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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