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## Course Catalog Description

Fundamentals of numerical methods for students in science and engineering;
floating-point computation, systems of linear equations, approximation of
functions and integrals, the single nonlinear equation, and the
numerical solution of ordinary differential equations; various
applications in science and engineering; programming exercises
and use of high quality mathematical library routines. Course
Information: Same as MATH 357. Credit is not given for CS 357
if credit for CS 450 has been earned. (Counts for advanced hours in LAS).

## Prerequisite

A 100-level computer science course; MATH 225 or MATH 415; MATH 241.

## Learning Objectives

- Analyze the sources of errors in mathematical operations on the computer
- Recognize major numerical methods and their merits and pitfalls
- Calculate the computational cost of a range of numerical methods
- Select and use software tools, based on their numerical methods, for a range of problems
- Estimate the accuracy in approximated numerical solutions

## Topic List

- Numerical experiments, randomness, Monte Carlo simulations
- Errors (rounding and truncation)
- Taylor series
- Floating point representation and operations
- Linear system of equations
- Sparse storage and computation
- Eigenvalue problems
- Singular value decomposition
- Data fitting
- Root finding
- Optimization