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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. Will use MATLAB.

 

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C- from (MATH340, MATH241); and 1 course with a minimum grade of C- from (CMSC106, CMSC131); and minimum grade of C- in MATH246.

 

Level of Rigor

Standard

 

Sample Textbooks

Numerical Analysis by R. Burden, J. Faires, A. Burden

Numerical Computing with Matlab, by Cleve B. Moler

 

Applications

Computer Science, Economics, Business, Engineering, Physics, Astronomy

 

If you like this course, you might also consider the following courses:

Math 420, Math 416, Stat 430.

 

Additional Notes

Duplicate credit with AMSC466 and CMSC466; cross-listed with CMSC460

Students interested in grad school in Applied Math should consider this course

Students interested in grad school in Statistics should consider this course

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

 

 

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