The goal of this course is to teach basic tools and principles of writing good code, in the context of scientific computing. Specific topics include an overview of relevant compiled and interpreted languages, build tools and source managers, design patterns, design of interfaces, debugging and testing, profiling and improving performance, portability, and an introduction to parallel computing in both shared memory and distributed memory environments. The focus is on writing code that is easy to maintain and share with others. Students develop these skills through a series of programming assignments and a group project.

An introductory course to plasma physics, with sample applications in fusion, space and astrophysics, semiconductor etching, microwave generation, plasma propulsion, high power laser propagation in plasma; characterization of the plasma state, Debye shielding, plasma and cyclotron frequencies, collision rates and mean-free paths, atomic processes, adiabatic invariance, orbit theory, magnetic confinement of single-charged particles, two-fluid description, magnetohydrodynamic waves and instabilities, heat flow, diffusion, kinetic description, and Landau damping. The course may be taken by undergraduates with permission of the instructor.

We cover fundamental aspects of the mechanics of soft matter and see how they provide useful insights about novel engineering designs and materials (3D printing, soft robotics, metamaterials). Particular attention is given to interfacial effects, which dominate the physics of small objects. Topics include, drops, bubbles, wetting, coatings, instabilities. We also cover the mechanics of thin elastic objects whose deformability characterizes many biological systems. Students learn how to build quantitative physical models, combining experimental observations, scaling analysis and formal approaches.

Lectures and readings focus on bridges, railroads, power plants, steamboats, telegraph, highways, automobiles, aircraft, computers, and the microchip. Historical analysis provides a basis for studying societal impact by focusing on scientific, political, ethical, and aesthetic aspects in the evolution of engineering over the past two and a half centuries. The precepts and the papers will focus historically on engineering ideas including the social and political issues raised by these innovations and how they were shaped by society as well as how they helped shape culture.

Lectures and readings focus on bridges, railroads, power plants, steamboats, telegraph, highways, automobiles, aircraft, computers, and the microchip. We study some of the most important engineering innovations since the Industrial Revolution. The laboratory centers on technical analysis that is the foundation for design of these major innovations. The experiments are modeled after those carried out by the innovators themselves, whose ideas are explored in the light of the social environment within which they worked.

This class acquaints the student with the state-of-art concepts and algorithms to design and analyze origami systems (assemblies, structures, tessellations, etc). Students will learn how to understand, create and transform geometries by folding and unfolding concepts, and thus apply origami concepts to solve engineering and societal problems. In addition, using origami as a tool, we will outreach to some fundamental concepts in differential geometry.

This course presents the Matrix Structural Analysis (MSA) and Finite Element Methods (FEM) in a cohesive framework. The first half of the semester is devoted to MSA topics: derivation of truss, beam, and frame elements; assembly and partitioning of the global stiffness matrix; and equivalent nodal loads. The second half covers the following FEM topics: strong and weak forms of boundary value problems including steady-state heat conduction, and linear elasticity, Galerkin approximations, constant strain triangles, and isoparametric quads. Other topics such as dynamic analysis will also be discussed. MATLAB is used for computer assignments.

This class acquaints the student with the state-of-art concepts and algorithms to design and analyze origami systems (assemblies, structures, tessellations, etc). Students learn how to understand, create and transform geometries by folding and unfolding concepts, and thus apply origami concepts to solve engineering and societal problems. In addition, using origami as a tool, we outreach to some fundamental concepts in differential geometry.

Robotic and AI systems are unlocking transformative impact but also raising urgent safety questions. This course covers the mathematical foundations of safety-critical autonomy and introduces the key algorithmic paradigms (control barrier functions, Hamilton-Jacobi reachability, model-predictive shielding) under a unified safety filter framework. By dissecting the safety challenges in autonomous driving, robot learning, human interaction, and AI alignment, students learn the importance of quantifying uncertainty, minding the gap between models and reality, and ensuring safety - even under black swan events - without sacrificing performance.

The class will discuss the physics of ocean surface waves and its impacts on human life. We will cover the principle of ocean waves propagation across the oceans, with analogies to optics and acoustics. Using historical observations and modern modeling tools, we will discuss wave forecasting with practical examples including planning of D-Day during the second world war, or local surf forecasting. The influence of ocean waves on human life will be discussed, from their role on beach morphology, mitigation of storm surge, or tsunamis. Finally, we will discuss the ubiquitous representation of waves in arts/movies.

The study of the oceans as a major influence on the atmosphere and the world environment. The contrasts between the properties of the upper and deep oceans; the effects of stratification; the effect of rotation; the wind-driven gyres; the thermohaline circulation.

Heat and work in physical systems. Concepts of energy conversion and entropy, primarily from a macroscopic viewpoint. Efficiency of different thermodynamic cycles, with applications to everyday life including both renewable and classical energy sources. In the laboratory, students will carry out experiments in the fields of analog electronics and thermodynamics.

Fundamental principles of solid mechanics: equilibrium equations, reactions, internal forces, stress, strain, Hooke's law, torsion, beam bending and deflection, and analysis of stress and deformation in simple structures. Integrates aspects of solid mechanics that have applications to mechanical and aerospace structures (engines and wings), as well as to microelectronic and biomedical devices. Topics include stress concentration, fracture, plasticity, and thermal expansion. The course synthesizes descriptive observations, mathematical theories, and engineering consequences.

This course provides a first independent work experience for MAE majors. Primarily intended for students in the sophomore year, the course may be suitable for juniors interested in exploring independent work for the first time. Students are required to complete a one-semester project under the supervision of a faculty member and compile a final report detailing the work accomplished. Final grade determined by faculty adviser.

A treatment of the theory and applications of ordinary differential equations with an introduction to partial differential equations. The objective is to provide the student with an ability to solve standard problems in this field.

This course presents key ideas at the core of computational engineering, and provides the students with a foundation for further development of the discipline, as well as for the informed and expert use of advanced computational mechanics software. Basic topics in interpolation and approximation (polynomial and trigonometric basis); representation of curves and surfaces, accuracy and stability of numerical methods for ODEs and PDEs, and selected topics in numerical linear algebra and root finding of nonlinear systems.

This course builds on the technical foundations established in MAE 321, and extends the scope to include a range of advanced mechanism designs. Students, working in teams, will be challenged to design and fabricate a robotic system that will draw upon multidisciplinary engineering elements. The robot tasks will be associated with search and rescue operations. CAD, CAE, and CAM will be utilized in the design/simulation/prototype process. Labs are designed to reinforce and expand CAD and CAE skills. A final competition will be held among the design teams.

Relates to the structures, properties, processing and performance of different materials including metals, alloys, polymers, ceramics, and semiconductors. This course satisfies the MAE departmental requirement in materials as well as the MSE certificate core requirement.

This course addresses the various concepts that form the basis of modern space flight and astronautics. The focus is on space flight analysis and planning and not hardware or spacecraft design. The topics include space flight history, orbital mechanics, orbit perturbations, near-Earth and interplanetary mission analysis, orbit determination and satellite tracking, spacecraft maneuvers and attitude control, launch and entry dynamics. Use of advanced software for the planning and analysis of space missions.

Robotics is a rapidly-growing field with applications including unmanned aerial vehicles, autonomous cars, and robotic manipulators. This course will provide an introduction to the basic theoretical and algorithmic principles behind robotic systems. The course will also allow students to get hands-on experience through project-based assignments on quadrotors. In the final project, students will implement a vision-based obstacle avoidance controller for a quadrotor. Topics include motion planning, control, localization, mapping, and vision.

This course is intended for juniors concentrators. Students are required to secure a faculty adviser, select a topic of their own interest, or select a project from a list prepared by the faculty. They develop a work plan in consultation with their faculty adviser and carry out the work independently. At the end of the term, students submit a written report, which is evaluated by the adviser and one additional reader assigned by the course coordinator.

The bioinspired design course offers interdisciplinary, advanced design and critical thinking experience. Students will work in teams to integrate biological knowledge into the engineering design process. The course uses case studies to show how biological solutions can be transferred into engineering design. The case studies will include themes such as locomotion, materials, and sensing. By the end of the course, students will be able to use analogical design concepts to engineer a prototype based on biological function.

The course introduces fundamentals of optics, lasers, and Fourier transforms through lectures and hands-on activities. The topics include ray and wave optics, imaging and image processing, optical Fourier transforms, principles of lasers, and applications in nuclear fusion for renewable energy, environmental sensing, space exploration, ultrafast metrology, chemistry, and physics.

This course will cover fundamentals of heat transfer and applications to practical problems in energy conversion and conservation, electronics, and biological systems. Emphasis will be on developing a physical and analytical understanding of conductive, convective, and radiative heat transfer. Numerical methods will be introduced to simulate a variety of steady and unsteady heat transfer applications and will form the basis of the final project.

To develop an understanding of feedback principles in the control of dynamic systems, and to gain experience in analyzing and designing control systems in a laboratory setting.

This course requires students to complete a substantial piece of independent research and scholarship under the supervision and advisement of a Princeton faculty member. The work requires sustained investment and attention throughout the semester, and must comprise an element of design. At the end of the term, students submit a written report which is evaluated by the adviser and one additional reader assigned by the course coordinator. This course fulfills the departmental requirement of senior independent work or thesis.

This course is the first term of a year-long individual thesis project in which students complete a substantial piece of research and scholarship under the supervision and advisement of a Princeton faculty member. While a year-long thesis is due in the student's final semester of study, the work requires sustained investment and attention throughout the academic year, and must comprise an element of design. Students need to pass a Preliminary Design Review (PDR) at the end of the fall term to be allowed to continue and complete the thesis by enrolling in MAE 499.

This course is the first term of a year-long senior independent project in which groups of students complete a substantial piece of research and scholarship under the supervision and advisement of a Princeton faculty member. While a comprehensive written report is due in the students' final semester of study, the work requires sustained investment and attention throughout the academic year, and must comprise an element of design. Students need to pass a Preliminary Design Review (PDR) at the end of the fall term to be allowed to continue and complete the project by enrolling in MAE 499G.

Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to linear algebra, matrices and their application, eigenvalue problems, ordinary differential equations, Sturm-Liouville theory and eigenvalue problems, Green's functions, partial differential equation, finite Fourier Transform, method of characteristics, self-similar solution.

Under the direction of a faculty member, the student carries out a one-semester research project chosen jointly by the student and the faculty member. Without prior approval of the Director Graduate Studies, directed research can only be taken during the first year of study. At the beginning of the semester, students must submit the topic of the project and the faculty advisor to the Graduate Office. The project culminates in a final presentation in the style of a conference talk at the end of the semester.

Independent project for Master of Engineering students under the direction of a faculty advisor. The project topic and faculty advisor must be sent to the Graduate Office at the beginning of the semester. The project culminates in a oral presentation at the end of the semester

This bioinspired design course offers interdisciplinary, advanced design and critical thinking experience. Students work in teams to integrate biological knowledge into the engineering design process. The course uses case studies to show how biological solutions can be transferred into engineering design. The case studies include themes such as locomotion, materials, and sensing. By the end of the course, students are able to use analogical design concepts to engineer a prototype based on biological function.

The course will give lectures on fuels and engine performance, chemical equilibrium, combustion kinetics, flames, ignition and burning limits, turbulent combustion and detonation transition, and pollutant emissions. In addition, it introduces physics and chemistry of plasma and discusses plasma assisted combustion, plasma-assisted green fuel synthesis. Finally, combustion and plasma modeling as well as in situ diagnostics are introduced. Focus is placed on hydrogen, syngas, ammonia, hydrocarbons, and oxygenated fuels.

This course covers the main principles of optimal control theory applied to deterministic continuous-time problems and provides guidance on numerical methods for their solution. Fundamental results are reached starting with parameter optimization, the calculus of variations, Pontryagin's principle(s), dynamic programming and ending with the Hamilton-Jacobi-Bellman theory. Geometric and analytic properties of the formulations and solutions are highlighted. Numerical methods for direct and indirect optimal control problems are covered with applications. Emphasis is placed on intuition between the various aspects of the course.

Robotics is a rapidly-growing field with applications including unmanned aerial vehicles, autonomous cars, and robotic manipulators. This course provides an introduction to the basic theoretical and algorithmic principles behind robotic systems. The course also allows students to get hands-on experience through project-based assignments on quadrotors. In the final project, students implement a vision-based obstacle avoidance controller for a quadrotor. Topics include motion planning, control, localization, mapping, and vision.

An introduction to fluid mechanics: from a rigorous derivation of basic conservation laws in integral and differential form to the exploration of flow physics. The course tackles foundational topics in mass, momentum and energy transport as well as classical topics including vorticity, potential flow, vortex dynamics, and brief introductions to boundary layers and turbulence.

This course examines chemical reaction kinetics and energy transfer processes in high-temperature gases. Course topics include molecular collision theory; Boltzmann equation; transition state theory (derived from both thermodynamics and statistical mechanics); unimolecular dissociation and recombination reactions and their pressure dependence (i.e., Lindemann theory, RRK(M) theory, Master Equation); reaction and explosion mechanisms relevant to propulsion systems; experimental methods and diagnostics used to study gas-phase chemical kinetics; an intro to kinetic modeling tools and solvers; photochemistry; and vibrational relaxation processes.

Overview and fundamentals of numerical algorithms and models for computational fluid dynamics. Numerical approaches discussed include finite difference, finite volume, finite element, and spectral methods on both structured and unstructured grids. Coverage includes asymptotically zero Mach number (incompressible), low-speed compressible, and high-speed compressible flows. Introduction to modeling of turbulent flows.

A lecture of graduate students and staff presenting the results of their research and recent advances in flight, space, and surface transportation; fluid mechanics; energy conversion; propulsion; combustion; environmental studies; applied physics; and materials sciences. Participation at presentations will be attended by distinguished outside speakers. There is one lecture and one precept discussion per week.

Emphasizes the connection between microstructure and properties in solid-state materials. Topics include crystallinity and defects, electronic and mechanical properties of materials, phase diagrams and transformations, and materials characterization techniques. Ties fundamental concepts in materials science to practical use cases with the goal of solving complex challenges in sustainability and healthcare, among others.

This course provides students with a basic technical understanding of the science and technology relevant to current and emerging national and global security issues. Topics covered in this course include nuclear weapons, biotechnology and biosecurity, delivery systems for weapons of mass destruction, cyberwarfare, global surveillance, quantum technologies, and artificial intelligence. In the second half of the semester, students work in small teams on in-depth case studies exploring a current or emerging global-security issue of their choice and combining both technical and policy analysis.