| Sheet | |
| Series terminology | download |
| Matrices terminology | download |
| Lecture notes (Epiphany) in one file | download |
| Lecture notes (Easter) in one file | download |
| Week | Lecture | Date | Topic | In Riley et al at... | Notes |
| 11 | 1 2 3 |
Mon 15/1 Tue 16/1 Fri 19/1 |
Collections exam Series basics Tricks for summing series |
4.1, 4.2 4.2 |
2.pdf 3.pdf |
| 12 | 4 5 6 |
Mon 22/1 Tue 23/1 Fri 26/1 |
Convergence of infinite series; comparison and quotient tests. Ratio, Cauchy's, and integral tests. Convergence for alternating series, absolute and conditional convergence. Power series. |
4.3 4.3 4.3, 4.5 |
4.pdf 5.pdf 6.pdf |
| 13 | 7 8 9 |
Mon 29/1 Tue 30/1 Fri 2/2 |
Convergence of power series, interval of convergence. Operations on power series Taylor polynomials, examples. Taylor series, Lagrange form of the remainder, approximation error, Taylor's theorem |
4.5 4.6 4.6 |
7.pdf 8.pdf 9.pdf |
| 14 | 10 11 12 |
Mon 5/2 Tue 6/2 Fri 9/2 |
Taylor series and limits Matrices: motivation, simple matrix operations, matrix multiplication, matrix transpose Further examples, functions of matrices; systems of linear equations: examples |
4.6 8.3, 8.4, 8.6 8.5, 8.18 |
10.pdf 11.pdf 12.pdf |
| 15 | 13 14 15 |
Mon 12/2 Tue 13/2 Fri 16/2 |
Systems of linear equations: Gaussian elimination, row echelon form Homogeneous systems, structure of general solution; systems depending on parameter Determinant of a matrix: definition and basic properties |
8.18 8.18 8.9 |
13.pdf 14.pdf 15.pdf |
| 16 | 16 17 18 |
Mon 19/2 Tue 20/2 Fri 23/2 |
Calculation of determinant, properties, determinants and Gauss elimination Inverse matrix using elementary row operations Inverse matrix using cofactors; symmetric, orthogonal, Hermitian matrices |
8.9 8.10 8.10, 8.7, 8.12 |
16.pdf 17.pdf 18.pdf |
| 17 | 19 20 21 |
Mon 26/2 Tue 27/2 Fri 2/3 |
Unitary and normal matrices; vector spaces: linear independence Bases of vector spaces; matrices and linear maps Kernel, image, rank of a linear map |
8.12, 8.1 8.1, 8.2 8.2, 8.11 |
19.pdf 20.pdf 21.pdf |
| 18 | 22 23 24 |
Mon 5/3 Tue 6/3 Fri 9/3 |
Example: solving ODE using matrices Eigenvalues and eigenvectors: definitions, characteristic polynomial, eigenspaces Eigenvalues of Hermitian and unitary matrices; diagonalization |
8.13, 8.14 8.13, 8.14, 8.16 |
22.pdf 23.pdf 24.pdf |
| 19 | 25 26 27 |
Mon 12/3 Tue 13/3 Fri 16/3 |
Diagonalization of 2x2 matrices, transformation matrix Diagonalization of matrices: criterion Polynomials and exponent of matrices |
8.16 8.16 8.16 |
25.pdf 26.pdf 27.pdf |
| 20 | 28 29 30 |
Mon 23/4 Tue 24/4 Fri 27/4 |
Groups of symmetries Dihedral groups, definitions Finite cyclic groups, subgroups |
28.1, 28.4 28.1, 28.4 28.2, 28.6 |
28.pdf 29.pdf 30.pdf |
| 21 | 31 32 33 |
Mon 30/4 Tue 01/5 Fri 04/5 |
Maps between groups Revision Revision |
28.5 |
31.pdf |