# CS/MA 321 Introduction to Numerical Methods

University of Kentucky
Department of Computer Science
CS/MA 321 Introduction to Numerical Methods

1.  Course Number/Name:  CS/MA 321, Introduction to Numerical Methods

2.  Credits and Contact Hours:  3 credits, 3 contact hours

3.   Instructor:  assigned by the department

4.   Textbook:  Numerical Mathematics and Computing (6th Ed. or later), W. Cheney, D. Kincaid, 2008.

5.   a.  Catalog Description:  Floating point arithmetic. Numerical linear algebra: elimination with partial pivoting and scaling.
Polynomial and piecewise interpolation. Least squares approximation. Numerical integration. Roots of nonlinear
equations. Ordinary differential equations. Laboratory exercises using software packages available at computer center
(Same as MA 321.)

b.  Prerequisites:  MA 114 and knowledge of procedural programming languages is required.

c.  Required course: Required

6.  a.   Outcomes of Instruction: Students will learn basic concepts, problems and methods used in numerical computing. They
will develop an ability to apply knowledge of mathematics, science, and engineering, and an ability to apply mathematical
foundations, algorithmic principles, and computer science theory in modeling and design of computer based systems in a
way that demonstrates  comprehension of the trade-offs involved in design choices.

Specifically, the student will be able to:

1.     estimate computed errors;
2.     select/propose methods that yield small errors (if possible);
3.     understand important properties for a number of basic methods (e.g., Gaussian elimination, Lagrange and spline
interpolation, Trapezoidal and Simpson’s quadratures, Newton’s iterations, Runge-Kutta methods);
4.     modify problems for better algorithm performance;
5.     analyze results computed in fl-arithmetic.

b.   Contributions to Student Outcomes (ABET Criterion 3 for Computer Science)

 Outcome a b c d e f g h i j k CS 321 3 3 3
3- Strongly supported   2 – Supported   1 – Minimally supported

7.   List of Topics Covered:

1.   Floating-point representation and errors
2.   Locating roots of equations
3.   Interpolation and numerical differentiation
4.   Numerical integration
5.   Numerical solution of systems of linear systems
6.   Approximation by spline functions
7.   Smoothing data and least-squares
8.   Numerical matrix decompositions and applications