Glossary
UW Bothell Course Descriptions
UW Tacoma Course Descriptions
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Course Descriptions |
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Detailed course offerings (Time Schedule) are available for
To see the detailed Instructor Class Description, click on the underlined instructor name following the course description.
AMATH 301 Beginning Scientific Computing (4) NW
Introduction to the use of computers to solve problems arising in the physical, biological and engineering sciences. Application of mathematical judgment, programming architecture, and flow control in solving scientific problems. Introduction to MATLAB routines for numerical programming, computation, and visualization. Prerequisite: either MATH 125, Q SCI 292, MATH 128, or MATH 135. Offered: AWSpS.
AMATH 351 Introduction to Differential Equations and Applications (3) NW
Introductory survey of ordinary differential equations. Linear and nonlinear equations. Taylor series. Laplace transforms. Emphasis on formulation, solution, and interpretation of results. Examples from physical and biological sciences and engineering. Introduction to MATLAB as a tool for solving differential equations. Prerequisite: MATH 125. Offered: AWSpS.
AMATH 352 Applied Linear Algebra and Numerical Analysis (3) NW
Analysis and application of numerical methods and algorithms to problems in the applied sciences and engineering. Applied linear algebra, including eigenvalue problems. Emphasis on use of conceptual methods in engineering, mathematics, and science. Extensive use of MATLAB package for programming and solution techniques. Prerequisite: either MATH 126 or Q SCI 293.
Instructor Course Description:
William R. Dickerson
Eleftherios Kirkinis
AMATH 353 Fourier Analysis and Partial Differential Equations (3) NW
Heat equation, wave equation, and Laplace's equation. Separation of variables. Fourier series in context of solving heat equation. Fourier sine and cosine series; complete Fourier series. Fourier and Laplace transforms. Solution of partial differential equations on infinite domains. D'Alembert's solution for wave equation. Prerequisite: either AMATH 351 or MATH 307. Offered: AWSp.
Instructor Course Description:
Eleftherios Kirkinis
AMATH 383 Introduction to Continuous Mathematical Modeling (3) NW
Introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. Formulation, solution, and interpretation of the results. Prerequisite: either AMATH 351 or MATH 307. Offered: AWSpS.
AMATH 401 Vector Calculus and Complex Variables (4) NW
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. Offered: A.
AMATH 402 Introduction to Dynamical Systems and Chaos (4) NW
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. Offered: W.
AMATH 403 Methods for Partial Differential Equations (4) NW
See 401. 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.
Instructor Course Description:
David George
AMATH 410 Computational Biology and Chemistry (4)
Introduction to computational methods in biology and chemistry. Applications focus on statistical models, equilibrium models, discrete- and continuous- time deterministic models, and stochastic models arising in the biological and life sciences, and chemistry. Uses MATLAB for numerical computation and data analysis. Teaches tools in parallel with their computational implementation.
AMATH 422 Introduction to Mathematical Biology (3) NW
Mathematical modeling in biology and medicine. Introduction to chaos and nonlinear dynamics, population models (predator-prey and competition systems), epidemic models with applications to sexually transmitted diseases and dynamic diseases, enzyme kinetics, biological oscillators and switches. Prerequisite: either AMATH 351, MATH 136, or MATH 307. Offered: A.
AMATH 423 Mathematical Biology: Stochastic Models (3) NW
Introduction to the basics of stochastic models. Applications are taken from the biomedical sciences such as random movement of cells and molecules, activation of neurons, cancer growth and spread, population dynamics, kinetics of unimolecular reactions. Prerequisite: either AMATH 351 or MATH 307, MATH/STAT 390. Offered: W.
AMATH 441 Introduction to Fluid Dynamics (3) NW
Eulerian equations of mass and motion. Surface forces. Vorticity and vortex dynamics. Water waves and interfacial waves; concept of phase and group velocities. Linear instability theory. Simple viscous flows; boundary layer theory, potential theory. Low Reynolds-number flows, application to biological fluid flows. Prerequisite: AMATH 353.
AMATH 490 Special Topics (1-5, max. 15)
Topics of current interest in applied mathematics not covered by other undergraduate courses.
AMATH 498 Senior Project or Thesis (1-6, max. 6)
Intended for Honors students and other advanced undergraduates completing a special project or senior thesis in applied mathematics. Offered: AWSpS.
AMATH 499 Undergraduate Reading and Research (1-6, max. 6)
Credit/no credit only. Offered: AWSpS.
AMATH 500 Special Studies in Applied Mathematics (*, max. 12)
Lectures and discussions of topics of current interest in applied mathematics. May not be offered every quarter; content may vary from one offering to another. Prerequisite: permission of instructor.
AMATH 501 Seminar in Applied Mathematics (1, max. 6)
Special topics and selected problems of current interest in applied mathematics. Credit/no credit only. Offered: AWSp.
AMATH 502 Applied Mathematics Clinic (1)
The clinic provides consulting service for problems from different academic units requiring assistance in formulation, analysis, and interpretation of mathematical models. Students learn to delineate sources of difficulties, identify or devise a method of solution, and effectively communicate it to clients. Credit/no credit only. Prerequisite: AMATH 568, AMATH 569, and AMATH 584. Offered: AWSp.
AMATH 503 Mathematical Biology I (3)
Mathematical modeling in biomedical sciences (mainly ecology, epidemiology, physiology, and zoology). Topics covered include modeling (continuous and discrete), population interactions, dynamic diseases, reaction kinetics, biological oscillators, oscillator generated wave phenomena, epidemics, and the dynamics of infectious diseases. Prerequisite: AMATH 402 or equivalent knowledge of ordinary differential equations. Offered: A.
AMATH 504 Mathematical Biology II (3)
Mathematical modeling in the biomedical sciences (mainly ecology, epidemiology, and zoology). Topics include spatial spread of populations, traveling wave phenomena in biology, reaction diffusion theory, biological pattern formation mechanisms, mechanochemical theory of morphogenesis, spatial spread of epidemics. (May be taken independently of 503.) Prerequisite: AMATH 402, AMATH 403 or equivalents; ordinary, partial differential equations. Offered: W.
AMATH 505 Introduction to Fluid Dynamics (4)
Eulerian equations for mass-motion; Navier-Stokes equation for viscous fluids, Cartesion tensors, stress-strain relations; Kelvin's theorem, vortex dynamics; potential flows, flows with high-low Reynolds numbers; boundary layers, introduction to singular perturbation techniques; water waves; linear instability theory. Prerequisite: AMATH 403 or permission of instructor. Offered: jointly with ATM S 505/OCEAN 511; A.
AMATH 506 Applied Probability Statistics (4)
Discreet and continuous random variables, independence and conditional probability, central limit theorem, elementary statistical estimation and inference, linear regression. Emphasis on physical applications. Prerequisite: some advanced calculus and linear algebra. Offered: jointly with STAT 506.
AMATH 507 Calculus of Variations (5)
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; recommended: AMATH 402 and AMATH 403 or MATH 428 and 429.
AMATH 509 Theory of Optimal Control (3)
Trajectories obtained from ordinary differential equations with control variables. Controllability, optimality, the maximum principle. Relaxation and the existence of solutions. Techniques of nonsmooth analysis. Prerequisite: real analysis on the level of MATH 426; background in optimization corresponding to AMATH 507 or AMATH 515. Offered: jointly with MATH 509; even years.
AMATH 510 Applications of Optimization in Engineering Design (3) Zabinsky
Discussion of issues arising in applications of optimization to engineering design. Emphasis on formulating problems and selecting appropriate solution techniques. Random search methods for problems otherwise computationally intractable. Individual projects in engineering optimal design. Prerequisite: AMATH/MATH/IND E 515 and MATH 328 or permission of instructor. Offered: jointly with IND E 516.
AMATH 512 Methods of Engineering Analysis (3)
Applications of mathematics to problems in chemical engineering; vector calculus; properties and methods of solution of first and second order partial differential equations; similarity transforms, separation of variables, Laplace and Fourier transforms. Offered: jointly with CHEM E 512; A.
AMATH 514 Networks and Combinatorial Optimization (3)
Networks and directed graphs. Paths and trees. Feasible and optimal flows and potentials. Transportation problems, matching and assignment problems. Algorithms and applications. Prerequisite: MATH 308 or AMATH 352 and MATH 324. Offered: jointly with MATH 514.
AMATH 515 Fundamentals of Optimization (5)
Maximization and minimization of functions of finitely many variables subject to constraints. Basic problem types and examples of applications; linear, convex, smooth, and nonsmooth programming. Optimality conditions. Saddlepoints and dual problems. Penalties, decomposition. Overview of computational approaches. Prerequisite: linear algebra and advanced calculus. Offered: jointly with IND E 515/MATH 515.
AMATH 516 Numerical Optimization (3)
Methods of solving optimization problems in finitely many variables, with or without constraints. Steepest descent, quasi-Newton methods. Quadratic programming and complementarity. Exact penalty methods, multiplier methods. Sequential quadratic programming. Cutting planes and nonsmooth optimization. Prerequisite: AMATH 515. Offered: jointly with MATH 516.
AMATH 517 Optimization Under Uncertainty (3)
Sequential optimization problems involving random variables. Dynamic programming, stochastic programming. Control of uncertain dynamic systems in finite, discrete time. Risk, feedback, adaptivity. Problems with imperfect state information. Applications to optimal stopping, inventory control, resource management. Prerequisite: AMATH 506 (or an introduction to basic concepts of probability such as STAT 390 or 394, 395), MATH 308 and 324. Offered: jointly with MATH 517.
AMATH 520 Special Topics in Mathematical Applications (5, max. 15)
In-depth study of an application topic in applied mathematics. Topics may include special studies in geophysical fluid dynamics, hydrodynamic stability, turbulence, analytic dynamics, solid mechanics, applied optimization, tensor analysis, stochastic analysis, and nonlinear optics and lasers. Offered: W.
AMATH 521 Special Topics in Mathematical Biology (5, max. 15)
DNA-folding, patter-forming systems, stochastic analysis. Prerequisite: AMATH 402 or equivalent. Offered: Sp.
AMATH 563 Methods of Partial Differential Equations II (3)
Nonlinear first-order partial differential equations: characteristics, applications to geometrical optics and Hamilton-Jacobi theory. Linear and quasilinear hyperbolic equations: conservation laws, characteristics, shocks, examples from fluid dynamics. Approximate solution methods: regular, singular, and multiple-scale perturbations. Prerequisite: AMATH 569. Offered: odd years.
AMATH 564 Methods of Partial Differential Equations III (3)
Nonlinear first-order partial differential equations: characteristics, applications to geometrical optics and Hamilton-Jacobi theory. Linear and quasilinear hyperbolic equations: conservation laws, characteristics, shocks, examples from fluid dynamics. Approximate solution methods: regular, singular, and multiple-scale perturbations. Prerequisite: AMATH 569. Offered: odd years.
AMATH 567 Complex Variables (5)
Complex variable and associated topics. Branch cuts, series and product expansions. Contour integration, numerical implications. Harmonic functions. Complex potential (and singularities) in physical problems. Conformal mapping; applications and examples. Fourier and Laplace transforms and applications. Recommended: 401 or equivalent. Offered: A.
AMATH 568 Advanced Methods for Ordinary Differential Equations (5)
Survey of practical solution techniques for ordinary differential equations. Linear systems of equations including nondiagonable case. Nonlinear systems; stability phase plane analysis. Asymptotic expansions. Regular and singular perturbations. Recommended: 402 or equivalent. Offered: W.
AMATH 569 Advanced Methods for Partial Differential Equations (5)
Analytical solution techniques for linear partial differential equations. Discussion of how these arise in science and engineering. Transform and Green's function methods. Classification of second-order equations, characteristics. Conservation laws, shocks. Prerequisite: AMATH 403, AMATH 568 or MATH 428 or permission of instructor. Offered: Sp.
AMATH 570 Asymptotic and Perturbation Methods (5)
Asymptotics for integrals, perturbation and multiple-scale analysis. Singular perturbations: matched asymptotic expansions, boundary layers, shock layers, uniformly valid solutions. Prerequisite: AMATH 567, AMATH 568, AMATH 569, or permission of instructor. Offered: A.
AMATH 571 Spectral Methods (5)
Analysis and application of spectral methods for the numerical solution of differential equations. Fourier methods and the FFT; collocation methods; polynomial interpolation and Chebyshev series; approximation theory and spectral accuracy; boundary conditions. Prerequisite: AMATH 584, AMATH 585, AMATH 586, or permission of instructor. Offered: W.
AMATH 572 Introduction to Applied Stochastic Analysis (5)
Introduction to the theory of probability and stochasitc processes based on differential equations with applications to science and engineering. Poisson processes and continuous-time Markov processes, Brownian motions and diffusion. Prerequisite: AMATH/STAT 506, AMATH 402, or equivalent knowledge of probability and ordinary differential equations. Offered: Sp.
AMATH 573 Solitons and Nonlinear Waves (5)
Methods for integrable and near-integrable nonlinear partial differential equations such as the Korteweg-de Vries equation and the Nonlinear Schrodinger equation; symmetry reductions and solitons; soliton interactions; infinite-dimensional Hamiltonian systems; Lax pairs and inverse scattering; Painleve analysis. Prerequisite: AMATH 569, or permission of instructor. Offered: A.
AMATH 574 Conservation Laws and Finite Volume Methods (5)
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. Offered: W.
AMATH 575 Dynamical Systems (5)
Overview of ways in which complex dynamics arise in nonlinear dynamical systems. Topics include bifurcation theory, universality, Poincare maps, routes to chaos, horseshoe maps, Hamiltonian chaos, fractal dimensions, Liapunov exponents, and the analysis of time series. Examples from biology, mechanics, and other fields. Prerequisite: AMATH 568 or equivalent.
AMATH 577 Perturbation Theory I (3)
Regular perturbations. Singular perturbations: matched asymptotic expansions, boundary layers, shock layers, uniformly valid solutions. The methods of multiple scales and averaging, weakly nonlinear wave propagation problems and resonance phenomena, homogenization, nonlinear wave propagation in fluid, solid, and particle mechanics. Prerequisite: AMATH 567, AMATH 568, AMATH 569, or equivalent. Offered: even years.
AMATH 578 Perturbation Theory II (3)
Regular perturbations. Singular perturbations: matched asymptotic expansions, boundary layers, shock layers, uniformly valid solutions. The methods of multiple scales and averaging, weakly nonlinear wave propagation problems and resonance phenomena, homogenization, nonlinear wave propagation in fluid, solid, and particle mechanics. Prerequisite: AMATH 567, AMATH 568, AMATH 569, or equivalent. Offered: even years.
AMATH 581 Scientific Computing (5)
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 584 Applied Linear Algebra and Introductory Numerical Analysis (5)
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. Offered: jointly with MATH 584; A.
Instructor Course Description:
David George
AMATH 585 Numerical Analysis of Boundary Value Problems (5)
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. Offered: jointly with MATH 585; W.
AMATH 586 Numerical Analysis of Time Dependent Problems (5)
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. Offered: jointly with ATM S 581/MATH 586; Sp.
AMATH 587 Asymptotics and Special Functions (3)
Origin and properties of higher transcendental functions; theoretical basis and applications of Laplace, Fourier, Bessel, Mellin transforms; asymptotic analysis, including methods of steepest descent and stationary phase, WKB. Prerequisite: AMATH 567, AMATH 568, AMATH 569, or equivalent.
AMATH 588 Green's Functions and Integral Equations (3)
Review of Sturm-Liouville theory. Green's functions and integral representation of solution to PDEs. Fredholm and Volterra integral equations. Hilbert-Schmidt theory. Singular integral equations of Cauchy type. Applications to science and engineering. Prerequisite: AMATH 567, AMATH 568, AMATH 569, or equivalent.
AMATH 592 Special Topics in Stochastic Analysis and Modeling (5)
Stochastic techniques and models with applications. Markov process and diffusion, stochastic differential equations, randomly perturbed dynamical systems, and statistical mechanics. Prerequisite: AMATH 572, or permission of instructor.
AMATH 594 Special Topics in Numerical Analysis (2-3, max. 15)
Various advanced topics in numerical analysis and scientific computing, such as iterative methods, eigenvalue computations, approximation theory, finite element methods, inverse problems, nonlinear conservation laws, computational fluid dynamics. Prerequisite: AMATH 584, 585, 586, or equivalent. Offered: jointly with MATH 594.
AMATH 595 Special Topics in Numerical Analysis (2-3, max. 15)
Various advanced topics in numerical analysis and scientific computing. See the description for 594 for sample topics. Prerequisite: AMATH 584, 585, 586, or equivalent. Offered: jointly with MATH 595.
AMATH 596 Special Topics in Numerical Analysis (2-3, max. 15)
Various advanced topics in numerical analysis and scientific computing. See the description for 594 for sample topics. AMATH 584, 585, 586, or equivalent. Offered: jointly with MATH 596.
AMATH 600 Independent Research or Study (*)
Credit/no credit only.
AMATH 700 Master's Thesis (*)
Credit/no credit only.
AMATH 800 Doctoral Dissertation (*)
Credit/no credit only.
