MATH1012 Summer 2017/18
Lectures and notes
Jump to Chapter 1 2 3 4 5 6 7 8 9 10
1 Systems of linear equations (SLE)
- 1.1 Linear equations
- 1.2 SLE
- 1.3 SLE in 3 variables
- 1.4 Elementary row operations
- 1.5 SLE in matrix form
- 1.6 Basic and free variables
2 Vector spaces and subspaces
- 2.5 Spanning sets
- 2.6 Spanning set redundancy
- 2.7 Linear independence
- 2.8 Basis and dimension
- 2.9 More on bases
3 Matrices and determinants
- 3.1 Subspaces from matrices
- 3.2 Matrix subspace examples
- 3.3 Rank and nullity
- 3.4 Inverse matrices
- 3.5 Finding inverses
- 3.6 Invertibility
- 3.7 Determinants
- 3.8 Determinants by ERO
4 Linear transformations
- 4.1 Review: functions
- 4.2 Linear transformations
- 4.3 Linear transformations from matrices
- 4.4 Matrices from linear transformations
5 Eigenvalues and eigenvectors
- 5.1 Eigenvalues and eigenvectors
- 5.2 Finding eigenvectors
- 5.3 Multiplicity of eigenvalues
- 5.4 Diagonalisation
6 Improper integrals
7 Probability and statistics
- 7.1 Probability review
- 7.2a Discrete random variables
- 7.2b Discrete random variables
- 7.3 Continuous random variables
- 7.4a Some probability density functions
- 7.4b The normal distribution
- 7.5 Statistical inference
- 7.6 The distribution of \(\bar X_n\), a computer simulation of the central limit theorem
- 7.7 Confidence intervals
- 7.8 Hypothesis testing, instructions for how to load dice
8 Sequences and series
- 8.1 Sequences and limits continued here
- 8.2 Diverging to infinity
- 8.3 Monotone sequences theorem
- 8.4 Infinite series continued here
- 8.5 Divergence test
The following are lecture captures from 2017 Semester 2.
notes (lecture 26 has been deliberately omitted, it was on improper integrals which we have covered already)
- 8.6 Comparison tests
- 8.7 The integral test
- 8.8 Alternating series test, ratio test
- 8.9 Ratio test, power series, Taylor series
9 Fourier series
The following are lecture captures from 2017 Semester 2.
- 9.1 Fourier series for \(2\pi\)-periodic functions
- 9.2 Arbitrary period, convergence
- 9.3 Periodic extension, half range expansion, Parseval’s theorem