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