#### 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.

#### Prerequisites

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

Note: Also listed as CMSC 460.

**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