Instructor:

Dr. Buchanan
Office: Wickersham 113, Phone: 872-3659, FAX: 871-2320
Office Hours: 8AM-10AM (M&F), 9:15AM-10AM (Tu&Th), or by appointment
Email: Robert.Buchanan@millersville.edu
URL: http://banach.millersville.edu/~bob

Textbook:

Numerical Analysis, 5th edition, Richard L. Burden and J. Douglas Faires, PWS Publishing Company, 1993.

Objectives:

MATH 375 is intended to be an introduction to modern approximation techniques. Development of algorithms and their precise mathematical analysis will be emphasized. As often as possible "real world" problems will be introduced and discussed.

Prerequisites:

Fundamentals of calculus (MATH 162) and linear algebra (MATH 242). Some elementary programming experience is required to implement specific algorithms in computer code (C, C++, FORTRAN, Pascal).

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:

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, 6, and 4. The final exam (Saturday, December 14, 8AM-10AM) will be comprehensive.

Grades:

Course grade will be calculated as follows.

Tests	40%
Exam	30%
Homework	30%

The course letter grades will be calculated as follows.

90-100	A
80-89	B
70-79	C
60-69	D
0-59	F

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
• Interpolation and Polynomial Approximation (Chap. 3)
  • Interpolation and the Lagrange Polynomial
  • Divided differences
  • Cubic spline interpolation
• Direct methods for solving linear systems (Chap. 6)
  • Linear systems of equations
  • Pivoting strategies
  • Linear algebra and matrix inversion
  • Matrix factorization
• Approximation Theory (Chap. 8)
  • Discrete least squares approximation
  • Orthogonal polynomials and least squares approximation
  • Rational function approximation
• Numerical differentiation and integration (Chap. 4)
  • Numerical differentiation
  • Elements of numerical integration
  • Adaptive quadrature methods
  • Gaussian quadrature
• 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