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Aeronautics and Astronautics


Office: Durand Building, 496 Lomita Mall
Mail Code: 94305-4035
Phone: (650) 723-3317
Web Site:

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
  • 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
  • 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


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 admitted 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 2 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 may consider HCP applications for Winter or Spring quarters as well as for Autumn Quarter; prospective applicants should contact the department’s student services office.

Further information and application forms for all graduate degree programs may be obtained from Graduate Admissions, the Registrar’s Office,

Waivers and Transfer Credits

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.

A similar procedure should be followed for 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 M.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 the nine-month academic year to cover tuition and living expenses. Stanford Graduate Fellowships, sponsored by the University, provide grants for 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, 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 and an undergraduate minor in Aeronautics and Astronautics. For further information, see the Handbook for Undergraduate Engineering Programs at

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.


24 units minimum 1
MATH 41 (or AP Calculus)5
MATH 42Calculus (or AP Calculus)5
CME 100/ENGR 154Vector Calculus for Engineers5
or Math 51
CME 102/ENGR 155AOrdinary Differential Equations for Engineers5
or MATH 53
CME 106/ENGR 155CIntroduction to Probability and Statistics for Engineers (or STATS 110, STATS 116, CS 109)4-5
or STATS 110
or STATS 116
or CS 109 Introduction to Probability for Computer Scientists
19 units minimum
PHYSICS 41Mechanics (or AP Physics)4
PHYSICS 43 (or AP Physics)4
CHEM 31X ( or CHEM 31A+B, AP Chemistry)4-5
or ENGR 31
Science elective 23-5
Technology in Society (one course required)
3 units minimum 33-5
Engineering Fundamentals (three courses required)
11 units minimum
ENGR 303
Fundamentals Elective 43-5
Engineering Depth
30 units minimum
AA 1003
AA 190Directed Research and Writing in Aero/Astro3-5
ME 704
ENGR 14Intro to Solid Mechanics4
ME 131A3
ENGR 154
ME 161Dynamic Systems, Vibrations and Control3-4
or PHYSICS 110
CEE 101A4
or ME 80
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 Units103-126

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


It is recommended that the CME series (100, 102, 104) be taken rather than the MATH series (51, 52, 53). If students take the MATH series, it is recommended to take MATH 51M , offered Autumn Quarter.


Courses that satisfy the Science elective are listed in Figure 3-2 in the Handbook for Undergraduate Engineering Programs at


Courses that satisfy the Technology in Society Requirement are listed in Figure 3-3 in the Handbook for Undergraduate Engineering Programs at


Courses that satisfy the Engineering Fundamentals elective are listed in Figure 3-4 in the Handbook for Undergraduate Engineering Programs at  ENGR 70B or X (same as CS 106B or X) is not allowed to fulfill the third fundamentals requirement.


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


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

AA-1. Engineering Electives: Two Courses Required
AA 250Nanomaterials for Aerospace3
ENGR 2403
ME 2104
ME 2203-4
ME 2273
ME 250Internal Combustion Engines3-5
ME 257Turbine and Internal Combustion Engines3
ME 260Fuel Cell Science and Technology3
ME 3244
ME 331A
ME 331B3
ME 345Fatigue Design and Analysis3
ME 3483
ME 351A
ME 351B
CS 107
CS 110
CS 140
CS 161
EE 102ASignal Processing and Linear Systems I4
EE 102B
EE 101ACircuits I4
EE 101B
ENERGY 191Optimization of Energy Systems3-4
ENERGY 226Thermal Recovery Methods3
MATSCI 155Nanomaterials Synthesis4
MATSCI 198Mechanical Properties of Materials3-4
* It is recommended that students review prerequisites for all courses.
AA-2. Depth Area: Four Courses Required, Two From Each of Two Areas
Dynamics and Controls
ENGR 105
ENGR 205
AA 203
AA 222Introduction to Multidisciplinary Design Optimization3-4
AA 242A
AA 271A
Systems Design
AA 236A
AA 236BSpacecraft Design Laboratory3-5
AA 241AIntroduction to Aircraft Design, Synthesis, and Analysis3
AA 241B
AA 284B
Fluids and CFD
AA 200Applied Aerodynamics3
AA 201AFundamentals of Acoustics3
AA 210A
AA 214A/CME 206/ME 300C
AA 2833
ME 131B
ME 140
AA 240AAnalysis of Structures3
AA 240B
AA 256
AA 280
ME 335A
* 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:

AA 1003
ENGR 14Intro to Solid Mechanics *4
ENGR 15 *4
ENGR 30 *3
ME 704
ME 131A3
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)9-14
Aerospace Systems Synthesis/Design
AA 236A
Spacecraft Design Laboratory
Introduction to Aircraft Design, Synthesis, and Analysis
AA 241B
AA 284B
Dynamics and Controls
ENGR 105
ENGR 205
AA 203
Introduction to Multidisciplinary Design Optimization
AA 242A
AA 271A
Applied Aerodynamics
Fundamentals of Acoustics
AA 210A
AA 214A
AA 283
ME 131B
ME 140
Analysis of Structures
AA 240B
AA 256
AA 280
ME 335A
Total Units30-35

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

Coterminal Degrees Program in Aeronautics and Astronautics

This special program allows Stanford undergraduates an opportunity to work simultaneously toward a B.S. in another field and an M.S. in Aeronautics and Astronautics. General requirements for this program and admissions procedures are described in the “School of Engineering” section of this bulletin. Admission is granted or denied through the departmental faculty Admissions and Awards Committee. A coterminal student must meet the course and scholarship requirements detailed for the M.S. below.

For University coterminal degree program rules and University application forms, see

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 qualify for the master’s degree in three quarters of work at Stanford. 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 would lengthen the time required to obtain the master’s degree. The following are departmental requirements.

Grade Point Averages

A minimum grade point average (GPA) of 2.75 is required to fulfill the department’s M.S. degree requirements; a minimum GPA of 3.5 is required for eligibility to attempt the Ph.D. qualifying examination. It is incumbent upon both M.S. and potential Ph.D. candidates to request letter grades in all courses except those that do not offer a letter grade option and those that fall into the categories of colloquia and seminars (for example, ENGR 298 Seminar in Fluid Mechanics ). 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 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.

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

M.S. candidates must select eight courses as follows:

(I) Five courses in the basic areas of Aeronautics and Astronautics (one in each area):
AA 200Applied Aerodynamics3
AA 210A3
AA 240AAnalysis of Structures3
Guidance and Control
ENGR 1053
ENGR 2053
AA 2833
Experimentation/Design Requirements (see courses under Related Courses tab above)
(II) Three courses (one each from three of the four areas below)
AA 200Applied Aerodynamics3
AA 210A3
AA 244A3
AA 240B3
AA 242BMechanical Vibrations3
AA 2563
AA 2803
Guidance and Control
AA 242A3
AA 242BMechanical Vibrations3
AA 2513
AA 271A3
AA 272CGlobal Positioning Systems3
AA 279A3
One course selected from AA courses numbered 200 and above, excluding seminars and independent research

 Candidates who believe they have satisfied a basic course requirement in previous study may request a waiver of one or more courses (see “Waivers and Transfer Credits” in the "Graduate Programs in Aeronautics and Astronautics" section of this bulletin).

Mathematics Courses

M.S. candidates are expected to exhibit  competence in applied mathematics. Students meet this requirement by taking 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 214A

AA 214B

AA 214C Numerical Computation of Viscous Flow

AA 215A

AA 215B Advanced Computational Fluid Dynamics

AA 218

AA 222 Introduction to Multidisciplinary Design Optimization

See the list of mathematics courses under Related Courses tab above for additional suggestions. All courses in the Mathematics Department numbered 200 or above are also included as suggestions.

Technical Electives

Students, in consultation with their advisers, select at least four courses (totaling at least 12 units) from among the graduate-level courses offered by departments of the School of Engineering and related science departments. Normally, one course (3 units) may be directed research.

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.

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 30 units of courses chosen as follows:

  1. 24 units of approved technical electives, of which 9 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. 6 units of free electives.
  3. The remaining 15 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.

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.

Qualifications for candidacy for the doctoral degree are contingent on:

  1. Having fulfilled department requirements for the master’s degree or its substantial equivalent.
  2. Maintaining a high scholastic record for graduate course work.
  3. Completing 3 units of a directed research problem (AA 290 ).
  4. In the first year of doctoral study, passing an oral Ph.D. qualifying examination given by the department during Autumn and Spring quarters.

Detailed information about the deadlines, nature, and scope of the Ph.D. qualifying examination can be obtained from the department. Research on the doctoral dissertation may not be formally started before passing this examination.

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 work is required beyond the master's degree, including a minimum of 36 units of approved formal course work (excluding research, directed study, and seminars). The courses should consist primarily of graduate courses in engineering and related 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 12 units from the minor program may be included in the 36 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 12 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 above 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.


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. Detailed deadlines for the qualifying exam may be obtained from the AA Student Services Office. 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. Reading committees in Aeronautics and Astronautics often include faculty from another department. 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 and Dissertation

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.

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 Aeronautics and Astronautics.

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: Brian J. Cantwell, Fu-Kuo Chang, Per Enge, Charbel Farhat , Sanjiva Lele, Stephen Rock

Research Professors: Antony Jameson, Ilan Kroo

Associate Professors: Juan Alonso, Sanjay Lall

Assistant Professors: Sigrid Close, Simone D'Amico, Mykel Kochenderfer, Marco Pavone, Debbie Senesky

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

Consulting Professors: G. Scott Hubbard

Consulting Assistant Professor: Andrew Barrows, Andrew Kalman, Steven Murray, Frank Van Diggelen

* Recalled to active duty.

Experimentation/Design Requirements Courses

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

EE 233Analog Communications Design Laboratory3-4
EE 234Photonics Laboratory3
EE 345Optical Fiber Communication Laboratory3
EE 412Advanced Nanofabrication Laboratory3
ENGR 206Control System Design3-4
MATSCI 160Nanomaterials Laboratory4
MATSCI 162X-Ray Diffraction Laboratory3-4
MATSCI 172X-Ray Diffraction Laboratory3-4
MATSCI 322Transmission Electron Microscopy Laboratory3
ME 218ASmart Product Design Fundamentals4-5
ME 310AProduct-Based Engineering Design, Innovation, and Development4
ME 310BProduct-Based Engineering Design, Innovation, and Development4
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 4 courses, with at least 6 units from courses numbered above 200.

AA 214CNumerical Computation of Viscous Flow3
AA 215BAdvanced Computational Fluid Dynamics3
AA 222Introduction to Multidisciplinary Design Optimization3-4
CEE 281Mechanics and Finite Elements3
CME 108Introduction to Scientific Computing3-4
CME 306Numerical Solution of Partial Differential Equations3
CME 326Numerical Methods for Initial Boundary Value Problems3
EE 264Digital Signal Processing3-4
ENGR 209AAnalysis and Control of Nonlinear Systems3
MATH 115Functions of a Real Variable3
MATH 132Partial Differential Equations II3
ME 300ALinear Algebra with Application to Engineering Computations3
ME 335CFinite Element Analysis3
ME 408Spectral Methods in Computational Physics3
ME 469Computational Methods in Fluid Mechanics3
MS&E 311Optimization3
STATS 217Introduction to Stochastic Processes2-3




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 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 202. Hypersonic Flow. 3 Units.

The fundamental principals and equations governing hypersonic flight and high temperature gas dynamics, including chemical and thermal equilibrium and non-equilibrium; statistical thermodynamics; kinetic theory; transport phenomena; radiation; surface heating; and scramjet engines. Prerequisite: understanding of aerodynamics. Recommended: AA 200A.

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 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 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.

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 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 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 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 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 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 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 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 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 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 294. Case Studies in Aircraft Design. 1 Unit.

Presentations by researchers and industry professionals. Registration for credit optional. 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 801. TGR Engineer Thesis. 0 Units.

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