CORE COURSES

Requirements
The core course requirement can be satisfied by taking AMATH 401, 402, 403, and either AMATH 581 or 584. Descriptions of all the AMATH courses offered online are below. Please note that the prerequisites listed for the AMATH courses are not offered online through the University of Washington. Course descriptions for the prerequisites are available at http://www.washington.edu/students/crscat/appmath.html (for AMATH courses) and http://www.washington.edu/students/crscat/math.html (for MATH courses).

Single-Course Enrollment
Individuals not seeking the degree may enroll in single courses on a space-available basis with instructor permission. For more information, see Admissions.


Vector Calculus and Complex Variables - AMATH 401 (4 credits)
Emphasis on acquisition of solution techniques; ideas illustrated with specific example problems arising in science and engineering. Applications of vector differential calculus, complex variables. Line-surface integrals; integral theorems; Taylor and Laurent series, contour integration. Prerequisite: MATH 126.

Introduction to Dynamical Systems and Chaos - AMATH 402 (4 credits)
Overview of methods to describe the qualitative behavior of solutions of nonlinear differential equations. Phase space analysis of fixed points and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications from engineering, physics, chemistry and biology. Prerequisite: either AMATH 351 or MATH 307 or permission of instructor. View on-campus course page for winter 2006.

Methods for Partial Differential Equations - AMATH 403 (4 credits)
Applications of partial differential equations; linear and quasilinear first order equations, characteristics, shocks; classification of linear second order equations; basic solution techniques for parabolic, elliptic, and hyperbolic equations; Green's functions and integral transform methods. Prerequisite: AMATH 402 or permission of instructor. View on-campus course page for spring 2006.

Calculus of Variations - AMATH 507 (5 credits)
Necessary and sufficient conditions for a weak and strong extremum. Legendre transformation, Hamiltonian systems. Constraints and Lagrange multipliers. Space-time problems with examples from elasticity, electromagnetics, and fluid mechanics. Sturm-Liouville problems. Approximate methods. Prerequisite: AMATH 351 or MATH 307; MATH 324, 327; or permission of instructor. Recommended: AMATH 402 and AMATH 403 or MATH 428 and 429.

Scientific Computing - AMATH 581 (5 credits)
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.

Applied Linear Algebra & Introductory Numerical Methods - AMATH 584 (5 credits)
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. View on-campus course page for autumn 2005.

Numerical Analysis of Boundary Value Problems - AMATH 585 (5 credits)
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 584/MATH 584 which may be taken concurrently, or permission of instructor. View on-campus course page for winter 2006.