student services office. Candidacy is valid for five years; this term is not affected by leaves of absence. 

Dissertation Reading Committee

Each Ph.D. candidate is required to establish a reading committee for the doctoral dissertation within six months after passing the department’s Ph.D. qualifying exam. Thereafter, the student should consult frequently with all members of the committee about the direction and progress of the dissertation research.

A dissertation reading committee consists of the principal dissertation adviser and at least two other readers. If the principal adviser is emeritus, there should be a non-emeritus co-adviser. It is expected that at least two members of the AA faculty be on each reading committee. If the principal research adviser is not within the AA department, then the student’s AA academic adviser should be one of those members. The initial committee, and any subsequent changes, must be approved by the department Chair.

Although all readers are usually members of the Stanford Academic Council, the department Chair may approve one non-Academic Council reader if the person brings unusual and necessary expertise to the dissertation research. Generally, this non-Academic Council reader will be a fourth reader, in addition to three Academic Council members.

University Oral Examination

The Ph.D. candidate is required to take the University oral examination after the dissertation is substantially completed (with the dissertation draft in writing), but before final approval. The examination consists of a public presentation of dissertation research, followed by substantive private questioning on the dissertation and related fields by the University oral committee (four faculty examiners, plus a chairman). The examiners usually include the three members on the student's Ph.D. reading committee. The chairman must not be in the same department as the student or the adviser. Once the oral has been passed, the student finalizes the dissertation for reading committee review and final approval. Forms for the University oral scheduling and a one-page dissertation abstract should be submitted to the AA student services office at least three weeks prior to the date of the oral for departmental review and approval. Students must be enrolled during the quarter when they take their University oral. If the oral takes place during the vacation time between quarters, the student must be enrolled in the prior quarter.

Doctoral Dissertation

See the Directions for Preparing Doctoral Dissertation, which outlines the University guidelines for preparing a Ph.D. dissertation.

When a student is ready for a final draft of the dissertation, the student should make an appointment to consult with the graduate degree progress officer to review the completion of the Ph.D. program and the strict formatting requirements for the dissertation. Students must submit the final version of the dissertation to the Registrar's Office no later than the posted deadline. Note: All members of the Reading Committee must sign the dissertation before the filing deadline.

The student’s Ph.D. reading committee and University oral committee must each include at least one faculty member from Aeronautics and Astronautics.

Ph.D. Minor in Aeronautics and Astronautics

A student who wishes to obtain a Ph.D. minor in Aeronautics and Astronautics should consult the department office for designation of a minor adviser. A minor in Aeronautics and Astronautics may be obtained by completing 20 units of graduate-level courses in the Department of Aeronautics and Astronautics, following a program and performance approved by the department’s candidacy chair. The student's Ph.D. reading committee and University oral committee must each include at least one faculty member from AA.

Emeriti: (Professors) Arthur E. Bryson, Robert H. Cannon, Richard Christensen*, Daniel B. DeBra, Robert W. MacCormack, Bradford W. Parkinson*, J. David Powell, George S. Springer, Charles R. Steele, Stephen W. Tsai*, Walter G. Vincenti

Chair: Charbel Farhat

Professors: Juan Alonso, Brian J. Cantwell, Fu-Kuo Chang, Per Enge (on leave Winter and Spring Quarters), Charbel Farhat , Ilan Kroo, Sanjay Lall (on leave Autumn, Winter, and Spring Quarters), Sanjiva Lele (on leave Autumn Quarter), Stephen Rock

Research Professors: Antony Jameson

Associate Professor: Sigrid Close

Assistant Professors: Simone D'Amico, Mykel Kochenderfer, Marco Pavone, Mac Schwager, Debbie Senesky

Courtesy Professors: J. Christian Gerdes, Ronald K. Hanson, Lambertus Hesselink

Adjunct Professors: Andrew Barrows, G. Scott Hubbard, Andrew Kalman, Abid Kemal, James Spilker

* Recalled to active duty.

Experimentation/Design Requirements Courses

The following courses satisfy the master's Experimentation/Design Requirements.

Units
AA 236ASpacecraft Design3-5
AA 236BSpacecraft Design Laboratory3-5
AA 236CSpacecraft Design Laboratory3-5
AA 241XAutonomous Aircraft: Design/Build/Fly3
AA 284BPropulsion System Design Laboratory3
CS 225AExperimental Robotics3
CS 402LBeyond Bits and Atoms - Lab1-3
EE 233Analog Communications Design Laboratory3-4
EE 234Photonics Laboratory3
EE 251High-Frequency Circuit Design Laboratory3
EE 312Integrated Circuit Fabrication Laboratory3-4
ENGR 207ALinear Control Systems I3
ENGR 341Micro/Nano Systems Design and Fabrication3-5
MATSCI 160Nanomaterials Laboratory4
MATSCI 164Electronic and Photonic Materials and Devices Laboratory3-4
MATSCI 171Energy Materials Laboratory3-4
MATSCI 172X-Ray Diffraction Laboratory3-4
MATSCI 173Mechanical Behavior Laboratory3-4
MATSCI 322Transmission Electron Microscopy Laboratory3
ME 210Introduction to Mechatronics4
ME 218ASmart Product Design Fundamentals4-5
ME 218BSmart Product Design Applications4-5
ME 218CSmart Product Design Practice4-5
ME 218DSmart Product Design: Projects3-4
ME 220Introduction to Sensors3-4
ME 310AProduct-Based Engineering Design, Innovation, and Development4
ME 310BProduct-Based Engineering Design, Innovation, and Development4
ME 310CProject-Based Engineering Design, Innovation, and Development4
ME 324Precision Engineering4
ME 348Experimental Stress Analysis3
ME 354Experimental Methods in Fluid Mechanics4-5
ME 367Optical Diagnostics and Spectroscopy Laboratory4
ME 385Tissue Engineering Lab1-2

Mathematics Courses

Each Aero/Astro degree has a mathematics requirement, for which courses on the following list are pre-approved. (Other advanced courses may also be acceptable.) Students should consult with their advisers in selecting the most appropriate classes for their field. M.S. candidates select 2 courses; they may also use the mathematics courses listed as common choices in the master's degree course requirements . Engineers select 3 courses; Ph.D. candidates select 3 courses, with at least 6 units from courses numbered above 200.

Units
AA 212Advanced Feedback Control Design3
AA 214ANumerical Methods in Engineering and Applied Sciences3
AA 214BNumerical Methods for Compressible Flows3
AA 214CNumerical Computation of Viscous Flow3
AA 215AAdvanced Computational Fluid Dynamics3
AA 218Introduction to Symmetry Analysis3
AA 222Introduction to Multidisciplinary Design Optimization3-4
AA 228Decision Making under Uncertainty3-4
AA 229Advanced Topics in Sequential Decision Making3-4
AA 242BMechanical Vibrations3
CEE 281Mechanics and Finite Elements3
CME 108Introduction to Scientific Computing3-4
CME 302Numerical Linear Algebra3
CME 303Partial Differential Equations of Applied Mathematics3
CME 306Numerical Solution of Partial Differential Equations3
CME 308Stochastic Methods in Engineering3
CME 326Numerical Methods for Initial Boundary Value Problems3
CS 221Artificial Intelligence: Principles and Techniques3-4
CS 229Machine Learning3-4
EE 261The Fourier Transform and Its Applications3
EE 263Introduction to Linear Dynamical Systems3
EE 264Digital Signal Processing3-4
EE 278Introduction to Statistical Signal Processing3
EE 364AConvex Optimization I3
EE 364BConvex Optimization II3
ENGR 207BLinear Control Systems II3
ENGR 209AAnalysis and Control of Nonlinear Systems3
MATH 113Linear Algebra and Matrix Theory3
MATH 115Functions of a Real Variable3
MATH 120Groups and Rings3
ME 300ALinear Algebra with Application to Engineering Computations3
ME 300BPartial Differential Equations in Engineering3
ME 300CIntroduction to Numerical Methods for Engineering3
ME 335AFinite Element Analysis3
ME 335BFinite Element Analysis3
ME 335CFinite Element Analysis3
ME 408Spectral Methods in Computational Physics3
ME 469Computational Methods in Fluid Mechanics3
ME 469BComputational Methods in Fluid Mechanics3
MS&E 201Dynamic Systems3-4
MS&E 207Interactive Management Science3
MS&E 211Linear and Nonlinear Optimization3-4
MS&E 221Stochastic Modeling3
MS&E 311Optimization3
MS&E 312Advanced Methods in Numerical Optimization3
PHYSICS 211Continuum Mechanics3
STATS 110Statistical Methods in Engineering and the Physical Sciences4-5
STATS 116Theory of Probability3-5
STATS 217Introduction to Stochastic Processes I2-3

Courses

AA 47SI. Why Go To Space?. 1 Unit.

Why do we spend billions of dollars exploring space? What can modern policymakers, entrepreneurs, and industrialists do to help us achieve our goals beyond planet Earth? Whether it is the object of exploration, science, civilization, or conquest, few domains have captured the imagination of a species like space. This course is an introduction to space policy issues, with an emphasis on the modern United States. We will present a historical overview of space programs from all around the world, and then spend the last five weeks discussing present policy issues, through lectures and guest speakers from NASA, the Department of Defense, new and legacy space industry companies, and more. Students will present on one issue that piques their interest, selecting from various domains including commercial concerns, military questions, and geopolitical considerations.

AA 100. Introduction to Aeronautics and Astronautics. 3 Units.

The principles of fluid flow, flight, and propulsion; the creation of lift and drag, aerodynamic performance including takeoff, climb, range, and landing performance, structural concepts, propulsion systems, trajectories, and orbits. The history of aeronautics and astronautics. Prerequisites: MATH 20, 21 or MATH 41, 42; elementary physics.

AA 115N. The Global Positioning System: Where on Earth are We, and What Time is It?. 3 Units.

Preference to freshmen. Why people want to know where they are: answers include cross-Pacific trips of Polynesians, missile guidance, and distraught callers. How people determine where they are: navigation technology from dead-reckoning, sextants, and satellite navigation (GPS). Hands-on experience. How GPS works; when it does not work; possibilities for improving performance.

AA 116Q. Electric Automobiles and Aircraft. 3 Units.

Transportation accounts for nearly one-third of American energy use and greenhouse gas emissions and three-quarters of American oil consumption. It has crucial impacts on climate change, air pollution, resource depletion, and national security. Students wishing to address these issues reconsider how we move, finding sustainable transportation solutions. An introduction to the issue, covering the past and present of transportation and its impacts; examining alternative fuel proposals; and digging deeper into the most promising option: battery electric vehicles. Energy requirements of air, ground, and maritime transportation; design of electric motors, power control systems, drive trains, and batteries; and technologies for generating renewable energy. Two opportunities for hands-on experiences with electric cars. Prerequisites: Introduction to calculus and Physics AP or elementary mechanics.

AA 118N. How to Design a Space Mission: from Concept to Execution. 3 Units.

Space exploration is truly fascinating. From the space race led by governments as an outgrowth of the Cold War to the new era of space commercialization led by private companies and startups, more than 50 years have passed, characterized by great leaps forward and discoveries. We will learn how space missions are designed, from concept to execution, based on the professional experience of the lecturer and numerous examples of spacecraft, including unique hardware demonstrations by startups of the Silicon Valley. We will study the essentials of systems engineering as applicable to a variety of mission types, for communication, navigation, science, commercial, and military applications. We will explore the various elements of a space mission, including the spacecraft, ground, and launch segments with their functionalities. Special emphasis will be given to the design cycle, to understand how spacecraft are born, from the stakeholders' needs, through analysis, synthesis, all the way to their integration and validation. We will compare the current designs with those employed in the early days of the space age, and show the importance of economics in the development of spacecraft. Finally, we will brainstorm startup ideas and apply the concepts learned to a notional space mission design as a team.

AA 119N. 3D Printed Aerospace Structures. 3 Units.

The demand for rapid prototyping of lightweight, complex, and low-cost structures has led the aerospace industry to leverage three-dimensional (3D) printing as a manufacturing technology. For example, the manufacture of aircraft engine components, unmanned aerial vehicle (UAV) wings, CubeSat parts, and satellite sub-systems have recently been realized with 3D printing and other additive manufacturing techniques. In this freshman seminar, a survey of state-of-the-art 3D printing processes will be reviewed and the process-dependent properties of 3D-printed materials and structures will be analyzed in detail. In addition, the advantages and disadvantages of this manufacturing approach will be debated during class! To give students exposure to 3D printing systems in action, tours of actual 3D printing facilities on campus (Stanford's Product Realization Laboratory), as well as in Silicon Valley (e.g., Made in Space) will be conducted.

AA 120Q. Building Trust in Autonomy. 3 Units.

Major advances in both hardware and software have accelerated the development of autonomous systems that have the potential to bring significant benefits to society. Google, Tesla, and a host of other companies are building autonomous vehicles that can improve safety and provide flexible mobility options for those who cannot drive themselves. On the aviation side, the past few years have seen the proliferation of unmanned aircraft that have the potential to deliver medicine and monitor agricultural crops autonomously. In the financial domain, a significant portion of stock trades are performed using automated trading algorithms at a frequency not possible by human traders. How do we build these systems that drive our cars, fly our planes, and invest our money? How do we develop trust in these systems? What is the societal impact on increased levels of autonomy?.

AA 121Q. It IS Rocket Science!. 3 Units.

It's an exciting time for space exploration. Companies like SpaceX and Blue Origin are launching rockets into space and bringing them back for reuse. NASA is developing the world's most powerful rocket. Startups are deploying constellations of hundreds of cubesats for communications, navigation, and earth monitoring. The human race has recently gotten a close look at Pluto, soft landed on a comet, and orbited two asteroids. The upcoming launch of the James Webb Space Telescope will allow astronomers to look closer to the beginning of time than ever before. The workings of space systems remain mysterious to most people, but in this seminar we'll pull back the curtain for a look at the basics of "rocket science." How does a SpaceX rocket get into space? How do Skybox satellites capture images for Google Earth? How did the New Horizons probe find its way to Pluto? How do we communicate with spacecraft that are so distant? We'll explore these topics and a range of others during the quarter. We'll cover just enough physics and math to determine where to look in the sky for a spacecraft, planet, or star. Then we'll check our math by going outside for an evening pizza party observing these objects in the night sky. We'll also visit a spacecraft production facility or Mission Operations Center to see theory put into practice.

AA 122N. Dawn of the Drones: How Will Unmanned Aerial Systems Change Our World?. 3 Units.

Unmanned aerial systems (UASs) have exploded on the scene in recent years, igniting a national debate about how to use them, how to regulate them, and how to make them safe. This seminar will dive into the many engineering challenges behind the headlines: in the future, how will we engineer UASs ranging in size from simple RC toys to highly-sophisticated autonomous scientific and military data gathering systems? This seminar will examine the key elements required to conceive, implement, deploy, and operate state-of-the-art of drone systems: What variety of problems can they help us solve? How autonomous are they and how autonomous do they need to be? What are the key technical bottlenecks preventing widespread deployment? How are they different from commercial aircraft? What kinds of companies will serve the market for UAV-related products and services? What business models will be successful and why? We will emphasize aspects of design, autonomy, reliability, navigation, sensing, and perception, as well as coordination/collaboration through a series of case studies drawn from our recent experience. Examples include imaging efforts to map the changing coral reefs in the South Pacific, using and controlling swarms of unmanned systems to perform search and rescue missions over large areas, and package delivery systems over large metropolitan areas. Hands-on experience with Stanford-developed UASs will be part of the seminar.

AA 190. Directed Research and Writing in Aero/Astro. 3-5 Units.

For undergraduates. Experimental or theoretical work under faculty direction, and emphasizing development of research and communication skills. Written report(s) and letter grade required; if this is not appropriate, enroll in 199. Consult faculty in area of interest for appropriate topics, involving one of the graduate research groups or other special projects. May be repeated for credit. Prerequisite: consent of student services manager and instructor.

AA 199. Independent Study in Aero/Astro. 1-5 Unit.

Directed reading, lab, or theoretical work for undergraduate students. Consult faculty in area of interest for appropriate topics involving one of the graduate research groups or other special projects. May be repeated for credit. Prerequisite: consent of instructor.

AA 200. Applied Aerodynamics. 3 Units.

Analytical and numerical techniques for the aerodynamic analysis of aircraft, focusing on airfoil theory, finite wing theory, far-field and Trefftz-plane analysis, two-dimensional laminar and turbulent boundary layers in airfoil analysis, laminar-to-turbulent transition, compressibility effects, and similarity rules. Biweekly assignments require MATLAB or a suitable programming language. Prerequisite: undergraduate courses in basic fluid mechanics and applied aerodynamics, AA 210A.

AA 201A. Fundamentals of Acoustics. 3 Units.

Acoustic equations for a stationary homogeneous fluid; wave equation; plane, spherical, and cylindrical waves; harmonic (monochromatic) waves; simple sound radiators; reflection and transmission of sound at interfaces between different media; multipole analysis of sound radiation; Kirchoff integral representation; scattering and diffraction of sound; propagation through ducts (dispersion, attenuation, group velocity); sound in enclosed regions (reverberation, absorption, and dispersion); radiation from moving sources; propagation in the atmosphere and underwater. Prerequisite: first-year graduate standing in engineering, mathematics, sciences; or consent of instructor.

AA 201B. Topics in Aeroacoustics. 3 Units.

Acoustic equations for moving medium, simple sources, Kirchhoff formula, and multipole representation; radiation from moving sources; acoustic analogy approach to sound generation in compact flows; theories of Lighthill, Powell, and Mohring; acoustic radiation from moving surfaces; theories of Curl, Ffowcs Williams, and Hawkings; application of acoustic theories to the noise from propulsive jets, and airframe and rotor noise; computational methods for acoustics. Prerequisite: 201A or consent of instructor.

AA 203. Introduction to Optimal Control and Dynamic Optimization. 3 Units.

Basic solution techniques for optimal control and dynamic optimization problems. Dynamic programming, calculus of variations, and numerical techniques for trajectory optimization. Special cases (chiefly LQR and robotic motion planning); modern solution approaches (such as MPC and MILP); and introduction to stochastic optimal control. Examples in MATLAB and CVX.

AA 206. Bio-Aerodynamics. 3 Units.

Topics: flapping flight, low Reynolds number aerodynamics, wing design, flocks, swarms, and dynamic soaring. Readings from current and historical literature dealing with theoretical and observational studies. Applications in aircraft design, and simulation-based problem sets. Prerequisite: course in aerodynamics such as 100, 200A, or 241A.

AA 208. Aerodynamics of Aircraft Dynamic Response and Stability. 3 Units.

Companion to 200A for those interested in control and guidance. Typical vehicles and the technical tradeoffs affecting their design. Equations of motion, stressing applications to dynamic performance, stability, and forced response. Forms and sources for the required aerodynamic data. Response to small disturbances and stability derivatives. Static stability and trim. Review of aerodynamic fundamentals, leading to airload predictions for wings, bodies, and complete aircraft. Paneling and other methods for derivative estimation. Natural motions of the aircraft, and the influence on them of various configuration parameters. Vehicle behavior in maneuvers of small and large amplitudes. Prerequisites: 200A, 210A, or equivalents (may be taken concurrently).

AA 210A. Fundamentals of Compressible Flow. 3 Units.

Topics: development of the three-dimensional, non-steady, field equations for describing the motion of a viscous, compressible fluid; differential and integral forms of the equations; constitutive equations for a compressible fluid; the entropy equation; compressible boundary layers; area-averaged equations for one-dimensional steady flow; shock waves; channel flow with heat addition and friction; flow in nozzles and inlets; oblique shock waves; Prandtl-Meyer expansion; unsteady one-dimensional flow; the shock tube; small disturbance theory; acoustics in one-dimension; steady flow in two-dimensions; potential flow; linearized potential flow; lift and drag of thin airfoils. Prerequisites: undergraduate background in fluid mechanics and thermodynamics.

AA 210B. Fundamentals of Compressible Flow. 3 Units.

Continuation of 210A with emphasis on more general flow geometry. Use of exact solutions to explore the hypersonic limit. Identification of similarity parameters. Solution methods for the linearized potential equation with applications to wings and bodies in steady flow; their relation to physical acoustics and wave motion in nonsteady flow. Nonlinear solutions for nonsteady constant area flow and introduction to Riemann invariants. Elements of the theory of characteristics; nozzle design; extension to nonisentropic flow. Real gas effects in compressible flow. Flows in various gas dynamic testing facilities. Prerequisite: 210A.

AA 212. Advanced Feedback Control Design. 3 Units.

Analysis and design techniques for multivariable feedback systems. State-space concepts, observability, controllability, eigenvalues, eigenvectors, stability, and canonical representations. Approaches for robust feedback control design, chiefly H2, H-infinity, and mu-synthesis. System identification and adaptive control design. Use of computer-aided design with MATLAB. Prerequisite: ENGR 105, ENGR 205. Recommended: Linear algebra (EE 263 or equivalent).

AA 214A. Numerical Methods in Engineering and Applied Sciences. 3 Units.

Scientific computing and numerical analysis for physical sciences and engineering. Advanced version of CME206 that, apart from CME206 material, includes nonlinear PDEs, multidimensional interpolation and integration and an extended discussion of stability for initial boundary value problems. Recommended for students who have some prior numerical analysis experience. Topics include: 1D and multi-D interpolation, numerical integration in 1D and multi-D including adaptive quadrature, numerical solutions of ordinary differential equations (ODEs) including stability, numerical solutions of 1D and multi-D linear and nonlinear partial differential equations (PDEs) including concepts of stability and accuracy. Prerequisites: linear algebra, introductory numerical analysis (CME 108 or equivalent).
Same as: CME 207, GEOPHYS 217

AA 214B. Numerical Methods for Compressible Flows. 3 Units.

For M.S.-level graduate students. Covers the hierarchy of mathematical models for compressible flows. Introduction to finite difference, finite volume, and finite element methods for their computation. Ideal potential flow; transonic potential flow; Euler equations; Navier-Stokes equations; representative model problems; shocks, expansions, and contact discontinuities; treatment of boundary conditions; time and pseudo-time integration schemes. Prerequisites: basic knowledge of linear algebra and ODEs (CME 206 or equivalent).

AA 214C. Numerical Computation of Viscous Flow. 3 Units.

Numerical methods for solving parabolic sets of partial differential equations. Numerical approximation of the equations describing compressible viscous flow with adiabatic, isothermal, slip, and no-slip wall boundary conditions. Applications to the Navier-Stokes equations in two and three dimensions at high Reynolds number. Computational problems are assigned. Prerequisite: 214B.

AA 215A. Advanced Computational Fluid Dynamics. 3 Units.

High resolution schemes for capturing shock waves and contact discontinuities; upwinding and artificial diffusion; LED and TVD concepts; alternative flow splittings; numerical shock structure. Discretization of Euler and Navier Stokes equations on unstructured meshes; the relationship between finite volume and finite element methods. Time discretization; explicit and implicit schemes; acceleration of steady state calculations; residual averaging; math grid preconditioning. Automatic design; inverse problems and aerodynamic shape optimization via adjoint methods. Pre- or corequisite: 214B or equivalent.
Same as: CME 215A

AA 215B. Advanced Computational Fluid Dynamics. 3 Units.

High resolution schemes for capturing shock waves and contact discontinuities; upwinding and artificial diffusion; LED and TVD concepts; alternative flow splittings; numerical shock structure. Discretization of Euler and Navier Stokes equations on unstructured meshes; the relationship between finite volume and finite element methods. Time discretization; explicit and implicit schemes; acceleration of steady state calculations; residual averaging; math grid preconditioning. Automatic design; inverse problems and aerodynamic shape optimization via adjoint methods. Pre- or corequisite: 214B or equivalent.
Same as: CME 215B

AA 218. Introduction to Symmetry Analysis. 3 Units.

Methods of symmetry analysis and their use in the reduction and simplification of physical problems. Topics: dimensional analysis, phase-space analysis of autonomous systems of ordinary differential equations, use of Lie groups to reduce the order of nonlinear ODEs and to generate integrating factors, use of Lie groups to reduce the dimension of partial differential equations and to generate similarity variables, exact solutions of nonlinear PDEs generated from groups. Mathematica-based software developed by the instructor is used for finding invariant groups of ODEs and PDEs.

AA 222. Introduction to Multidisciplinary Design Optimization. 3-4 Units.

Design of aerospace systems within a formal optimization environment. Mathematical formulation of the multidisciplinary design problem (parameterization of design space, choice of objective functions, constraint definition); survey of algorithms for unconstrained and constrained optimization and optimality conditions; description of sensitivity analysis techniques. Hierarchical techniques for decomposition of the multidisciplinary design problem; use of approximation theory. Applications to design problems in aircraft and launch vehicle design. Prerequisites: multivariable calculus; familiarity with a high-level programming language: FORTRAN, C, C++, MATLAB, Python, or Julia.
Same as: CS 361

AA 228. Decision Making under Uncertainty. 3-4 Units.

This course is designed to increase awareness and appreciation for why uncertainty matters, particularly for aerospace applications. Introduces decision making under uncertainty from a computational perspective and provides an overview of the necessary tools for building autonomous and decision-support systems. Following an introduction to probabilistic models and decision theory, the course will cover computational methods for solving decision problems with stochastic dynamics, model uncertainty, and imperfect state information. Topics include: Bayesian networks, influence diagrams, dynamic programming, reinforcement learning, and partially observable Markov decision processes. Applications cover: air traffic control, aviation surveillance systems, autonomous vehicles, and robotic planetary exploration. Prerequisites: basic probability and fluency in a high-level programming language.
Same as: CS 238

AA 229. Advanced Topics in Sequential Decision Making. 3-4 Units.

Survey of recent research advances in intelligent decision making for dynamic environments from a computational perspective. Efficient algorithms for single and multiagent planning in situations where a model of the environment may or may not be known. Partially observable Markov decision processes, approximate dynamic programming, and reinforcement learning. New approaches for overcoming challenges in generalization from experience, exploration of the environment, and model representation so that these methods can scale to real problems in a variety of domains including aerospace, air traffic control, and robotics. Students are expected to produce an original research paper on a relevant topic. Prerequisites: AA 228/CS 238 or CS 221.
Same as: CS 239

AA 236A. Spacecraft Design. 3-5 Units.

The design of unmanned spacecraft and spacecraft subsystems emphasizing identification of design drivers and current design methods. Topics: spacecraft configuration design, mechanical design, structure and thermal subsystem design, attitude control, electric power, command and telemetry, and design integration and operations.

AA 236B. Spacecraft Design Laboratory. 3-5 Units.

Continuation of 236A. Emphasis is on practical application of systems engineering to the life cycle program of spacecraft design, testing, launching, and operations. Prerequisite: 236A or consent of instructor.

AA 236C. Spacecraft Design Laboratory. 3-5 Units.

.

AA 240A. Analysis of Structures. 3 Units.

Elements of two-dimensional elasticity theory. Boundary value problems; energy methods; analyses of solid and thin walled section beams, trusses, frames, rings, monocoque and semimonocoque structures. Prerequisite: ENGR 14 or equivalent.

AA 240B. Analysis of Structures. 3 Units.

Thin plate analysis. Structural stability. Material behavior: plasticity and fracture. Introduction of finite element analysis; truss, frame, and plate structures. Prerequisite: 240A or consent of instructor.

AA 241A. Introduction to Aircraft Design, Synthesis, and Analysis. 3 Units.

New aircraft systems emphasizing commercial aircraft. Economic and technological factors that create new aircraft markets. Determining market demands and system mission performance requirements; optimizing configuration to comply with requirements; the interaction of disciplines including aerodynamics, structures, propulsion, guidance, payload, ground support, and parametric studies. Applied aerodynamic and design concepts for use in configuration analysis. Application to a student-selected aeronautical system; applied structural fundamentals emphasizing fatigue and fail-safe considerations; design load determination; weight estimation; propulsion system performance; engine types; environmental problems; performance estimation. Direct/indirect operating costs prediction and interpretation. Aircraft functional systems; avionics; aircraft reliability and maintainability. Prerequisite: 100 or equivalent.

AA 241B. Introduction to Aircraft Design, Synthesis, and Analysis. 3 Units.

New aircraft systems emphasizing commercial aircraft. Economic and technological factors that create new aircraft markets. Determining market demands and system mission performance requirements; optimizing configuration to comply with requirements; the interaction of disciplines including aerodynamics, structures, propulsion, guidance, payload, ground support, and parametric studies. Applied aerodynamic and design concepts for use in configuration analysis. Application to a student-selected aeronautical system; applied structural fundamentals emphasizing fatigue and fail-safe considerations; design load determination; weight estimation; propulsion system performance; engine types; environmental problems; performance estimation. Direct/indirect operating costs prediction and interpretation. Aircraft functional systems; avionics; aircraft reliability and maintainability. Prerequisite: 100 or equivalent.

AA 241X. Autonomous Aircraft: Design/Build/Fly. 3 Units.

Students grouped according to their expertise to carry out the multidisciplinary design of a solar-powered autonomous aircraft that must meet a clearly stated set of design requirements. Design and construction of the airframe, integration with existing guidance, navigation, and control systems, and development and operation of the resulting design. Design reviews and reports. Prerequisites: expertise in any of the following disciplines by having satisfied the specified courses or equivalent work elsewhere: conceptual design (241A,B); applied aerodynamics (200A,B); structures (240A); composite manufacturing experience; guidance and control (208/271, ENGR 205).

AA 242A. Classical Dynamics. 3 Units.

Accelerating and rotating reference frames. Kinematics of rigid body motion; Euler angles, direction cosines. D'Alembert's principle, equations of motion. Inertia properties of rigid bodies. Dynamics of coupled rigid bodies. Lagrange's equations and their use. Dynamic behavior, stability, and small departures from equilibrium. Prerequisite: ENGR 15 or equivalent.

AA 242B. Mechanical Vibrations. 3 Units.

For M.S.-level graduate students. Covers the vibrations of discrete systems and continuous structures. Introduction to the computational dynamics of linear engineering systems. Review of analytical dynamics of discrete systems; undamped and damped vibrations of N-degree-of-freedom systems; continuous systems; approximation of continuous systems by displacement methods; solution methods for the Eigenvalue problem; direct time-integration methods. Prerequisites: AA 242A or equivalent (recommended but not required); basic knowledge of linear algebra and ODEs; no prior knowledge of structural dynamics is assumed.
Same as: ME 242B

AA 244A. Introduction to Plasma Physics and Engineering. 3 Units.

Physics and engineering of plasmas, including space and laboratory plasmas. Debye length and distribution functions. Single-particle motion and drifts. Plasmas as fluids and fluid drifts. Waves in plasmas, including electrostatic and electromagnetic. Diffusion and resistivity. Magnetohydrodynamics.

AA 244B. Advanced Plasma Physics and Engineering. 3 Units.

Equilibrium and instability. Turbulent flow in plasmas. Kinetic theory and the Vlasov equation. Nonlinear effects and solutions. Radiation in a plasma. Plasma diagnostics in ground- and space-based experiments.

AA 250. Nanomaterials for Aerospace. 3 Units.

Properties of nanomaterials and current approaches for engineering spacecraft, aircraft, and subsystems with nanotechnology. Manufacturing of nanomaterials; nano-fiber reinforced composites; structural mechanics of nanomaterials; structure-property relationships; and application of nanotechnology for lightweight structures, thermal protection, nanopropellants, and nanoelectronics.

AA 251. Introduction to the Space Environment. 3 Units.

The environment through which space probes and vehicles travel and orbit. Survey of physical phenomena in the sun, solar wind, magnetospheres, ionospheres, and upper atmospheres of objects in the solar system. Introduction to the physical processes governing space plasmas, solar-terrestrial interactions, and ionized and neutral media surrounding the Earth and other solar system bodies. Prerequisite: AA 244A.

AA 252. Techniques of Failure Analysis. 3 Units.

Introduction to the field of failure analysis, including fire and explosion analysis, large scale catastrophe projects, traffic accident reconstruction, aircraft accident investigation, human factors, biomechanics and accidents, design defect cases, materials failures and metallurgical procedures, and structural failures. Product liability, failure modes and effects analysis, failure prevention, engineering ethics, and the engineer as expert witness.

AA 256. Mechanics of Composites. 3 Units.

Fiber reinforced composites. Stress, strain, and strength of composite laminates and honeycomb structures. Failure modes and failure criteria. Environmental effects. Manufacturing processes. Design of composite structures. Individual design project required of each student, resulting in a usable computer software. Prerequisite: ENGR 14 or equivalent.

AA 257. Design of Composite Structures. 3 Units.

Hands-on design, analysis, and manufacturing in composites. Composite beams, columns, and plates; application of finite element methods to composite structures; failure analysis and damage tolerance design of composite structures; and impact damage, compression after impact, and bolted and bonded composites joints. Class divided into working teams (design, analysis, manufacturing, and tests) to design and build a composite structure to be tested to failure; the structure may enter the national SAMPE composite bridge design contest. Prerequisite: 256 or consent of instructor.

AA 260. Sustainable Aviation. 3 Units.

Quantitative assessment of the impact of aviation on the environment including noise, local, and global emissions, and models used to predict it. Current and future technologies that may allow the air transportation system to meet anticipated growth while reducing or minimizing environmental problems. Atmospheric effects of NOx, CO2, particulates, unburned hydrocarbons, and water vapor deposition at high altitudes and metrics for assessing global climate effects. Noise sources, measurement, and mitigation strategies. Fundamentals of aircraft and engine performance needed to assess current and future concepts. Major national and international policy implications of existing and future technology choices. Recommended: AA 241B.

AA 271A. Dynamics and Control of Spacecraft and Aircraft. 3 Units.

The dynamic behavior of aircraft and spacecraft, and the design of automatic control systems for them. For aircraft: non-linear and linearized longitudinal and lateral dynamics; linearized aerodynamics; natural modes of motion; autopilot design to enhance stability, control the flight path, and perform automatic landings. For spacecraft in orbit: natural longitudinal and lateral dynamic behavior and the design of attitude control systems. Prerequisites: AA242A, ENGR 105.

AA 272C. Global Positioning Systems. 3 Units.

The principles of satellite navigation using GPS. Positioning techniques using code tracking, single and dual frequency, carrier aiding, and use of differential GPS for improved accuracy and integrity. Use of differential carrier techniques for attitude determination and precision position determination. Prerequisite: familiarity with matrix algebra and MatLab (or another mathematical programming language).

AA 272D. Integrated Navigation Systems. 3 Units.

Navigation satellites (GPS, GLONASS), GPS receivers, principles of inertial navigation for ships, aircraft, and spacecraft. Kalman Filters to integrate GPS and inertial sensors. Radio navigation aids (VOR, DME, LORAN, ILS). Doppler navigation systems. Prerequisites: 272C; ENGR 15, 105. Recommended: ENGR 205.

AA 273. State Estimation and Filtering for Aerospace Systems. 3 Units.

Kalman filtering, recursive Bayesian filtering, and nonlinear filter architectures including the extended Kalman filter, particle filter, and unscented Kalman filter. Observer-based state estimation for linear and non-linear systems. Examples from aerospace, including state estimation for fixed-wing aircraft, rotorcraft, spacecraft, and planetary rovers, with applications to control, navigation, and autonomy.

AA 274. Principles of Robotic Autonomy. 3 Units.

Basic principles for endowing mobile autonomous robots with perception, planning, and decision-making capabilities. Algorithmic approaches for robot perception, localization, and simultaneous localization and mapping; control of non-linear systems, learning-based control, and robot motion planning; introduction to methodologies for reasoning under uncertainty, e.g., (partially observable) Markov decision processes. Extensive use of the Robot Operating System (ROS) for demonstrations and hands-on activities. Prerequisite: CS 106A or equivalent.

AA 277. Multi-robot Control, Communication, and Sensing. 3 Units.

Survey of current research topics in multi-robot systems including multi-agent consensus, formation control, coverage control and sensor deployment, collision avoidance, cooperative mapping, and distributed Bayesian filtering. Students will develop skills in evaluating and critiquing research papers, and will conduct a final research project.

AA 279A. Space Mechanics. 3 Units.

Orbits of near-earth satellites and interplanetary probes; relative motion in orbit; transfer and rendezvous; orbit determination; influence of earth's oblateness; sun and moon effects on earth satellites; decay of satellite orbits; invited lectures from industry. Prerequisite: ENGR 15 and familiarity with MatLab.

AA 279B. Advanced Space Mechanics. 3 Units.

Restricted 3-body problem. Relative motion, Hill's and Clohessy-Wiltshire equations. Lambert's problem. Satellite constellations and optimization. Communications and link budgets. Space debris. High fidelity simulation. Interplanetary mission planning, launch windows and gravity assists. Basic trajectory optimization. Several guest lectures from practitioners in the field. Individual final project chosen in consultation with instructor. Prerequisites: 279A or equivalent with permission of instructor. Fluency with MATLAB (or another mathematical programming language with 2D and 3D plotting capabilities).

AA 279C. Spacecraft Attitude Determination and Control. 3 Units.

Attitude representation and parametrization; unperturbed and perturbed attitude dynamics and stability; attitude sensors and actuators; linear and nonlinear attitude control; optimal attitude maneuvers; dynamics of flexible spacecraft and space tethers; invited lectures from industry. Prerequisites: AA 242A, ENGR 105, AA 279A, and familiarity with MatLab.

AA 279D. Distributed Space Systems. 3 Units.

Keplerian orbital mechanics and orbital perturbations; the general relative motion problem; linear formation flying dynamics and control; impulsive station-keeping and reconfiguration; high order relative motion equations; formulation of relative motion using orbital elements; perturbation-invariant formations; nonlinear formation control; low-thrust propulsion for formation flying; relative navigation using GNSS and optical navigation; applications: sparse-aperture imaging, remote sensing, on-orbit servicing, rendezvous, and docking. Prerequisite: AA 242A, ENGR 105, AA 279A, and familiarity with MatLab.

AA 280. Smart Structures. 3 Units.

Mechanics of smart materials and current approaches for engineering smart structures to monitor health, self heal, and adapt to environment. Definition of smart structures; constitutive models for smart materials; piezoelectric ceramics; electro-active polymers; shape memory alloys; bio-inspired materials and structures; self-healing materials; sensors and sensor networks; structural health monitoring; and energy harvesting. Prerequisite: AA 240A or consent of instructor.

AA 283. Aircraft and Rocket Propulsion. 3 Units.

Introduction to the design and performance of airbreathing and rocket engines. Topics: the physical parameters used to characterize propulsion system performance; gas dynamics of nozzles and inlets; cycle analysis of ramjets, turbojets, turbofans, and turboprops; component matching and the compressor map; introduction to liquid and solid propellant rockets; multistage rockets; hybrid rockets; thermodynamics of reacting gases. Prerequisites: undergraduate background in fluid mechanics and thermodynamics.

AA 284A. Advanced Rocket Propulsion. 3 Units.

The principles of rocket propulsion system design and analysis. Fundamental aspects of the physics and chemistry of rocket propulsion. Focus is on the design and analysis of chemical propulsion systems including liquids, solids, and hybrids. Nonchemical propulsion concepts such as electric and nuclear rockets. Launch vehicle design and optimization issues including trajectory calculations. Limited enrollment. Prerequisites: 283 or consent of instructor.

AA 284B. Propulsion System Design Laboratory. 3 Units.

Propulsion systems engineering through the design and operation of a sounding rocket. Students work in small teams through a full project cycle including requirements definition, performance analysis, system design, fabrication, ground and flight testing, and evaluation. Prerequisite: 284A and consent of instructor.

AA 284C. Propulsion System Design Laboratory. 3 Units.

Continuation of 284A,B. Prerequisite: 284B, and consent of instructor.

AA 290. Problems in Aero/Astro. 1-15 Unit.

(Undergraduates register for 190 or 199.) Experimental or theoretical investigation. Students may work in any field of special interest. Register for section belonging to your research supervisor. May be repeated for credit.

AA 291. Practical Training. 1-3 Unit.

Educational opportunities in high-technology research and development labs in aerospace and related industries. Internship integrated into a student's academic program. Research report outlining work activity, problems investigated, key results, and any follow-on projects. Meets the requirements for Curricular Practical Training for students on F-1 visas. Student is responsible for arranging own employment and should see department student services manager before enrolling. May be repeated for credit.

AA 294. Case Studies in Aircraft Design. 1 Unit.

Presentations by researchers and industry professionals. Registration for credit optional. May be repeated for credit.

AA 295. Aerospace Structures and Materials. 1 Unit.

Presentations by researchers and industry professionals in aerospace structures and materials. May be repeated for credit.

AA 297. Seminar in Guidance, Navigation, and Control. 1 Unit.

For graduate students with an interest in automatic control applications in flight mechanics, guidance, navigation, and mechanical design of control systems; others invited. Problems in all branches of vehicle control, guidance, and instrumentation presented by researchers on and off campus. Registration for credit optional. May be repeated for credit.

AA 300. Engineer Thesis. 1-15 Unit.

Thesis for degree of Engineer. Students register for section belonging to their thesis adviser.

AA 301. Ph.D. Dissertation. 1-15 Unit.

Prerequisite: completion of Ph.D qualifying exams. Students register for section belonging to their thesis adviser. (Staff).

AA 801. TGR Engineer Thesis. 0 Units.

Engineer's thesis or non-doctoral work for a TGR student.

AA 802. TGR Ph.D. Dissertation. 0 Units.

Doctoral dissertation for a TGR student in PhD program.