Asymptotic methods, Dominant balance, ODEs: initial and Boundary value problems, Wronskian, Green's functions, Complex Variables: Cauchy's theorem, Taylor and Laurent expansions, Approximate Solution of Differential Equations, singularity type, Series expansions. Asymptotic Expansions. Stationary Phase, Saddle Points, Stokes phenomena. WKB Theory: Stokes constants, Airy function, Derivation of Heading's rules, bound states, barrier transmission. Asymptotic evaluation of integrals, Laplace's method, Stirling approximation, Integral representations, Gamma function, Riemann zeta function. Boundary Layer problems, Multiple Scale Analysis

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.

This is an introductory course in astronomy focusing on planets in our Solar System, and around other stars (exoplanets). First we review the formation, evolution and properties of the Solar system. Following an introduction to stars, we then discuss the exciting new field of exoplanets; discovery methods, earth-like planets, and extraterrestrial life. Core values of the course are quantitative analysis and hands-on experience, including telescopic observations. This SEN course is designed for the non-science major and has no prerequisites past high school algebra and geometry. See www.astro.princeton.edu/planets for important changes

The Space Physics Laboratory course sequence provides undergraduates at all levels the opportunity to participate in a laboratory developing NASA space flight instrumentation. The courses teach space physics laboratory skills, including ultrahigh vacuum, space instrument cleanroom, mechanical, electrical, and other laboratory skills, which then allow students to propose and carry out a significant group research project in the Laboratory. The sequence comprises two semesters with AST 250 as a prerequisite for AST 251, a credit bearing (P/F) course.

How do we observe and model the universe? We discuss the wide range of observational tools available to the modern astronomer: from space-based gamma ray telescopes, to globe-spanning radio interferometry, to optical telescopes and particle detectors. We review basic statistics and introduce students to techniques used in analysis and interpretation of modern data sets containing millions of galaxies, quasars and stars, as well as the numerical methods used by theoretical astrophysicists to model these data. The course is problem-set-based and aims to provide students with tools needed for independent research in astrophysics.

The astrophysics of the interstellar medium: theory and observations of the gas, dust, plasma, energetic particles, magnetic field, and electromagnetic radiation in interstellar space. Emphasis is on theory, including elements of: fluid dynamics; excitation of atoms, molecules, and ions; radiative processes; radiative transfer; and physical properties of dust grains. The theory is applied to phenomena including: interstellar clouds (both diffuse atomic clouds and dense molecular clouds); H II regions; shock waves; supernova remnants; cosmic rays; interstellar dust; star formation; and global equilibrium models for the ISM.

Designed to stimulate students in the pursuit of research. Participants in this seminar discuss critically papers given by seminar members. Ordinarily, several staff members also participate. Often topics are drawn from published data that present unsolved puzzles of interpretation.

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.

Hydrodynamic and kinetic models of nonmagnetized and magnetized plasma dispersion; basic plasma waves and their applications; basic instabilities; mechanisms of collisionless dissipation; geometrical-optics approximation; conservation laws and transport equations for the wave action, energy, and momentum; mode conversion; quasilinear theory.

Advances in experimental and theoretical studies or laboratory and naturally-occurring high-termperature plasmas, including stability and transport, nonlinear dynamics and turbulence, magnetic reconnection, selfheating of "burning" plasmas, and innovative concepts for advanced fusion systems. Advances in plasma applications, including laser-plasma interactions, nonneutral plasmas, high-intensity accelerators, plasma propulsion, plasma processing, and coherent electromagnetic wave generation.

A comprehensive introduction to the theory of nonlinear phenomena in fluids and plasmas, with emphasis on turbulence and transport. Experimental phenomenology; fundamental equations, including Navier-Stokes, Vlasov, and gyrokinetic; numerical simulation techniques, including pseudo-spectral and particle-in-cell methods; coherent structures; transition to turbulence; statistical closures, including the wave kinetic equation and direct-interaction approximation; PDF methods and intermittency; variational techniques. Applications from neutral fluids, fusion plasmas, and astrophysics.

This course is an introduction to plasma propulsion with focus on mechanisms that control performance of plasma thrusters. A review of various plasma propulsion concepts and applicability to space missions; a review of fundamentals of low-temperature collisional plasmas, needed to discuss plasma propulsion before discussing the acceleration & dissipation mechanisms in Hall thrusters, magnetoplasmadynamic thrusters, pulsed plasma thrusters & inductive plasma thrusters, to derive expressions for the propulsive efficiencies of each of these concepts. The discussions are at a first-year graduate student or senior undergraduate level.