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
Fall 2016 Graduate Courses
Analytical Techniques in Differential Equations
Instructors: Jong-Kyu Park
Fusion Plasmas & Plasma Diagnostics
Introduction to experimental plasma physics, with emphasis on high-temperature plasmas for fusion. Requirements for fusion plasmas: confinement, beta, power and particle exhaust. Discussion of tokamak fusion and alternative magnetic and inertial confinement systems. Status of experimental understanding: what we know and how we know it. Key plasma diagnostic techniques: magnetic measurements, Langmuir probes, microwave techniques, spectroscopic techniques, electron cyclotron emission, Thomson scattering.
Instructors: Philip Charles Efthimion, Richard P. Majeski
General Plasma Physics I
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.
Instructors: Nathaniel J. Fisch, Hong Qin
Introduction to Plasma Astrophysics
Introductory course to plasma physics, as it applies to space and astrophysical systems. Fundamental concepts are developed with mathematical rigor, and application to the physics of a wide variety of astrophysical systems are made. Topics include magnetohydrodynamics, kinetic theory, waves, instabilities, and turbulence. Applications to the physics of the solar wind and corona, the intracluster medium of galaxy clusters, the interstellar medium of galaxies, and a wide variety of accretion flows are given.
Instructors: Amitava Bhattacharjee, Matthew Walter Kunz, James McLellan Stone
Plasma Waves and Instabilities
Hydrodynamic and kinetic models of nonmagnetized and magnetized plasma dispersion; basic plasma waves and their applications; basic instabilities; mechanisms of collisionless dissipation; geometrics-optics approximation, including ray tracing, field-theoretical description of continuous waves, and ponderomotive effects; conservation laws and transport equations for the wave action, energy, and momentum; mode conversion; quasilinear theory.
Instructors: Ilya Yevgenyevich Dodin
Seminar in Plasma Physics
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.
Instructors: Samuel A. Cohen, Allan H. Reiman
Seminar in Theoretical Astrophysics
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.
Instructors: Matthew Walter Kunz
Software Engineering for Scientific Computing
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 will develop these skills through a series of programming assignments and a group project.
Instructors: James McLellan Stone
Structure of the Stars
Theoretical and numerical analysis of the structure of stars and their evolution. Topics include a survey of the physical process important for stellar interiors (equation of state, nuclear reactions, transport phenomena); and the integrated properties of stars and their evolution.
Instructors: Adam S. Burrows