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MTH 437 ,438: Advanced Calculus and Application I,II
3.00 Credits
University of Rhode Island
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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MTH 437 ,438 - Advanced Calculus and Application I,II
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MTH 441: Introduction to Partial Differential Equations
3.00 Credits
University of Rhode Island
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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MTH 441 - Introduction to Partial Differential Equations
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MTH 442: Introduction to Difference Equations
3.00 Credits
University of Rhode Island
Introduction to linear and nonlinear difference equations; basic theory, z-transforms, stability analysis, and applications. (Lec. 3) Pre: 243.
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MTH 442 - Introduction to Difference Equations
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MTH 445: Introduction to Chaotic Dynamical Systems
3.00 Credits
University of Rhode Island
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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MTH 445 - Introduction to Chaotic Dynamical Systems
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MTH 447: Discrete Mathematical Structures )
3.00 Credits
University of Rhode Island
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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MTH 447 - Discrete Mathematical Structures )
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MTH 451: Introduction to Probability and Statistics
3.00 Credits
University of Rhode Island
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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MTH 451 - Introduction to Probability and Statistics
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MTH 452: Mathematical Statistics
3.00 Credits
University of Rhode Island
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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MTH 452 - Mathematical Statistics
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MTH 456: Introduction to Random Processes
3.00 Credits
University of Rhode Island
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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MTH 456 - Introduction to Random Processes
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MTH 462: Functions of a Complex Variable
3.00 Credits
University of Rhode Island
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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MTH 462 - Functions of a Complex Variable
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MTH 471: Introduction to Numerical Analysis I
3.00 Credits
University of Rhode Island
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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MTH 471 - Introduction to Numerical Analysis I
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