M348: Scientific Computation in Numerical Analysis

Course information:

Textbook:

Prerequisite and degree relevance:

M318M, CS303E or equivalent exposure to basic programming, M408D with a grade of at least C, and M341 or M340L with a grade of at least C.

Course description:

Introduction to the mathematical properties of numerical methods and their applications in computational science and engineering. We will study primarily chapters 1-6 of the Burden & Faires textbook listed above. A partial outline of these chapters follows.
  1. (1.5 weeks) Mathematical preliminaries and error analysis: Algorithms, convergence, and errors.
  2. (2 weeks) Solutions of equations in one variable: Bisection, method of false position, fixed point iteration, and Newton's methods.
  3. (2.5 weeks) Direct methods for solving linear systems: Gaussian elimination and LU factorization, stability and condition number, and pivoting strategies.
  4. (2.5 weeks) Interpolation and polynomial approximation: Lagrange, Hermite, and cubic spline interpolation.
  5. (2.5 weeks) Numerical differentiation and integration: Forward, backward, and multi-point differencing, richardson's extrapolation, Newton-Cotes rule, Romberg, and Gauss integration.
  6. (2.5 weeks) Initial value problems for ordinary differential equations: Euler, Taylor, Runge-Kutta, variable step size, stability, convergnece, stiffness.

Programming references:

Computer Facility

Undergraduate Computer Lab is at RLM 7.122. A computer account on the Mathematics Department network can be obtained from the Department of Mathematics.

Grading:

One homework will be assigned each week. Late homeworks will not be accepted. The current plan is to have 2 exams during the semester and the final at the end of the semester.

Midterm 1: Sept 24 during class.
Midterm 2: Oct 27 during class.
Final Exam: TBD

There will be no make-up exams unless in some emergent situation.

Homeworks:

Late homework will not be accepted. Problems are from Bradie's book.

Homework 11.

Homework 10. Due Nov 24.

Homework 9. Due Nov 17. Solution

Homework 8. Due Nov 10. Solution

Homework 7. Due Oct 29. Solution

Homework 6. Due Oct 20. Solution

Homework 5. Due Oct 13. Solution

Homework 4. Due Oct 6. Solution

Homework 3. Due Sep 22. Solution

Homework 2. Due Sep 15. Solution

Homework 1. Due Sep 8. Solution

Exams

Midterm 2, Solution

Midterm 1, Solution

Disabilities:

The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

Policy on scholastic dishonesty:

Students who violate university rules on scholastic dishonesty are subject to disciplinary penalties, including the possibility of failing in the course and/or dismissal from the University. Since such dishonesty harms the individual, all students, and the integrity of the University, policies on scholastic dishonesty will be strictly enforced. For further infomation, please visit the Student Judicial Services web site at http://deanofstudents.utexas.edu/.