Fall2008

M348: Scientific Computation in Numerical Analysis

Course information:

Instructor: Lexing Ying, lexing@math.utexas.edu, 471-3149, RLM 10.164

Lecture: TTh 2:00-3:30P, CPE 2.206

Office hour: TTh 1:00-2:00P

Webpage: http://www.math.utexas.edu/users/lexing/courses/Fall2008_M348/index.html

Textbook:

R. L. Burden and J. D. Faires, Numerical analysis, 8th ed., 2005, Thomson Brooks/Cole (ISBN 0-534-39200-8).
J. M. Ortega and A. S. Grimshaw, An introduction to C++ and numerical methods, 1999, Oxford (ISBN 0-19-511767-0).

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.

Mathematical preliminaries and error analysis: Algorithms, errors, and convergence.
Solutions of equations in one variable: Bisection, fixed point iteration, and Newton's methods.
Interpolation and polynomial approximation: Lagrange, Hermite, and cubic spline interpolation.
Numerical differentiation and integration: Forward, backward, and multi-point differencing; Richardson's extrapolation; and trapezoidal, midpoint, Simpson, Romberg, and Gauss integration.
Initial value problems for ordinary differential equations: Euler, Taylor, Runge-Kutta, and Runge-Kutta-Fehlberg methods; and stability.
Direct methods for solving linear systems: Gaussian elimination and LU factorization, stability and condition number, and pivoting strategies.

Programming references:

C / C++

C Language tutorial http://www.lysator.liu.se/c/bwk-tutor.html

C++ tutorial http://www.cplusplus.com/doc/tutorial/

C++ tutorial www.idiap.ch/~fleuret/files/Francois_Fleuret_-_C++_Lecture_Notes.pdf

Programming (C/C++) in Linux

A quick start http://www.linuxquestions.org/linux/answers/Programming/Building_C_programs_on_Linux

Matlab

Complete documentation available at http://www.mathworks.com/access/helpdesk/help/techdoc/

Check out the following Getting Started Guide http://www.mathworks.com/access/helpdesk/help/pdf_doc/matlab/getstart.pdf

Another tutorial at http://www.math.ufl.edu/help/matlab-tutorial/

Emacs

A quick start: http://www2.lib.uchicago.edu/keith/tcl-course/emacs-tutorial.html

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. There will be 2 exams during the semester and one final at the end of the semester.

Exam 1: Sept 30, (Sec 1.1- 3.3)
Exam 2: Nov 4, (Sec 3.4 - 5.3)
Final Exam: Dec 11 (9-12n) at CPE 2.212.

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

Homework: 30%.
Exam 1: 20%.
Exam 2: 20%.
Final exam: 30%.

Lectures

Homeworks:

Late homework will not be accepted.

Homework 11. Not to be handed in.
BF 6.6 #3(ac), 5, 12(a)

Homework 10. Due 11/25 before class.
BF 6.2 #1(bd), 3(bd), 5(bd), 31
BF 6.3 #2(ab)
BF 6.5 #1, 5(ac)
Program in C++/Java and in Matlab to solve BF 6.5 #5(ac).
Solution

Homework 9. Due 11/18 before class.
BF 6.1 #4(ab), 6(ab), 12
Program in C++/Java and in Matlab to solve BF 5.11 #2(ab), 8(ab), 14(ab).
Solution

Homework 8. Due 11/11 before class.
BF 5.3 #2(ac)
BF 5.4 #2(ab), 6, 27
Program in C++/Java and in Matlab to solve BF 5.4 #14(ab) and BF 5.9 #2(a), 4(a).
Solution

Homework 7. Due 10/28 before class.
BF 5.1 #1, 4
BF 5.2 #2(ab), 12
Program in C++/Java and in Matlab to solve BF 5.2 #2(ab), #6(cd).
Solution

Homework 6. Due 10/21 before class.
BF 4.4 #2(ab), 4, 6, 16
BF 4.7 #1(ae), 3, 6, 8
Program in C++/Java and in Matlab to solve BF 4.5 #2(ab).
Solution

Homework 5. Due 10/14 before class.
BF 4.1 #5(ac), 20, 22
BF 4.2 #1(b), 9, 10
BF 4.3 #2(ab), 4, 16, 20
Solution

Homework 4. Due 10/7 before class.
BF 3.3 #1
BF 3.4 #2, 12, 13
Program in Matlab an algorithm to construct the cubic spline interpolation for BF 3.4 #2. Use c=M\f to solve the linear system Mc=f.
Solution

Homework 3. Due 9/23 before class.
BF 3.1 #2(a), 19, 23, 31
BF 3.2 #2(ab)
Program Neville's method (Algorithm 3.1) in C++/Java and Matlab to solve BF 3.1 #2(a).
Program Newton's divided difference (Algorithm 3.2) in C++/Java and Matlab to solve BF 3.2 #2(a).
(Submit your code and printed result along with the paper exercises).
Solution

Homework 2. Due 9/16 before class.
BF 2.1 #6(a), 14, 16
BF 2.2 #1(ac), 7, 20
BF 2.3 #2, 4(a), 25
BF 2.4 #2
Download, run, and understand the files in this directory (or this tar file). Start with the README file.
Solution

Homework 1. Due 9/9 before class.
BF 1.1 # 4(a), 18, 26
BF 1.2 # 4(ab), 17, 21
BF 1.3 # 1, 3, 4, 6, 9
Download, run, and understand the files in this directory (or this tar file). Start from the README file.
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/.