I. Catalog Description
COSC 450 Applied Numerical Methods
3c-01-3sh
Prerequisite: COSC 250, MATH 171, and MATH 241 or equivalents
Polynomial approximations using finite differences, with applications in numerical integration and differentiation. Numerical solution of initial value ordinary differential equations. The APL language will be introduced and used along with Fortran, in programming selected algorithms.
II. Course Objectives
- Students should be able to use the APL language to implement numerical algorithms.
- Students should be able to use polynomial approximation techniques in solving problems.
- Students should be able to find numerical solutions of initial value ordinary differential equations.
III. Course Outline
Topic and Hours
- APL
- Introduction: 2
- Arrays, Functions, and Matrix Algebra: 8
- Logicals, Simulation, and Statistics: 6
- Advanced Array Manipulation and Sorting: 4
- Advanced Function Definition: 3
- Gaussian Quadrature: 2
- LU Factorization of Matrices: 2
- B Splines: 4
- Ordinary Differential Equations: 4
- Systems of Ordinary Differential Equations: 3
- Boundary Value Problems: 3
IV. Evaluation Methods
The final grade for the course will be determined as follows:
50% Tests. At least two tests (mid term and final) consisting of mathematical problems and programming questions.
50% Homework and Projects. At least six computer projects will be assigned. Projects will be graded on output and style. Short homework papers from the textbook problem sets may also be assigned.
V. Required Textbooks, Supplemental Books, and Readings
Textbooks
- Reiter, Clifford A. and William R. Jones, APL With a Mathematical Accent, Brooks/Cole Publishing Company, 1990.
- Cheny, Ward and David Kincaid, Numerical Mathematics and Computing, Third Edition, Brooks/Cole, 1994.
Supplemental Book
- Metcalf, Michael and John Reid, Fortran 90 Explained, Oxford University Press, 1990.
VI. Special Resource Requirements
There are no special resource requirements for this course.
VII. Bibliography
- Burden, Richard and J. Douglas Faires, Numerical Analysis, Third Edition, Prindle, Weber, and Schmidt, 1985.
- Fortran 90, ISO/IEC JTC1/SC22/WGS Internal document N692, Submitted as Text for ISO/IEC 1539:1991, 1991.
- Gerald, Curtis F. and Patrick O. Wheatley, Applied Numerical Analysis, Fourth Edition, Addison-Wesley Publishing Company, 1989.
- Lastman, Gary J. and Naresh K. Sinha, Microcomputer-Based Numerical Methods for Science and Engineering, Saunders, 1989.
- Mathews, John H., Numerical Methods for Mathematics, Science, and Engineering, Prentice Hall, 1992.
