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Course Criteria
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3.00 Credits
Credits: 3 Contemporary topics in nonlinear dynamical systems illustrated in mathematical models from physics, ecology, and population dynamics. Traditional qualitative analysis of difference and differential equations provides background for understanding chaotic behavior when it occurs in these models. Topics include stability theory, fractals, Lyapunov exponents, and chaotic attractors. Prerequisites Elementary courses in linear algebra and differential equations. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Introduces stochastic calculus and differential equations. Includes Wiener process, Ito and Stratonovich integrals, Ito formula, martingales, diffusions, and applications, including financial applications. Simulations and numerical approximations of solutions. Prerequisites MATH 214 and 351 Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Metric spaces, normed linear spaces, completeness, compactness, continuous (bounded) linear transformations, Banach spaces, Hilbert spaces, and orthogonal series. Prerequisites MATH 315 or equivalent. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Qualitative and quantitative theory of ordinary differential equations. Phase portrait analysis of linear and nonlinear systems, including classification of stable and unstable equilibrium states and periodic orbits. Poincare-Bendixson theorem, Lyapunov stability and Lyapunov functions, and bifurcation theory. Optional topics include averaging and perturbation methods, numerical solution techniques, and chaos. Prerequisites MATH 214 or equivalent. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Physical examples, characteristics, boundary value problems, integral transforms, and other topics, such as variational, perturbation, and asymptotic methods. Prerequisites Elementary differential equations course. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Special topics not covered in regular analysis sequence. May be repeated for credit. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Takes examples from industry and goes through complete solution process: formulation of mathematical model of problem; solution, possibly by numerical approximation; and interpretation and presentation of results. Emphasizes working in groups, relating mathematics to concrete situations, and communication and presentation skills. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Cross-Listed with OR 641 Takes in-depth look at simplex method. Includes computational enhancements such as revised simplex method, sparse-matrix techniques, bounded variables and generalized upper bounds, and large-scale decomposition methods. Also includes computational complexity of simplex algorithm, and Khachian and Karmarkar algorithms. Prerequisites OR 541, or permission of instructor. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Introduces basic mathematical ideas and methods for solving linear and nonlinear programming problems, with emphasis on mathematical aspects of optimization theory. Reviews classical topics of linear programming, and covers recent developments in linear programming, including interior point method. Considers basic results in nonlinear programming, including very recent developments in this field. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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3.00 Credits
Credits: 3 Cross-Listed with CSI 700 Computational techniques for solving problems arising in science and engineering. Includes theoretical development as well as implementation, efficiency, and accuracy issues in using algorithms and interpreting results. Specific topics include linear and nonlinear systems of equations, polynomial interpolation, numerical integration, and introduction to numerical solution of differential equations. Prerequisites Computer literacy, including some programming experience. Hours of Lecture or Seminar per week 3 Hours of Lab or Studio per week 0
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