A broad introduction to numerical algorithms used in scientific computing. The course begins with a review of the basic principles of numerical analysis, including sources of error, stability, and convergence. The theory and implementation of techniques for linear and nonlinear systems of equations and ordinary and partial differential equations are covered in detail. Examples of the application of these methods to problems in engineering and the sciences permeate the course material. Issues related to the implementation of efficient algorithms on modern high-performance computing systems are discussed.

Subject of course is 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 will be on theory, including elements of: fluid dynamics; excitation of atoms, molecules and ions; radiative processes; radiative transfer; simple interstellar chemistry; and physical properties of dust grains.The theory will be applied to phenomena including; interstellar clouds (both diffuse atomic clouds and dense molecular clouds); HII regions; shock waves; supernova remnants; cosmic rays; interstellar dust; and star formation.

Students are introduced to basic principles of fluid dynamics.

This is an introductory graduate course in plasma physics, focusing on magnetohydrodynamics (MHD) and its extension to weakly collisional or collisionless plasmas. Topics to be covered include: the equations of MHD and extended MHD, the structure of magnetic fields, static and rotating MHD equilibria and their stability, magnetic reconnection, MHD turbulence, and the dynamo effect. Applications are drawn from fusion, heliophysical, and astrophysical plasmas.

Introduction to theory of fluctuations and transport in plasma. Origins of irreversibility. Random walks, Brownian motion, and diffusion; Langevin and Fokker-Planck theory. Fluctuation-dissipation theorem; test-particle superposition principle. Statistical closure problem. Derivation of kinetic equations from BBGKY hierarchy and Klimontovich formalism; properties of plasma collision operators. Classical transport coefficients in magnetized plasmas; Onsager symmetry. Introduction to plasma turbulence, including quasilinear theory. Applications to current problems in plasma research.

Advances in experimental and theoretical studies or laboratory and naturally-occurring high-temperature 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.

Analysis of methods for the numerical solution of the partial differential equations of plasma physics, including those of elliptic, parabolic, hyperbolic, and eigenvalue type. Topics include finite difference, finite element, spectral, particle-in-cell, Monte Carlo, moving grid, and multiple-time-scale techniques, applied to the problems of plasma equilibrium, transport and stability. Basic parallel programming concepts are discussed.

Develop skills, knowledge, and understanding of basic and advanced laboratory techniques used to measure the properties and behavior of plasmas. Representative experiments are: cold-cathode plasma formation and architecture; ambipolar diffusion in afterglow plasmas; Langmuir probe measurements of electron temperature and plasma density; period doubling and transitions to chaos in glow discharges; optical spectroscopy for species identification; microwave interferometry and cavity resonances for plasma density determination; and momentum generated by a plasma thruster.