Math 715: Numerical Analysis

Fall 2005

Department of Mathematical Sciences, UWM

Lecture Time and Place

  4:00 PM - 5:15 PM, Tuesday and Thursday, Physics Building, Room 149.

Instructor

  Dr. Dexuan Xie
  Office:	EMS-489
  Telephone:	(414) 229-3528
  E-mail:	dxie@csd.uwm.edu
  Homepage:	http://www.uwm.edu/~dxie/
  Office Hours: 10:00 - 11:30 AM, Tuesday and Thursday.

Computer Lab Place

EMS Building, Room E425.

Textbook

Numerical Analysis, Richard L. Burden and J. Douglas Faires, 8th edition, Thomson, Brooks/Cole, 2005.

Reference: Introduction to Numerical Analysis, J. Stoer and R. Bulirsch, 2nd edition, Springer-verlag, 1993.

Prerequisite

Pass Math 413 and Math 521 (or equivalent levels), and know one of C, C++, Fortran, Pascal, Maple, Matlab, and Mathematica. Matlab is used in class teaching.

Course Overview

Interpolation by Polynomials: Sections 3.1 to 3.4. It includes Lagrange polynomial, Newton's divided-difference, and Hermite interpolation.
Approximation by Rational, Trigonometric, and Spline Functions: Sections 8.2 to 8.6, and 3.4. It includes Chebeyshev polynomials, least squares approximation, fast Fourier transforms, and cubic spline functions.
Numerical Differentiation and Integration: Sections 4.1, 4.3, 4.4 and 4.7. It includes derivative approximation formulas, numerical integration formulas, and Gaussian quadrature.
Initial Value Problems for Ordinary Differential Equations: Sections 5.2 to 5.4, 5.6, 5.9, and 5.10. It includes Euler's method, higer-order Taylor methods, Runge-Kutta methods, multistep methods, Runge-Kutta method for system of differential equations, and stability.
Direct Methods for Solving Linear Systems: Sections 6.1, 6.2, 6.5, and 6.6. It includes Gaussian elimination, pivoting strategies, Cholesky algorithm, and Crout factorization for tridiagonal linear systems.
Numerical solutions of Nonlinear Equations: Sections 2.2 to 2.4, and 10.1 to 10.4. It includes Newton's method, quasi-Newton methods, steepest descent method, and error analyses.

Grading

Three homework evaluations: 15 %. Each 5 %
Two tests: 50 %. Test 1 for 25 % and Test 2 for 25 %.
Attendance: 5 %. 1 % reduction for one class missing.
Final Exam: 30 %.
Grading scale: A (90-100), B+ (86-89), B (80-85), C (70-79), D (60-69), F (below 59)

Examination Schedule:

Homework evaluation 1: Due on October 11
Test 1: October 20
Homework evaluation 2: Due on November 8
Homework evaluation 3: Due on December 13
Test 2: December 1
Final Exam: Thursday, December 22, 3:00 - 5:00 pm

Important Dates

September 6: First class October 3: Last day to drop without a "W" on academic record 
October 28: Last day to drop 
November 24 - 27: Thanksgiving Holiday - No classes 
December 13: Last class

Attendance:

Attendance at the lectures, tests, and final examination is required. Attendance at the lectures will be taken after the first week. Each class missing results in one point reduction. The maximum of class missing reduction points is 5. In other words, perfect attendance will gain 5 points of your course grade.

There is no provision for absences due to vacations, family outings and other social activities, other special plans and appointments, etc. Absences due to illness require a medical excuse on Physician's letterhead, signed by the physician. Students will be allowed to complete examinations or other requirements that are missed because of religious observances with a letter signed by the priest. They must be submitted before any alternate arrangements for a missing test will be considered.

Homework:

You are expected to do the required assigned homework on a regular basis. The homework will be collected as scheduled for evaluations. It includes some program assignments, which you can complete using any computer programming language.

Statement of Academic Misconduct

The university has a responsibility to promote academic honesty and integrity and to develop procedures to deal effectively with instances of academic dishonestly. Students are responsible for the honest completion and representation of their work, for the appropriate citation of sources, and for respect of others' academic endeavors. Further information can be found at http://www.uwm.edu/Dept/Acad_Aff/policy/academicmisconduct.html.

Statement of Sexual Harassment

Sexual harassment is reprehensible and will not be tolerated by the University. It subverts the mission of the University and threatens the careers, educational experience, and well being of students, faculty and staff. The University will not tolerate behavior between or among members of the University community which creates an unacceptable working environment.