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)