TW776 (2020) Numeriese Metodes / Numerical Methods Stellenbosch University Applied Mathematics

#### Announcements

• Due date for Assignment 3 postponed to April 22. Problems 4(b) and 8(b) have been dropped. (You can still submit them for a few bonus marks.)
• New video to accompany Week 7 self-study: here
• If you have questions on any Assignment, please send email. I will share my response with everyone. This will be done anonymously (that is, even if you think your question is trivial nobody will know :-)
• #### MATLAB

• This course assumes some previous experience with MATLAB (or Python).
• MATLAB is now FREE for all SU students. Download instructions here.
Alternatively, you can use MATLAB in your browser. (But this may be slower.)
• Strongly recommended: complete the (free) online MATLAB Onramp as a refresher.

#### Timetable

Tuesday 11:00 and 12:00; Wednesday 12:00

#### Information Sheets

• Information sheet available here.

#### Assignments

Assignment Date out Date in Solutions
Assignment 1 11/02/2020 25/02/2020 Solutions 1
Assignment 2 25/02/2020 11/03/2020 Solutions 2
Assignment 3 11/03/2020 22/04/2020 Solutions 3
Assignment 4 Solutions 4
Assignment 5 Solutions 5
Assignment 6 Solutions 6

#### Tests

Test 1: Tuesday April 7, 11:00-13:00, A308 (closed book, closed notes) Postponed

Test 1 will cover the material of Weeks 1-6 in the SCHEDULE box below.

Excluded material:
• Lecture slides chapter 2: pages 24, 28, 64, 70, 73-74, 84-85, 91, 96-100
• Lecture slides chapter 3: pages 18, 24-25, 54-66

Suggestions for preparation:
• Study lecture slides and additional whiteboard notes
• Study the text book and solve the exercises at the end of each chapter
• Read further on each topic by consulting Wikipedia, MathWorld and other reputable Web resources
• Work the practice exams below

#### Schedule

Week 1 (Chapter 2)
• Linear systems; Existence and uniqueness of solutions
• Vector and matrix norms

Week 2 (Chapter 2)
• Condition numbers. (Classroom demo of 11 Feb here)
• Conditioning of linear systems. (Undergraduate slides: eng / afr)
• Solving linear systems

Week 3 (Chapter 2)
• Gaussian elimination and LU factorisation (Classroom demo of 18 Feb here)
• Pivoting
• Stability of GE and the growth factor
Week 4 (Chapter 2)
• Complexity (operation count) of LU factorization and triangular solves
• Symmetric positive definite matrices and Cholesky factorization
• Band matrices and sparse matrices
• Condition number estimation

Week 5 (Chapter 3)
• Overdetermined systems and the method of least squares (Undergraduate slides: eng / afr)
• Derivation of the normal equations by differentiation and by geometry
• QR factorization

Week 6 (Chapter 3)
• QR factorization by the Gram-Schmidt and modified Gram-Schmidt procedures.