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UW Bothell Course Descriptions
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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.
Instructor Course Description:
Eli Shlizerman
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.
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 (5)
Emphasizes acquisition of solution techniques; illustrates ideas with specific example problems arising in science and engineering. Includes applications of vector differential calculus, complex variables; line-surface integrals; integral theorems; and Taylor and Laurent series, and contour integration. Prerequisite: MATH 126. Offered: A.
AMATH 402 Introduction to Dynamical Systems and Chaos (5)
Overview methods describing qualitative behavior of solutions on nonlinear differential equations. Phase space analysis of fixed pointed and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications: engineering, physics, chemistry, and biology. Prerequisite: either AMATH 351 or MATH 307. Offered: W.
AMATH 403 Methods for Partial Differential Equations (5)
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.
AMATH 410 Computational Biology and Chemistry (5)
Introduction to computational methods in biology and chemistry. Applications on statistical models, equilibrium models, discrete- and continuous- time deterministic models, 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 (5)
Modeling biological systems with differential and difference equations. Examples from: ecology (population growth, disease dynamics): biochemistry and cell biology; and neurobiology (Hodgkin-Huxley and neural networks). Methods include linear stability analyses, phase-plane analyses, and perturbation theory. Prerequisite: either MATH 307 or AMATH 351. Offered: A.
AMATH 423 Mathematical Biology: Stochastic Models (5)
Focuses on stochastic modeling and analysis of biological and medical systems. Biological topics include biochemistry, population genetics, genomics, population and community ecology, and neuroscience. Mathematical topics include generating functions, the Poisson process, Markov processes and master equations, branching processes, and elementary diffusion theory. Prerequisite: either AMATH 351 or MATH 307, MATH/STAT 390. Offered: W.
AMATH 424 Mathematical Biology: Spatiotemporal Models (3)
Examines partial differential equations for biological dynamics in space and time. Draws examples form molecular and cell biology, ecology, epidemiology, and neurobiology. Topics include reaction-diffusion equations for biochemical reactions, calcium wave propagation in excitable medium, and models for invading biological populations. Prerequisite: AMATH 353.
AMATH 481 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: AMATH 301.
AMATH 482 Computational Methods for Data Analysis (5)
Exploratory and objective data analysis methods applied to the physical, engineering, and biological sciences. Brief review of stastistical 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.
AMATH 483 High-Performance Scientific Computing (5)
Introduction to hardware, software, and programming for large-scale scientific computing. Overview of multicore, cluster, and supercomputer architectures; procedure and object oriented languages; parallel computing paradigms and languages; graphics and visualization of large data sets; validation and verification; and scientific software development. Prerequisite: either CSE 142 or AMATH 301.
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 Vector Calculus and Complex Variables (5)
Emphasizes acquisition of solution techniques; illustrates ideas with specific example problems arising in science and engineering. Includes applications of vector differential calculus, complex variables; line-surface integrals; integral theorems; and Taylor and Laurent series, and contour integration. Prerequisite: MATH 126.
AMATH 502 Introduction to Dynamical Systems and Chaos (5)
Overview methods describing qualitative behavior of solutions on nonlinear differential equations. Phase space analysis of fixed pointed and periodic orbits. Bifurcation methods. Description of strange attractors and chaos. Introductions to maps. Applications: engineering, physics, chemistry, and biology. Prerequisite: either AMATH 351 or MATH 307.
AMATH 503 Methods for Partial Differential Equations (5)
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.
AMATH 504 Mathematical Epidemiology (5)
Focuses on the construction and analysis of mathematical models for infectious disease transmission and control. Emphasizes evaluation and comparison of vaccination programs. Applications are presented for a variety of diseases such as measles, rubella, smallpox, rabies, etc. Prerequisite: AMATH 351 or equivalent. 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 Computational Biology and Chemistry (5)
Introduction to computational methods in biology and chemistry. Applications on statistical models, equilibrium models, discrete- and continuous- time deterministic models, 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 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 522 Introduction to Mathematical Biology (5)
Modeling biological systems with differential and difference equations. Examples from: ecology (population growth, disease dynamics): biochemistry and cell biology; and neurobiology (Hodgkin-Huxley and neural networks). Methods include linear stability analyses, phase-plane analyses, and perturbation theory. Prerequisite: either MATH 307 or AMATH 351.
AMATH 523 Mathematical Biology: Stochastic Models (5)
Focuses on stochastic modeling and analysis of biological and medical systems. Biological topics include biochemistry, population genetics, genomics, population and community ecology, and neuroscience. Mathematical topics include generating functions, the Poisson process, Markov processes and master equations, branching processes, and elementary diffusion theory.
AMATH 524 Mathematical Biology: Spatiotemporal Models (5)
Examines partial differential equations for biological dynamics in space and time. Draws examples form molecular and cell biology, ecology, epidemiology, and neurobiology. Topics include reaction-diffusion equations for biochemical reactions, calcium wave propagation in excitable medium, and models for invading biological populations. Prerequisite: AMATH 353.
AMATH 567 Applied Analysis (5)
Reviews applications of metric and normed spaces, types of convergence, upper and lower bounds, and completion of a metric space; Banach spaces and Hilbert spaces, bounded linear operators, orthogonal sets and Fourier series, and the Riesz representation theorem; and the spectrum of a bounded linear operator and the Fredholm alternative. Introduces distributions. Recommended: AMATH 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 Coherent Structures, Pattern Formation and Solitons (5)
Methods for nonlinear partial differential equations (PDEs) leading to coherent structures and patterns. Includes symmetries, conservations laws, stability Hamiltonian and variation methods of PDEs; interactions of structures such as waves or solitons; Lax pairs and inverse scattering; and 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 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: AMATH 301.
AMATH 582 Computational Methods for Data Analysis (5)
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.
AMATH 583 High-Performance Scientific Computing (5)
Introduction to hardware, software, and programming for large-scale scientific computing. Overview of multicore, cluster, and supercomputer architectures; procedure and object oriented languages; parallel computing paradigms and languages; graphics and visualization of large data sets; validation and verification; and scientific software development. Prerequisite: either CSE 142 or AMATH 301.
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.
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 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.
