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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 undergraduate and 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 Bachelor of Science, 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, autonomous systems, computational engineering, embedded programming, fluids engineering, and heat transfer. The major prepares students for careers in aircraft and spacecraft engineering, autonomy, robotics, unmanned aerial vehicles, drones, space exploration, air and space-based telecommunication industries,computational engineering, 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 Aeronautics and Astronautics.

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 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 5 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,

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, 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.

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, autonomous systems, computational engineering, embedded programming, fluids engineering, and heat transfer. The major prepares students for careers in aircraft and spacecraft engineering, autonomy, robotics, unmanned aerial vehicles, drones, space exploration, air and space-based telecommunication industries, computational engineering, teaching, research, military service, and other related technology-intensive fields.

Completion of the undergraduate program in Aeronautics and Astronautics leads to the conferral of the Bachelor of Science in Aeronautics and Astronautics.


MATH 19Calculus (required ) 23
MATH 20Calculus (required) 23
MATH 21Calculus (required) 24
CME 100/ENGR 154Vector Calculus for Engineers (required) 35
or MATH 51 Linear Algebra and Differential Calculus of Several Variables
CME 102/ENGR 155AOrdinary Differential Equations for Engineers (required) 35
or MATH 53 Ordinary Differential Equations with Linear Algebra
CME 106/ENGR 155CIntroduction to Probability and Statistics for Engineers (required)4-5
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
CME 104Linear Algebra and Partial Differential Equations for Engineers (recommended) 35
or MATH 52 Integral Calculus of Several Variables
CME 108Introduction to Scientific Computing (recommended )3
PHYSICS 41Mechanics (required) 44
PHYSICS 43Electricity and Magnetism (required) 44
PHYSICS 45Light and Heat (required)4
CHEM 31XChemical Principles Accelerated ( or CHEM 31A and CHEM 31B, or AP Chemistry) (required)5
ENGR 80Introduction to Bioengineering (Engineering Living Matter) (recommended)4
ENGR 131Ethical Issues in Engineering (recommended )4
ENGR 21Engineering of Systems (required)3
ENGR 70A/CS 106AProgramming Methodology (required)5
ENGR 10Introduction to Engineering Analysis (recommended )4
ENGR 40MAn Intro to Making: What is EE (recommended )3-5
ENGR 14Intro to Solid Mechanics (required)3
ENGR 15Dynamics (required)3
ENGR 105Feedback Control Design (required)3
ME 30Engineering Thermodynamics (required)3
AA 100Introduction to Aeronautics and Astronautics (required)3
AA 141 (required)3
AA 190Directed Research and Writing in Aero/Astro3-5
AA 272CGlobal Positioning Systems3
AA 279ASpace Mechanics3
AA 199Independent Study in Aero/Astro1-5
MS&E 178The Spirit of Entrepreneurship2

For additional information and sample programs see the Handbook for Undergraduate Engineering and the Aeronautics and Astronautics Undergraduate Program Sheet .

All courses taken for the major must be taken for a letter grade if that option is offered by the instructor.

Minimum Combined GPA for all courses in Engineering Topics (Engineering Fundamentals and Depth courses) is 2.0.

Transfer and AP credits in Math, Science, Fundamentals, and the Technology in Society course must be approved by the School of Engineering Dean's office.

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. If any core classes (aside from ENGR 21; see footnote) are part of student's major or other degree program, the AA adviser can help select substitute courses to fulfill the AA minor requirements; no double counting allowed.  All courses taken for the minor must be taken for a letter grade if that option is offered by the instructor. Minimum GPA for all minor courses combined is 2.0.

The following core courses fulfill the minor requirements:

ENGR 21Engineering of Systems 23
AA 100Introduction to Aeronautics and Astronautics3
AA 1413
AA 272CGlobal Positioning Systems3
AA 279ASpace Mechanics3
ENGR 105Feedback Control Design3

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:

AA 200Applied Aerodynamics3
AA 210AFundamentals of Compressible Flow3
AA 240AAnalysis of Structures3
ENGR 105Feedback Control Design3
ENGR 205Introduction to Control Design Techniques3
AA 283Aircraft and Rocket Propulsion3
AA 200Applied Aerodynamics3
AA 210AFundamentals of Compressible Flow3
AA 244AIntroduction to Plasma Physics and Engineering3
AA 240BAnalysis of Structures3
AA 242BMechanical Vibrations3
AA 256Mechanics of Composites3
AA 280Smart Structures3
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

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 203 Introduction to Optimal Control and Dynamic Optimization
  • 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 218 Introduction to Symmetry Analysis
  • AA 222 Engineering 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.


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-M.S. 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 Quarter), Charbel Farhat , Ilan Kroo, Sanjay Lall, Sanjiva Lele, 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: Lambertus Hesselink

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

* Recalled to active duty.

The following courses satisfy the master's .

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 310AEngineering Design Entrepreneurship and Innovation: exploring the problem space4
ME 310BEngineering Design Entrepreneurship and Innovation: exploring the solution space4
ME 310CEngineering Design Entrepreneurship and Innovation: making it REAL4
ME 324Precision Engineering4
ME 348Experimental Stress Analysis3
ME 354Experimental Methods in Fluid Mechanics4-5
ME 367Optical Diagnostics and Spectroscopy Laboratory4

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.

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 222Engineering Design Optimization3-4
AA 228Decision Making under Uncertainty3-4
AA 229Advanced Topics in Sequential Decision Making3-4
AA 242BMechanical Vibrations3
AA 284CPropulsion System Design Laboratory3
CEE 281Mechanics and Finite Elements3
CME 108Introduction to Scientific Computing3
CME 302Numerical Linear Algebra3
CME 303Partial Differential Equations of Applied Mathematics3
CME 306Numerical Solution of Partial Differential Equations3
CME 307Optimization3
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 221Stochastic Modeling3
MS&E 311Optimization3
MS&E 312Advanced Methods in Numerical Optimization3
MS&E 351Dynamic Programming and Stochastic Control3
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


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 93. Building Trust in Autonomy. 1 Unit.

Preparatory course for Bing Overseas Studies summer course in Edinburgh. Prerequisite: Requires instructor consent.

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

This class introduces the basics of aeronautics and astronautics through applied physics, hands-on activities, and real world examples. The principles of fluid flow, flight, and propulsion for aircraft will be illustrated, including the creation of lift and drag, aerodynamic performance including takeoff, climb, range, and landing. The principles of orbits, maneuvers, space environment, and propulsion for spacecraft will be illustrated. Students will be exposed to the history and challenges of aeronautics and astronautics.

AA 108N. Surviving Space. 3 Units.

Space is dangerous. Anything we put into orbit has to survive the intense forces experienced during launch, extreme temperature changes, impacts by cosmic rays and energetic protons and electrons, as well as hits by human-made orbital debris and meteoroids. If we venture beyond Earth's sphere of influence, we must also then endure the extreme plasma environment without the protection of our magnetic field. With all of these potential hazards, it is remarkable that our space program has experienced so few catastrophic failures. In this seminar, students will learn how engineers design and test spacecraft to ensure survivability in this harsh space environment. We will explore three different space environment scenarios, including a small satellite that must survive in Low Earth Orbit (LEO), a large spacecraft headed to rendezvous with an asteroid, and a human spaceflight mission to Mars.

AA 109Q. Aerodynamics of Race Cars. 3 Units.

Almost as soon as cars had been invented, races of various kinds were organized. In all its forms (open-wheel, touring car, sports car, production-car, one-make, stock car, etc.), car racing is today a very popular sport with a huge media coverage and significant commercial sponsorships. More importantly, it is a proving ground for new technologies and a battlefield for the giants of the automotive industry. While race car performance depends on elements such as engine power, chassis design, tire adhesion and of course, the driver, aerodynamics probably plays the most vital role in determining the performance and efficiency of a race car. Front and/or rear wings are visible on many of them. During this seminar, you will learn about many other critical components of a race car including diffusers and add-ons such as vortex generators and spoilers. You will also discover that due to the competitive nature of this sport and its associated short design cycles, engineering decisions about a race car must rely on combined information from track, wind tunnel, and numerical computations. It is clear that airplanes fly on wings. However, when you have completed this seminar, you will be able to understand that cars fly on their tires. You will also be able to appreciate that aerodynamics is important not only for drag reduction, but also for increasing cornering speeds and lateral stability. You will be able to correlate between a race car shape and the aerodynamics effects intended for influencing performance. And if you have been a fan of the Ferrari 458 Italia, you will be able to figure out what that black moustache in the front of the car was for.

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.

- Бринкерхофф посмотрел на нее осуждающе.  - Дай парню передохнуть. Ни для кого не было секретом, что Мидж Милкен недолюбливала Тревора Стратмора. Стратмор придумал хитроумный ход, чтобы приспособить Попрыгунчика к нуждам агентства, но его схватили за руку.