Announcements
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.
Lecturer
 Prof JAC Weideman, Office: A315, Email: weideman@sun.ac.za
Timetable
Tuesday 11:00 and 12:00; Wednesday 12:00Information Sheets
 Information sheet available here.
Notes

Chapter 1;
Lecture Slides 1
(Undergraduate slides: eng1,
eng2 / afr1,
afr2)
(Background Material) < Read!
 Chapter 2; Lecture Slides 2 (Linear Systems)

Chapter 3;
Lecture Slides 3
(Least Squares)
 Chapter 4; Lecture Slides 4 (Eigenvalues)
 Chapter 11 (pp.335350); Lecture slides 11 (long) / (short) (Direct and Iterative Methods for Sparse Systems)
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, 11:0013:00, A308 (closed book, closed notes) PostponedTest 1 will cover the material of Weeks 16 in the SCHEDULE box below.
Excluded material:
 Lecture slides chapter 2: pages 24, 28, 64, 70, 7374, 8485, 91, 96100
 Lecture slides chapter 3: pages 18, 2425, 5466
 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
 Test 1 2015 (no solutions given, collaborate with your class mates)
 Test 1 2019 and solutions
 Test 2 2019 and solutions
Schedule
Week 1 (Chapter 2) Linear systems; Existence and uniqueness of solutions
 Vector and matrix norms
 Condition numbers. (Classroom demo of 11 Feb here)
 Conditioning of linear systems. (Undergraduate slides: eng / afr)
 Solving linear systems
 Gaussian elimination and LU factorisation (Classroom demo of 18 Feb here)
 Pivoting
 Stability of GE and the growth factor
 Complexity (operation count) of LU factorization and triangular solves
 Symmetric positive definite matrices and Cholesky factorization
 Band matrices and sparse matrices
 Condition number estimation
 Overdetermined systems and the method of least squares (Undergraduate slides: eng / afr)
 Derivation of the normal equations by differentiation and by geometry
 QR factorization
 QR factorization by the GramSchmidt and modified GramSchmidt procedures.
 Householder reflectors (additional note)
 Givens rotations
 Revision of eigenvalues/vectors and the eigenvalue decomposition
 Special properties of eigenvalues/vectors for symmetric matrices; application to quadratic curves
 Instability of the characteristic polynomial in fp arithmetic, companion matrices