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Course Criteria
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3.00 Credits
Theory and techniques of modern computational mathematics, computing environments, computational linear algebra, optimization, approximation, parameter identification, finite difference and finite element methods and symbolic computation. Project-oriented course; modeling and analysis of physical systems using state-of-the-art software and packaged subroutines. Pre: 2214, 3214. (2H,3L,3 Credits)
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3.00 Credits
Separation of variables for heat, wave, and potential equations. Fourier expressions. Application to boundary value problems. Bessel functions. Integral transforms and problems on unbounded domains. 4425: I, II. 4426: II. Pre: (2214, 2224), (3224 or 4525) for 4425; (2214, 2224), (3224 or 4525), 4425 for 44 26. (3H,3 Credits)
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3.00 Credits
4445: Vector spaces and review of linear algebra, direct and iterative solutions of linear systems of equations, numerical solutions to the algebraic eigenvalue problem, solutions of general non-linear equations and systems of equations. 4446: Interpolation and approximation, numerical integration and differentiation, numerical solutions of ordinary differential equations. Computer programming skills required. Pre: 2214, 2224. (3H,3 Credits) 4445: I,III; 4446
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3.00 Credits
Analysis of classical and modern applications of mathematics in the physical, biological and social sciences. Emphasis on problem formulating, modeling, solving, simulating, and analyzing results. Programming language required. (3H,3 Credits)
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3.00 Credits
Binary relations, groups, semigroups, monoids, rings, fields, Boolean algebras, and Polya's theory of Enumerations. Partially duplicates 3124. Pre: 1114, 1206. (3H,3 Credits)
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3.00 Credits
4525: Elementary calculus review, real number system, continuity of single variable functions, integration, sequences and infinite series. 4526: Differential calculus of several variable functions, multiple integration, curves and surfaces, line and surface integrals. For non-mathematics majors: 4525 partially duplicates 3224, 4526 partially duplicates 3214. Pre: 2224 for 4525; 4525 for 4526. (3H,3 Credits)
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5.00 Credits
Ordinary differential equations: first order, second and higher order linear equations, power series and Laplace transform methods. Partial differential equations: Fourier series, separation of variables for heat, wave and potential equations. Sturm-Liouville theory. Bessel functions. Legendre polynomials. Partially duplicates 2214 and 4564. Pre: 1114, 1206. (5H,5 Credits)
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3.00 Credits
Root-finding, interpolation, linear algebraic systems, numerical integration, and numerical solution of ordinary and partial differential equations. Duplicates 3414 and 4404, and can not be taken by mathematics majors. Computer programming required. Pre: 2214. (3H,3 Credits)
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3.00 Credits
Laplace transformations, Fourier series, partial differential equations and separation of variables, boundary value problems, and Sturm-Liouville theory. Duplicates 4544. Pre: 2214. (3H,3 Credits) I,II,III,IV.
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3.00 Credits
Vector Analysis: Green's theorem, potential theory, divergence, and Stokes' theorem. Complex Analysis: Analyticity, complex integration, Taylor series, residues, conformal mapping, applications. I,II,III Pre: 2224. (3H,3 Credits)
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