Math 152 - Course Outline

(January - April 2008)

Note numbers below refer to the course notes available online on the main page.

Week 1 January 7-11: notes I pp. 2-13

• vectors and coordinate representation;
• vector length, dot product, projection;
• determinants

Week 2 January 14-18: notes I pp. 13-20

• cross product;
• lines and planes in 2D and 3D;
• planes in 3D

Week 3 January 21-25: notes I pp. 23-26, II pp. 27-31

• geometry of solutions of linear systems;
• linear dependence and independence;
• solving linear systems

Week 4 January 28-February 1: notes II pp. 31-33

• solving linear systems (cont.);
• review;
• Test #1 on Chapter I, Chapter II to p.33

Week 5 February 4-8: notes II pp. 33-43

• echelon form and rank;
• homogeneous equations and relationship to linear dependence;
• quadratic minimization

Week 6 February 11-15: notes II pp. 43-44, 46-48, III pp. 49-52

• least squares fit;
• resistor networks;
• matrix multiplication, linear transformations

Spring Break February 18-22

Week 7 February 25-29 notes III pp. 53-59

• rotations, projections and reflections in 2D;
• matrix representation and composition of linear transformations;
• random walks

Week 8 March 3-7 notes III pp. 60-68, 72-74

• transpose, least squares;
• matrix inverse;
• determinants

Week 9 March 10-14 notes III pp. 75-83

• determinants (cont.);
• review;
• test #2

Week 10 March 17-21 notes IV pp. 84-90

• eigenvalues and eigenvectors;
• Good Friday

Week 11 March 24-28 notes IV pp. 91-95

• Easter Monday;
• complex numbers;
• complex eigenvalues and eigenvectors;

Week 12 March 31-April 4 notes IV pp. 95-97, 100-102

• diagonalization, powers of a matrix;
• application to random walks;
• vector differential equations

Week 13 April 7-11 notes IV pp. 97-99, 104-105

• vector DEs, complex eigenvalues;
• application to electrical networks;
• review

Material in the notes not covered:

• Chapter I: 3-D graphics application
• Chapter II: Least squares application to springs
• Chapter III: Elementary matrices (quote results for det calculation)
• Chapter IV: Spring-mass DE systems

Some additional notes on the use of eigen-analysis to analyse the long time behaviour of random walks will be provided

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Last modified: Jan 4, 2008