CM 770: Numerical Analysis (Fall 2008)

 

Instructor: Prof. Hans De Sterck, office: MC5016, email: hdesterck@uwaterloo.ca

Lectures: 10:00-11:20TueTh (MC4060)

Office hours: TBA (MC5016)

  

TA: Killian Miller, office: MC6091H, email: killianmiller7@hotmail.com

Office hours: TBA (MC6091H)

 

Course objectives: The goal of this course is twofold. You will receive a solid introduction to the theory of several important classes of numerical methods (with derivations of the methods and some proofs), and you will learn to implement the numerical methods efficiently in Matlab.

 

Who should take this course: This is a core course in the Computational Mathematics MasterŐs program, providing base knowledge in the numerical methods that are employed in further courses in this program. This course can also be taken as a solid introductory course on numerical methods by graduate students from other programs in Mathematics, Science and Engineering. In particular, CM 770 may be a good preparation for AM 741/CS 778: Numerical Solution of Partial Differential Equations, for students without much previous experience in numerical methods.

 

Prerequisites: A basic undergraduate course on numerical methods, as well as some experience in Matlab programming, are recommended but not absolutely required. Students who have previously taken two or more courses on numerical methods, including a course on numerical linear algebra, are not recommended to take this course.

 

Tentative outline:

Numerical methods: 5 weeks

  1. Floating point number system and error propagation (1 week)
  2. Rootfinding methods (1 week)
  3. Approximation (1 week)
  4. ODEs (2 weeks)

Numerical linear algebra: 7 weeks

  1. LU decomposition (1 week)
  2. Least Squares and QR decomposition (1 week)
  3. Basic iterative methods for linear systems (1 week)
  4. Multigrid methods (2 weeks)
  5. Conjugate gradient method (1 week)
  6. Eigenvalues and/or SVD (1 week)

  

Required textbook: Introduction To Numerical Computation, by Elden, Wittmeyer-Koch, and Nielsen, Studentlitteratur AB, 2004 (available from UW Bookstore).

 

 

Other references:

á      Numerical linear algebra, by Trefethen and Bau, SIAM, 1997.

á      A Multigrid Tutorial, by Briggs, Henson and McCormick, SIAM, 2000.

 

Course website: The ACE system will be used extensively for all course communications.

  

Assignments: There will be approximately six assignments, with a mix of theoretical questions and programming questions.

 

Academic honesty: You are allowed to discuss theoretical and computational assignment problems and your solution strategies with your classmates, but you are not allowed to copy any material. All assignment material that you submit (including written documents, program code and graphical output) should be strictly your own work. Students are expected to know what constitutes academic integrity, to avoid committing offences, and to take responsibility for their actions (see http://uwaterloo.ca/academicintegrity).

 

Final grade: 40% Assignments, 60% Final Exam.

 

First lecture: Tuesday September 9, 10:00-11:20 (MC4060).