Math2061: Linear Mathematics Component - Course Summary January 2010
(Chapter references are for "Linear Mathematics" J.Henderson)
Week 1: Chapter 1, part of Chapter 2
Review of previous knowledge of Linear systems
Gaussian elimination
Null Space of a Matrix
Vector spaces
Week 2: Chapter 2, Chapter 3
Vector spaces and subspaces
Linear combinations
Span of a set of vectors
Column Space of a Matrix
Week 3: Chapter 4
Linear Dependence and Linear Independence
Basis and dimension of a vector space
Basis and Subspace Theorems
Week 4: Chapter 5, part of Chapter 6
Special Bases, Lagrange Polynomials
Column space, Null space and rank
Linear transformations as maps between vector spaces
Week 5: Chapter 6, Chapter 7
Geometric interpretation of matrix transformations
Eigenvalues and eigenvectors
Diagonalisation of a matrix
Mathematical modelling and eigenvalues
Week 6: Chapter 8, Chapter 9
Leslie population model
Linear recurrence relations
Systems of linear differential equations
Review of previous examinations