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