Description
Floating point computations, direct methods for linear systems, interpolation, solution of nonlinear equations, numerical differentiation and integration. 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 MATH410.
Level of Rigor
Advanced
Sample Textbooks
An Introduction to Numerical Analysis, by E. Suli & D. Mayers
Numerical Analysis by W. Gautschi
Applications
Computer Science, Economics, Business, Engineering, Physics, Astronomy
If you like this course, you might also consider the following courses
Math 420, Math 462, Math 464
Additional Notes
Duplicate credit with AMSC460 and CMSC460; crosslisted with CMSC466
Students interested in grad school in Applied Math should consider this course
Students interested in grad school in MATH should consider this course
Students interested in grad school in Statistics should consider this course
Topics
Floating point computation (1 week)
Properties of machine arithmetic
Direct methods for linear systems (4 weeks)
Gaussian elimination
Pivoting strategies
Cholesky factorization
Vector and matrix norms
Conditioning and the effect of rounding error
Interpolation (2 weeks)
Polynomial approximation
Newton and Lagrange forms
Error formula (derived)
Solution of nonlinear equations (3 weeks)
Bisection, Secant, and Newton's method
Fixed point methods
Newton's method for systems
Numerical differentiation and integration (3 weeks)
Numerical differentiation
Numerical integration