Week
1
Section(s)
of Poole
1.1
2
1.1
3
1.3
4
1.3
2.3
5
6
7
2.0, 2.1
2.2
3.0
3.1, 3.2
3.1, 3.2
3.1, 3.2
3.3
8
3.3
4.2
9
4.2
4.1
10
4.3
11
4.4
12
3.7
3.7
4.6
13
Topics
1A: Notation
1B: Vectors in the plane
1C: Vectors in R3
1D: Vectors in Rn
2A: Linear combinations of vectors
2B: Dot product
2C: Length of vectors
2D: Angle between vectors
2E: Orthogonal vectors
2F: Projections
3A: Cross product
3B: Cross product, length and area
3C: Lines in R2 - general form and normal form
3D: Lines in R2 - vector form and parametric equations
3E: Lines in R3
4A: Planes in R3
4B: Spans
4C: Linear independence
4D: Introduction to systems of linear equations
5A: Matrices and echelon form
5B: Elementary row operations
5C: Gaussian elimination
5D: Gauss–Jordan elimination
6A: Matrices
6B: Matrix addition and scalar multiplication
6C: Matrix multiplication
6D: Transpose of a matrix
7A: Inverse of a matrix
7B: Inverses and determinants of 2 × 2 matrices
7C: Inverses and elementary row operations
7D: Inverses and systems of linear equations
8A: Elementary matrices
8B: Determinants
8C: Determinant method for cross product
9A: Determinants and elementary row operations
9B: Properties of determinants
9C: Introduction to eigenvalues and eigenvectors
9D: Characteristic polynomials
10A: Eigenvalues of triangular matrices
10B: Multiplicities of eigenvalues
10C: Eigenvalues, trace and determinants
11A: Similar matrices
11B: Diagonal matrices
11C: Diagonalisation
11D: Powers of diagonal matrices
11E: Leslie model of population growth
12A: Probability vectors and stochastic matrices
12B: Markov chains
12C: Steady-state vectors
12D: Regular Markov chains
Revision