AMSC/CMSC 460 (Computational Methods)
| DESCRIPTION |
Basic computational methods for interpolation, least squares,
approximation,
numerical quadrature, numerical solution of nonlinear equations,
systems
of linear equations, and initial value problems for ordinary
differential
equations. Emphasis on the methods and their computational
properties
rather on their analytic aspects. |
| PREREQUISITES |
Math 240 and 241, CMSC 105 or CMSC 106 or CMSC 114 or
ENEE 114 |
| TOPICS |
Computer Arithmetic and Errors
Machine arithmetic
Error analysis
Stability and conditioning
Solving linear systems of equations
Gaussian elimination
well-conditioning vs. ill-conditioning, matrix
and vector norms
Software for Gaussian elimination
Interpolation
Polynomial interpolation
Piecewise polynomial interpolation
Spline interpolation
Software for interpolation
Numerical Integration
Elementary integration formulas (midpoint,
trapezoidal rules, etc.)
Gaussian quadrature
Adaptive quadrature
Software for adaptive integration
Solution of nonlinear systems of equations
Bisection method, secant method, Newton's
method
Methods for systems of equations
Software for solving nonlinear equations
Numerical solution of ordinary differential equations
Stability and stiffness
Basic numerical methods
Stepsize control
Methods for stiff systems
Software for solving initial value problems
Linear least squares problems
Data fitting and least squares
QR factorization
Software for least squares problems
|
| TEXT |
Text(s)
typically used in this course. |
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