AMATH 500A (1-2) High-Performance Scientific Computing
This course will introduce aspects of scientific computing and computational science that go beyond the Matlab-based introduction of AMath 301 or 352 and will introduce other languages (primarily Fortran 90/95/2003 and Python), debugging strategies, parallel computing (at the multi-core and cluster level), visualization tools for large data sets, and concepts such as Validation and Verification (V&V), uncertainty quantification (UQ), reproducible research, and scientific software design.
AMATH 574 (5) Conservation Laws and Finite Volume Methods
Theory of linear and nonlinear hyperbolic conservation laws modeling wave propagation in gases, fluids, and solids. Shock and rarefaction waves. Finite volume methods for numerical approximation of solutions; Godunov’s method and high-resolution TVD methods. Stability, convergence, and entropy conditions. Prerequisite: AMATH 586 or permission of instructor.
AMATH 581 (5) Scientific Computing
Project-oriented computational approach to solving problems arising in the physical/engineering sciences, finance/economics, medical, social and biological sciences. Problems requiring use of advanced MATLAB routines and toolboxes. Covers graphical techniques for data presentation and communication of scientific results. Prerequisite: Proficiency in basic MATLAB or AMATH 301, or permission of instructor.
AMATH 582 (5) Computational Methods for Data Analysis
Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of statistical methods and their computational implementation for studying time series analysis, spectral analysis, filtering methods, principal component analysis, orthogonal mode decomposition, and image processing and compression. Prerequisite: either MATLAB and linear algebra or permission of instructor.
Jose Nathan Kutz
AMATH 583 (5) High-Performance Scientific Computing
This class will cover a selection of topics in high-performance computing (HPC), briefly introducing many of the issues that arise when solving large scale computational problems in science and engineering.
AMATH 584 (5) Applied Linear Algebra and Introductory Numerical Analysis
Numerical methods for solving linear systems of equations, linear least squares problems, matrix eigen value problems, nonlinear systems of equations, interpolation, quadrature, and initial value ordinary differential equations.
AMATH 585 (5) Numerical Analysis of Boundary Value Problems
Numerical methods for steady-state differential equations. Two-point boundary value problems and elliptic equations. Iterative methods for sparse symmetric and non-symmetric linear systems: conjugate-gradients, preconditioners. Prerequisite: AMATH 581 or MATH 584 which may be taken concurrently.
AMATH 586 (5) Numerical Analysis of Time Dependent Problems
Numerical methods for time-dependent differential equations, including explicit and implicit methods for hyperbolic and parabolic equations. Stability, accuracy, and convergence theory. Spectral and pseudospectral methods. Prerequisite: AMATH 581 or AMATH 584.