This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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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 MATH 241) or (MATH 340 and MATH 341); and (CMSC 106 or CMSC131)

Note: Also listed as CMSC 460.

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