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MATH 570: Partial Differential Equations
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 364A and 463. Cauchy's problem; classification of second order equations; methods of solution of hyperbolic, parabolic, and elliptic equations. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 570 - Partial Differential Equations
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MATH 573: Scientific Computing
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 323 or consent of instructor. Introduction to programming languages, implementations of numerical algorithms for solution of linear algebraic equations, interpolation and extrapolation, integration and evaluation of functions, root finding and nonlinear equations, fast Fourier transforms, minimization and maximization of functions, numerical solutions of differential equations. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 573 - Scientific Computing
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MATH 574: Stochastic Calculus and Applications
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 361B, 364A or 370A, 380. Review of probability theory. Markov processes. Wiener processes. Stochastic integrals. Stochastic differential equations. Applications to Finance and Engineering. (Lecture 3 hrs.)
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MATH 574 - Stochastic Calculus and Applications
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MATH 575: Calculus of Variations
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 563 and one of MATH 364A, 370A. Classical theory. Necessary and sufficient conditions for extrema of multiple integrals. Hamilton-Jacobi theory. Applications to eigenvalue problems. Direct methods. Pontryagin maximum principle. Principle of optimality. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 575 - Calculus of Variations
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MATH 576: Numerical Analysis
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 323, 361B, 364A. Advanced numerical methods. Introduction to error analysis, convergence, and stability of numerical algorithms. Topics may include solution of ordinary differential equations, partial differential equations, systems of linear and nonlinear equations, and optimization theory. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 576 - Numerical Analysis
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MATH 577: Numerical Solution of Partial Differential Equations
3.00 Credits
California State University-Los Angeles
Prerequisite: MATH 423 or MATH 576 or consent of instructor. Finite difference methods solving hyperbolic, parabolic, elliptic PDE'S; accuracy, convergence, and stability analysis. Selected initial-value boundary-value problems, characteristics, domain of dependence, matrix, and von Neumann's methods of stability analysis. Solutions of large sparse linear systems. Finite element method. (Lecture 3 hrs.)
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MATH 577 - Numerical Solution of Partial Differential Equations
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MATH 578: Numerical Linear Algebra
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 247 and 323 or consent of instructor. Numerical solutions of linear systems, least squares problems, eigenvalue problems. Matrix factorization: LU, QR, SVD, iterative methods. Error analysis. Applications with attention to linear algebra problems arising in numerical solutions of partial differential equations. Numerical implementation of algorithms. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 578 - Numerical Linear Algebra
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MATH 579 /479: Mathematical Modeling
3.00 Credits
California State University-Los Angeles
Prerequisites: MATH 247, 364A or 370A, 323, and one additional mathematics course, or consent of instructor. (Undergraduates register in MATH 479; graduates in MATH 579.) Application of mathematics to develop models of phenomena in science, engineering, business, and other disciplines. Evaluation of benefits and limitations of mathematical modeling. Letter grade only (A-F). (Lecture 3 hrs.)
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MATH 579 /479 - Mathematical Modeling
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MATH 695: Seminar in Mathematics
3.00 Credits
California State University-Los Angeles
Prerequisite: Consent of instructor. Presentation and discussion of advanced work, including original research by faculty and students. Topics announced in the Schedule of Classes. May be repeated to a maximum of 6 units. Letter grade only (A-F).
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MATH 695 - Seminar in Mathematics
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MATH 697: Directed Studies
1.00 - 3.00 Credits
California State University-Los Angeles
Prerequisite: Consent of instructor. Research on a specific area in mathematics. Topics for study to be approved and directed by faculty advisor in the Mathematics and Statistics Department. Letter grade only (A-F).
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MATH 697 - Directed Studies
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