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Course Criteria
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3.00 Credits
Sequences, limits, continuity, differentiability, Riemann integrals, functions of several variables, multiple integrals, space curves, line integrals, surface integrals, Green's theorem, Stokes theorem, series, improper integrals, uniform convergence, Fourier series, Laplace transforms. Applications to physics and engineering emphasized. (Lec. 3) Pre: (for 437) 243 and credit or concurrent enrollment in 215 or 362. Pre: (for 438) 437.
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3.00 Credits
One-dimensional wave equation. Linear second order partial differential equations in two variables. Separation of variables and Fourier series. Nonhomogeneous boundary value problems. Green's functions. (Lec. 3) Pre: 244 or 442.
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3.00 Credits
Introduction to linear and nonlinear difference equations; basic theory, z-transforms, stability analysis, and applications. (Lec. 3) Pre: 243.
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3.00 Credits
Introduction to nonlinear dynamical systems on the real line and/or the plane. (Lec. 3) Pre: 142 and 215 and junior standing, or permission of instructor.
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3.00 Credits
Concepts and techniques in discrete mathematics. Finite and infinite sets, graphs, techniques of counting, Boolean algebra and applied logic, recursion equations. (Lec. 3) Pre: junior standing or better in physical or mathematical sciences, or in engineering, or permission of instructor.
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3.00 Credits
Theoretical basis and fundamental tools of probability and statistics. Probability spaces, properties of probability, distributions, expectations, some common distributions, and elementary limit theorems. (Lec. 3) Pre: 243 or equivalent.
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3.00 Credits
Continuation of 451 in the direction of statistics. Basic principles of statistical testing and estimation, linear regression and correlation. (Lec. 3) Pre: 451.
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3.00 Credits
Conditional probability and expectation. Mean and covariance functions. Calculus of random processes. Introduction to Gaussian processes, Poisson processes, stationary processes, and Markov chains with applications. (Lec. 3) Pre: 451 or equivalent.
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3.00 Credits
First course in the theory of functions of a single complex variable, including analytic functions, power series, residues and poles, complex integration, conformal mapping, and applications. (Lec. 3) Pre: 243 or equivalent.
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3.00 Credits
Interpolation, solution of nonlinear equations, numerical evaluation of integrals, special topics. (Lec. 3) Pre: 243, CSC 201 or equivalent, or permission of instructor.
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