| One purpose of attending lectures is to learn faster and better than if you study on your own with a book. In addition, lectures have the advantage of being interactive; you can ask if you need a clarification. To take full advantage of lectures you need to do a lot of work on your own before each lecture (by reviewing the previous lecture and looking ahead) and after each lecture (by making sure that you understood everything and by working on the exercises). Otherwise lectures are quickly forgotten. |
| Day | Time | Location |
| Tuesday | 11:00 | CG 93 |
| Thursday | 10:00 | CG 93 |
| Friday | 17:00 | CG 93 |
| Week | Lecture | Date | Topic | In Riley et al at... |
| 11 | 1 2 3 |
T 17/1 Th 19/1 F 20/1 |
Collections exam Series basics Tricks for summing series |
4.1,4.2 4.2 |
| 12 | 4 5 6 |
T 24/1 Th 26/1 F 27/1 |
Convergence of infinite series; absolute vs conditional convergence, tests. Integral test, Conditional convergence for alternating series. Power series, interval of convergence, complex power series. |
4.3 4.5 4.5 |
| 13 | 7 8 9 |
T 31/1 Th 2/2 F 3/2 |
Operations on power series, Taylor polynomials, Taylor series. Examples of Taylor series, Approximation error, Taylor's theorem Approximation error, Taylor series and limits. |
4.6 4.6 4.6 |
| 14 | 10 11 12 |
T 7/2 Th 9/2 F 10/2 |
Motivation, simple matrix operations, matrix multiplication Matrix transpose, Hermitian conjugate Systems of linear equations: Gaussian elimination |
8.3, 8.4 8.5-8.7 8.8 |
| 15 | 13 14 15 |
T 14/2 Th 16/2 F 17/2 |
Systems of linear equations: redundant equations, homogeneous equations Vector spaces, matrices as linear operators, linear independence and basis Change of basis, rank and nullity |
8.8 8.1, 8.2 - |
16 | 16 17 18 |
T 21/2 Th 23/2 F 24/2 |
Trace and determinant, calculation of determinant Properties of determinant, relation of determinant to systems of equations Determinants and rank. Inverse of a matrix: companion matrix |
8.9 8.9 8.11,8.10 |
| 17 | 19 20 21 |
T 28/2 Th 1/3 F 2/3 |
Inverse using cofactors Symmetric, orthogonal, Hermitian, unitary matrices Eigenvalues and eigenvectors: definition, characteristic equation |
8.10 8.12 8.14, 8.13 |
| 18 | 22 23 24 |
T 6/3 Th 8/3 F 9/3 |
Determining eigenvectors, examples Properties of eigenvalues and eigenvectors, defective matrices Eigenvalues for Hermitian matrices, commuting matrices share eigenvectors |
8.14 8.13 8.13 |
| 19 | 25 26 27 |
T 13/3 Th 15/3 F 16/3 |
Change of basis: similarity transformation Diagonalisation of matrices: finding S Diagonalisation of matrices: finding an orthogonal S |
8.16 8.16 8.16 |
| 20 | 28 29 30 |
T 24/4 Th 26/4 F 27/4 |
Quadratic forms Diagonalisation of quadratic forms Solving systems of linear ODEs by diagonalization |
8.17 8.17 - |
| 21 | 31 32 33 |
T 1/5 Th 3/5 F 4/5 |
Systems of equations: LU decomposition, Cramer's rule Systems of equations: singular value decomposition Revision lecture |
8.18 8.18 - |