CSC 302 - Introduction to Numerical Methods

Catalog Description:

Numerical computations with digital computers; floating point arithmetic and implications of round-off error; Monte Carlo methods. Algorithms and computer techniques for the numerical solution of problems in: function evaluation; zeros of functions; interpolation; numerical differentiation and integration; linear systems of equations; curve fitting; solutions of non-linear equations; optimization.

Contact Hours:

• Lecture: 3 hours

Prerequisites: CSC116 with a grade of C or higher and MA305 or MA405
Co-requisites: None
Restrictions: None
Coordinator: Dr. Matthias Stallmann
Textbook: Numerical Mathematics and Computing

Course Outcomes:
Upon successful completion of this course, a student will be able to..

1. use numerical computing languages like Julia
2. take a textual problem description and convert it into a mathematical model that the computer can solve
3. obtain the Taylor series expansion of a given function
4. convert a decimal (or octal or hexadecimal) number to its IEEE floating point representation, and vice versa
5. identify rounding and truncation errors and explain their impact on numerical computations
6. explain and apply numerical methods for
   • Monte Carlo approaches
   • solving systems of linear equations
   • finding solutions of nonlinear equations
   • obtaining numerical approximation using interpolation and cubic splines
   • performing numerical differentiation and integration
   • basic optimization (linear and integer programming)

Topics:

• using Julia for numerical computations and plotting
• floating point numbers
• Monte Carlo methods
• numerical differentiation and integration
• finding solutions of nonlinear equations
• solving systems of linear equations
• obtaining numerical approximation using interpolation and cubic splines
• basic optimization

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