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Linear system solvers, optimization techniques, interpolation and approximation of functions, solving systems of nonlinear equations, eigenvalue problems, least squares, and quadrature; numerical handling of ordinary and partial differential equations. Course Information: Same as CSE 401, ECE 491, and MATH 450. 3 undergraduate hours. 3 or 4 graduate hours. Credit is not given toward graduation for both CS 450 and CS 457. Prerequisite: One of CS 101, CS 124 or CS 125; one of CS 357, MATH 257, MATH 357, MATH 415, or MATH 416; MATH 285.

Scientific Computing : An Introductory Survey, 2nd E, by Michael T. Heath

Analyze the conditioning of common numerical problems such as solving a linear system, finding eigenvalues, numerical differentiation and integration, etc. (1)

Calculate numerical approximations to solutions to linear and nonlinear systems, eigenvalues/eigenvectors, optimization problems, integrals, derivatives, and solutions to differential equations.(6)

Compare the accuracy and cost of different numerical methods for solving a numerical problem. (1)(6)

Estimate the accuracy and efficiency of numerical approximations.(6)

Write code to solve numerical problems.(2)(6)

Design and carry out numerical experiments to test various numerical methods. (2)(6)

Approximations, Error Analysis, and Floating-Point Arithmetic
Systems of Linear Equations
Linear Least Squares
Eigenvalue Problems
Nonlinear Equations
Optimization
Interpolation
Numerical Integration and Differentiation
Initial Value Problems for ODEs
Boundary Value Problems for ODEs
Partial Differential Equations
Fast Fourier Transform

Selected Elective.