Mathematics 150 Spring 2005 Information

Instructor: J. Gehrmann
Office: Brighton Hall Room 146 (BRH 146)
Telephone: 278-7116
Email: jgehrmann@csus.edu
Office Hours: TR 10:30-11:30 a.m.,W 4-5:30 p.m., or by appointment

Course Objective: To provide an introduction to techniques of numerical analysis including solutions of nonlinear equations, linear systems, interpolation, curve fitting, numerical differentiation, numerical integration, and numerical optimization. Each method is described, examples are given, and limitations for each method are investigated.

Required Textbook: Numerical Methods Using Matlab (4th Edition) by John H. Mathews and Kurtis D. Fink

Homework and Quizzes: Homework is very important and should be completed as the topics are covered in class. In completing this material you will gain an understanding of ideas considered in class and in your textbook. To encourage you to do this homework, announced and unannounced quizzes comprised of problems like those on the homework assignments will be given approximately once each week of the semester. In addition, you may be asked to turn in some exercises. The quizzes and exercises will be graded and averaged, and will constitute 10% of your numerical score.

Examinations: Three midterm examinations will constitute between 35% and 55% of your numerical score, and the comprehensive final examination will constitute between 35% and 55% of your numerical score (55% given to the higher of the final examination and average of the midterm examination scores, whichever is higher, and 35% to the other score).

Final Examination Time: Tuesday, May 17, 8-10 A.M.

Grading: Your final numerical score will be computed from quiz, hour examination, and final examination scores using the percentages mentioned above. Letter grades will be assigned as follows: for an A, your numerical score must be 90 or greater, for a B, it must be between 80 and 89, for a C, between 65 and 79, and for a D, between 55 and 64.

Tentative Schedule by Topic:

Math 150 Webpage: This includes links to information about problems discussed in class, announcements of exams and homework, and other class-related information. This page will be updated after each class session.

Preliminaries (2 Weeks)

Review of Calculus
Binary Numbers
Error Analysis

Solutions of Nonlinear Equations (2 Weeks)

Iteration for Solving x=g(x)
Bracketing Methods for Locating a Root
Initial Approximation and Convergence Criteria
Newton-Raphson and Secant Methods

Solutions of Linear Systems (2 Weeks)

Introduction
Matrix Properties
Upper Triangular Systems and Triangular Factorization
Iterative Methods for Linear Systems

Interpolation and Polynomial Approximation ( 2Weeks)

Taylor Series and Calculation of Functions
Introduction to Interpolation
Lagrange Approximation
Newton Polynomials
Pade Approximation (Time permitting)

Curve Fitting (2 Weeks)

Least-Squares Line
Methods of Curve Fitting
Interpolation by Splines
Fourier Series and Trigonometric Polynomials
Bezier Curves

Numerical Differentiation (1 Week)

Approximating the Derivative
Numerical Differentiation Formulas

Numerical Integration (2 Weeks)

Introduction
Composite Trapezoidal and Simpson's Rule
Recursive Rules and Romberg Integration
Adaptive Quadrature

Numerical Optimization (2 Weeks)

Minimization of a Function of One Variable
Nelder-Mead and Powell's Methods
Gradient and Newton's Methods