#### Description

Floating point computations, direct methods for linear systems, interpolation, solution of nonlinear equations, numerical differentiation and integration.

#### Prerequisites

(MATH 240 and MATH 241) or (MATH 340 and MATH 341); and (CMSC 106 or CMSC131)

Note: Also listed as CMSC 466.

**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