MAT/CSC 381 Textbook: Numerical Methods, 2nd ed.  Faires and Burden

Prerequisites:  MAT 122 and CSC 116 or instructor's consent

Course Description: In engineering and other scientific areas, various mathematical problems arise which need to be solved. However, not all problems have solutions that are easy to find by hand or in a reasonable amount of time. The use of a computer in solving these problems is introduced. But, most of these engineering problems involve continuous mathematical models whereas a computer is only capable of a finite number of computations. Hence, finite approximation methods which may be implemented on a computer must be developed that give good and reasonable answers to the continuous problems. Numerical Analysis is the systematic and mathematical study of the errors in using such methods. For this class, we will consider only the design and programming of good algorithms and leave much of the detailed study for MAT/CSC 481.

This course carried three hours of academic credit.
 

(From the college catalog: This course looks into the modeling of mathematical concepts on a computer.  Algorithms will be discussed and implemented which find roots of equations, give polynomial approximations to discrete data, approximate integrals and derivatives, solve ordinary differential equations and solve linear systems of equations.)

Learning Objectives:  This term, the following topics will be discussed:

Errors in Computations

Root-finding

• Bisection method
• Newton's method
• Mueller's method

Polynomial approximation

• Lagrange polynomials
• Hermite polynomials
• Cubic splines
• Bezier curves
• Surfaces

Integration and Differentiation

• Trapezoidal Rule
• Simpson's rule
• Gaussian Quadrature
• Difference Rules

Solving Differential Equations

• Euler's method
• Tailors methods
• Runge-Kutta methods

Systems of Equations

• Gaussian Elimination
• Matrix Factorizations
• Jacobi method
• Gauss-Seidel method

Meetings: The format of class meetings will alternate between lectures by the instructor and group discussion sessions, often around a computer.  Student participation will be encouraged via these classroom discussions as well as problem sessions where the student might present their work.

This class meets as scheduled. You are expected to be in class on time.  University policy states that a student cannot miss more than 25% of class meetings and receive credit for the course. Further, attendance will be necessary in order to understand the material and make a good grade. The student is responsible for work and material missed when absent. Cheating in any way will be properly rewarded according to University policy (Tomahawk; Undergrad. Bulletin, pp. 46;  http://www.mc.edu/publications/policies/219.html).

If you need special accommodations due to learning, physical, psychological, or other disabilities, please contact Dr. Buddy Wagner in the Counseling and Career Development Center. He may be reached by phone at (601)925-3354 or by mail at P.O. Box 4013, Clinton, MS 39058.

Grading: There will be at least four exams during the semester. Also, there will be a number of homework problems, computing assignments and reading assignments. An average of these grades will count as one exam grade.  Your final average will be computed using an average of all the exam grades.

The grading scale:

A=90-100

B=80-89

C=70-79

D=65-69

F=0-64

Aim now for the desired grade. Makeup exams for excused absences may be administered at the end of the term at the discretion of the instructor. Finally, all graded work will be returned to the student for keeping. If there were any question later about your grade, you would be expected to show these papers.