California Institute of Technology

Master of Science in Space Engineering


Space Propulsion

Ae 121 is designed to introduce the fundamentals of chemical, electric and advanced propulsion technologies.  The course focuses on the thermochemistry and aerodynamics of chemical and electrothermal propulsion systems, the physics of ionized gases and electrostatic and electromagnetic processes in electric thrusters.  These analyses provide the opportunity to introduce the basic concepts of non-equilibrium gas dynamics and kinetic theory. Specific technologies such as launch vehicle rocket engines, monopropellant engines, arcjets, ion thrusters, magnetoplasmadynamic engines and Hall thrusters will be discussed.  Ae 121 also provides an introduction to advanced propulsion concepts such as solar sails and antimatter rockets.

Planetary Entry

This course provides an integrated overview of planetary entry, descent, and landing systems. The course content includes entry vehicle systems, entry flight mechanics and dynamics, hypersonic aerodynamics, aerothermodynamics and thermal protection systems, aerodynamic decelerators and landing systems, and case studies based on recent developments in robotic and human exploration. Four homework sets and a group project will be assigned. Homework assignments require a modest degree of computer programming. The group project integrates many of the analyses discussed in this course.


Aerospace Engineering

Part a: Introduction to spacecraft systems and subsystems, mission design, fundamentals of orbital and rocket mechanics, launch vehicles and space environments; JPL-assisted design exercise; spacecraft mechanical, structural, and thermal design; numerical modeling, test validation. Part b: Introduction to guidance, navigation, and control (GNC), measurement systems, Kalman filtering, system analysis, simulation, statistical error analysis, case studies of JPL GNC applications; preliminary discussion and setup for team project leading to system requirements review. Part c: Team project leading to preliminary design review and critical design review.

Mechanics of Structures and Solids

Two- and three-dimensional theory of stressed elastic solids. Analysis of structural elements with applications in a variety of fields. Variational theorems and approximate solutions, finite elements. A variety of special topics will be discussed in the third term such as, but not limited to, elastic stability, wave propagation, and introductory fracture mechanics.

Fluid Mechanics

Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli’s equation; potential flow; thin-airfoil theory; surface gravity waves; buoyancy-driven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi one-dimensional compressible flow; shock waves; unsteady compressible flow; and acoustics.


Embry-Riddle Aeronautical University

Bachelor of Science in Engineering Physics
Bachelor of Science in Computational Mathematics
Minor in Computer Science

Engineering Physics

Nanomaterials & Nanoscience

Nanomaterials are substances that have dimensions on the order of 1 nm to 100 nm. This is an introductory course designed to acquaint upper-level science and engineering students with the new and rapidly changing field of nanotechnology. Topics include the synthesis and characteristics of nanodots, nanowires, and nanotubes; characterization methods such as atomic force microscopy, scanning electron microscopy, and x-ray diffraction; and the large number of applications that employ nanomaterials; and nanotoxicology.

Space Science Seminar

Seminar-style course, with lectures, readings, and writing on topics of current interest in Space Science..

Spaceflight Dynamics

Basic topics in analytical dynamics, two body orbits and the initial value problem, the two body orbital boundary value problem, Earth coverage and space mission geometry, non-Keplerian effects, orbital maneuvers and rendezvous, and interplanetary transfer. Fundamentals of ascent flight mechanics, launch vehicle selection, fundamentals of entry flight mechanics, and the associated thermal control problem.

Electro-Optical Engineering

Geometrical optics of mirrors, thin and thick lenses, prisms, and systems. Ray tracing with optical CAD. Fiber optics applications. Physical optics including interference, diffraction, and polarization. Phaser methods. Engineering considerations in choice of different types of detectors. Space systems applications. Image processing. Emphasis on design.

Microcomputers and Electronic Instrumentation

This course will provide students with a background as it applies to the design circuits of measuring instruments and to interface sensors and computers. The program of study will concentrate on following the form of the electrical signal from light, pressure temperature and other sensors as it proceeds through signal conditioning circuits and into the microcomputer for further processing.

Space Systems Engineering

Development of the fundamental principles used in the engineering and design of space systems. Several major subsystems including power, telemetry and command, communications, thermal control and guidance, navigation, and control subsystems are covered. Topics on space environmental control and life support systems, space system integration and testing, and space system operations are also discussed.

Space Physics

Origin, evolution, and structure of neutral and ionized terrestrial atmosphere. Effect of suns electromagnetic radiation on ozone shield. Photoionization and thermal structure of the neutral atmosphere as well as the ionosphere and magnetosphere. Solar disturbances and their effects on satellite orbit decay and on long-distance communication. Studies of composition, thermodynamics, and physical processes of the near-Earth space environment. Rocket and satellite monitoring and remote sensing. Numerical and instrument design projects.

Spacecraft Instrumentation

The course will undertake the study of space environment and models used for engineering analysis. Topics include considerations for instrument design in space environment, such as plasma interactions, chemical reactions, optical and other radiation effects, and thermal issues. These will include theory, engineering, and data reduction techniques for in situ spacecraft instrumentation and for spacecraft command and telemetry systems.

Engineering Electricity & Magnetism

Solutions of electrostatics problems using Poisson’s equation and Laplace’s equation, electrostatic energy, electric current, magnetic field, electromagnetic induction, physics of plasmas, Maxwell’s equations, and application of Maxwell’s equations (reflection, refraction, waveguides, antenna radiation). Students will write some simple computer programs.

Space Systems Design

A program of undergraduate research, supervised by physics or engineering faculty, leading to the writing of a technical design report in an area of current interest in engineering physics.

Software Engineering

Software Engineering Practices

This variable credit course introduces students to the fundamental principles and methodologies of large-scale software development. Students learn about the theory and practice of software engineering and work as part of a team on a full life-cycle software project that includes planning, software specification, software design, coding, inspections, and testing. A closed laboratory is required, and includes activities that guide project teams through a software development process and support team project activities such as team building, planning, requirements analysis and specification, design, testing, and the use of tools.

Computer Engineering

Digital Circuit Design

Introduction to logic design and interfacing digital circuits. Boolean algebra, combinatorial logic circuits, digital multiplexers, circuit minimization techniques, flip-flop storage elements, shift registers, counting devices, and sequential logic circuits.

Signals & Systems

Introduction to signal processing systems for both digital and analog systems. Mathematics of signal representation and signal processing, including functional descriptions of signals and systems. Implications of linearity and time-invariance, and input-output behavior of linear, time-invariant systems. Causality and stability. Zero-input and zero-state responses. Z and Laplace Transforms. Fourier Series and Fourier Transforms for discrete and continuous systems. Extensive use of MATLAB and Simulink.

Microprocessor Systems

Study of digital computer organizations. Introduction to microcomputer systems using a current microprocessor. Assembly language programming techniques for microcomputers will be used to study digital computer operation. Input and output techniques, memory devices, RS 232, and other interfacing techniques will be studied. Hardware and software relationships will also be discussed.

Digital Signal Processing

Specification, design, and implementation of offline signal processing systems on general-purpose computers and real-time signal processing systems on special-purpose digital signal processing microprocessors (DSPs). Review of sampling theory and discrete time filtering. Filter design tools. Digital-to-analog and analog-to-digital conversion hardware. DSP core architectures and hardware interrupts. Aspects of system-on-a-chip DSPs for data transfer, cache management, external memory reference, and co-processor interface. Real-time operating systems for DSPs. Applications to modern communication and control systems.


Probability and Statistics

Finite sample spaces; conditional probability and Bayes Theorem, discrete and continuous random variables and their functions; expected value, variance, and standard deviation; systematic study of the major discrete and continuous distributions; moment generating functions; hypothesis testing and estimation.

Mathematical Methods for Engineering and Physics I

Line and surface integrals; vector fields with the study of Green, Gauss, and Stokes Theorems; applications of vector field theory; Fourier series.

Mathematical Methods for Engineering and Physics II

The solution of linear differential equations with variable coefficients; study of the derivation, characteristics, and solutions of partial differential equations; Fourier series, Fourier transform, Laplace transform, and Green’s function; applications in science and engineering.

Digital Signal Processing

Specification, design, and implementation of offline signal processing systems on general-purpose computers and real-time signal processing systems on special-purpose digital signal processing microprocessors (DSPs). Review of sampling theory and discrete time filtering. Filter design tools. Digital-to-analog and analog-to-digital conversion hardware. DSP core architectures and hardware interrupts. Aspects of system-on-a-chip DSPs for data transfer, cache management, external memory reference, and co-processor interface. Real-time operating systems for DSPs. Applications to modern communication and control systems.

Numerical Analysis I

Floating point arithmetic, error analysis, algorithms in interpolation, integration, differentiation, matrix algebra, approximation and solution of equations, use of numerical software packages.

Complex Variables

Algebra of complex numbers; complex functions, analytic functions; mapping by elementary functions; conformal mappings and their applications; additional topics may include complex integration, power series expansion.

Partial Differential Equations

Introduction to first order linear, quasi-linear, and nonlinear partial differential equations, with an introduction to numerical solutions; existence and uniqueness of solutions to second order equations, with emphasis on the heat, wave, and Laplace’s equation. Uniform convergence with application to Fourier series and integrals. Green’s functions, introduction to integro-differential equations. Difference equations.

Linear Algebra

Review of vector and matrix operations including matrix inverses, eigenvectors, and eigenvalues. Equations of lines and planes, vector spaces including basis and dimensions, linear transformations, change of basis, diagonalization of matrices, inner products and orthonormal bases, applications.


Modern Physics

This is an introductory course in non-classical (modern) physics; it introduces students to the modern concepts in physics. Topics discussed include scattering of electromagnetic radiation; special relativity; wave-particle duality; the uncertainty principle and quantum theory of atomic structure; x-rays; lasers; and nuclear reactions.

Classical Mechanics

Fundamentals of mechanics, oscillatory motion, systems of particles, varying mass, motion under central forces, motion in three dimensions, gyroscopic motion, generalized coordinates, normal coordinates, Lagrangian and Hamiltonian formulations. Students will write some simple computer programs.

Quantum Mechanics

The Schrodinger equation in one and three dimensions and its solutions for step potentials, the harmonic oscillator, and the hydrogen atom. Operators and their matrix representations: Dirac bracket formalism, angular momentum and spin, and spin-orbit interaction. Identical particles and exchange symmetries. Time-independent and time-dependent perturbation theory and approximation methods: transition rates, Fermis rule, scattering theory. Classical and quantum statistical distributions.