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