Fall 2000

MATH 375.01 (3 credits), Tu_Th, 11:00AM-12:15PM, Wickersham 109

**Prerequisites:**Grades of C- or better in each of MATH 261 (

*Calculus III*), MATH 242 (*Linear Algebra*), and CSCI 161 (*Introduction to Computing I*) are the prerequisites for this course.**Instructor:**Dr. Buchanan

Office: Wickersham 113, Phone: 872-3659, FAX: 871-2320

Office Hours: 1:00PM-2:00PM (MTuWThF), or by appointment

Email:`Robert.Buchanan@millersville.edu`

URL:`http://banach.millersville.edu/~bob`**Textbook:***Numerical Analysis*, 6th edition, Richard L. Burden and J. Douglas Faires, Brooks/Cole Publishing Company, 1997.**Objectives:**MATH 375 is intended to be an introduction to modern approximation techniques. Development of algorithms, their precise mathematical analysis, and an analysis of their errors will be emphasized. As often as possible ``real world'' problems will be introduced and discussed.

**Course Contents:**- Mathematical preliminaries (Chap. 1)
- Review of calculus
- Round-off errors and computer arithmetic
- Algorithms and convergence

- Solutions of equations in one variable (Chap. 2)
- Bisection method
- Fixed-point iteration
- Newton-Raphson method
- Error analysis for iterative methods
- Accelerating convergence

- Direct methods for solving linear systems (Chap. 6)
- Linear systems of equations
- Pivoting strategies
- Linear algebra and matrix inversion
- Matrix factorization

- Numerical differentiation and integration (Chap. 4)
- Numerical differentiation
- Elements of numerical integration
- Adaptive quadrature methods
- Gaussian quadrature

- Interpolation and Polynomial Approximation (Chap. 3)
- Interpolation and the Lagrange Polynomial
- Divided differences
- Cubic spline interpolation

- Approximation Theory (Chap. 8)
- Discrete least squares approximation
- Orthogonal polynomials and least squares approximation
- Rational function approximation

- Iterative techniques in matrix algebra (Chap. 7)
- Norms of vectors and matrices
- Eigenvalues and eigenvectors
- Iterative techniques for solving linear systems
- Error estimates and iterative refinement

If time permits other topics may be covered as well.

- Mathematical preliminaries (Chap. 1)
**Attendance:**Students are expected to attend all class meetings. If you must be absent from class you are expected to complete class requirements (tests and/or homework assignments) prior to the absence. Students who miss a test should provide a valid excuse, otherwise you will not be allowed to make up the test. Tests should be made up within one week of their scheduled date. No final exam exemptions.

**Homework:**Homework assignments will consist of a mixture of pencil and paper written assignments and programming assignments. Programming assignments must be submitted electronically through email. Students are expected to do their homework and participate in class. Students should submit all homework by the date due. Late homework will not be accepted without valid excuse. Discussion between students on homework assignments is encouraged, but homework submitted for grading should be written up separately.

**Tests:**A test will be given after completing the material from each of Chapters 2, 4, and 8. The final exam (Thursday, December 14, 2:45PM-4:45PM) will be comprehensive.

**Grades:**Course grade will be calculated as follows.

Tests 42% Homework 38% Exam 20% I keep a record of students' test, homework, and exam scores. Students should also keep a record of graded assignments, tests, and other materials. The course letter grades will be calculated as follows.

90-92 A 93-100 A 80-82 B 83-86 B 87-89 B 70-72 C 73-76 C 77-79 C 60-62 D 63-66 D 67-69 D 0-59 F **Final Word:**Math is not a spectator sport. What you learn from this course and your final grade depend mainly on the amount of work you put forth. Daily contact with the material through homework assignments and review of notes taken during lectures is extremely important.

Robert.Buchanan@millersville.edu

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