AOS 576 / APC 576: Current Topics in Dynamic Meteorology - Large-Scale Structure/Atmosphere
Isaac M. Held
Dynamical concepts needed to develop a qualitative understanding of the large-scale structure of the atmospheric circulation. The control of the angular momentum budget by Rossby wave fluxes. Theories for the Hadley circulation in the tropics and the "macro-turbulence" of midlatitudes. Linear theories for deviations from zonal symmetry of the mean flow.
APC 503 / AST 557: Analytical Techniques in Differential Equations
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.
APC 524 / MAE 506 / AST 506: Software Engineering for Scientific Computing
James M. Stone
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.
CBE 502 / APC 502: Mathematical Methods of Engineering Analysis II
Solutions of ordinary differential, partial differential and finite difference equations with emphasis on second order linear partial differential equations and their applications. Topics include special functions, eigenvalues and eigenfunctions, Sturm-Liouville analysis, Green's functions, explicit and implicit finite difference methods, stability analysis, transform methods, asymptotic analysis.
* EGR 192 / MAT 192 / PHY 192 / APC 192 (QR): An Integrated Introduction to Engineering, Mathematics, Physics
Christine J. Taylor
Taken concurrently with EGR/MAT/PHY 191, this course offers an integrated presentation of the material from PHY 103 (General Physics: Mechanics and Thermodynamics) and MAT 201 (Multivariable Calculus) with an emphasis on applications to engineering. Math topics include: vector calculus; partial derivatives and matrices; line integrals; simple differential equations; surface and volume integrals; and Green's, Stokes', and divergence theorems.
MAT 321 / APC 321 (QR): Numerical Methods
Introduction to numerical methods with emphasis on algorithms, applications and numerical analysis. Topics covered include solution of nonlinear equations; numerical differentiation, integration, and interpolation; direct and iterative methods for solving linear systems; numerical solutions of differential equations; two-point boundary value problems; and approximation theory. Lectures are supplemented with numerical examples using MATLAB.
MAT 323 / APC 323 (QR): Topics in Mathematical Modeling - Mathematical Neuroscience
Philip J. Holmes
Draws problems from the sciences & engineering for which mathematical models have been developed and analyzed to describe, understand and predict natural and man-made phenomena. Emphasizes model building strategies, analytical and computational methods, and how scientific problems motivate new mathematics.
* MAT 377 / APC 377 (QR): Combinatorial Mathematics
Introduction to combinatorics, a fundamental mathematical discipline as well as an essential component of many mathematical areas. While in the past many of the basic combinatorial results were at first obtained by ingenuity and detailed reasoning, modern theory has grown out of this early stage and often relies on deep, well-developed tools. Topics include Ramsey Theory, Turan Theorem and Extremal Graph Theory, Probabilistic Argument, Algebraic Methods and Spectral Techniques. Showcases the gems of modern combinatorics.