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MM311: Mathematics 4B by Mind Map: MM311: Mathematics 4B
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MM311: Mathematics 4B

0. Probability and Statistics

53.202 Materials

Presentation and Summarisation of Data


Basic Laws

Probability Theory

Measures of Spread

Measures of Locaion

Z-test, samples and confidence

Coursework (Semester 2)

Sheet 1

Sheet 2

Sheet 3

1. Fourier Series

Periodic Functions

Extended Functions

Sketching Functions

Odd and Even Functions

Half Range Fourier Series

Continuous Fourier Series

Term-by-Term Differentiation

Complex Exponential Form


Worked Examples

2. Partial Differential Equations

Solving Simple PDE's

Change of Variables

Real Examples of PDE's

Linearity, Homogeneity and Superposition

Constant Coefficient ODE's

Separation of Variables


Worked Examples

3. Complex Analysis

Complex Numbers

Points in the Complex Plane

Complex Functions


Analytic Functions

The Cauchy-Riemann Equations

Harmonic Functions

Functions of Complex Variables

Line Integrals in the Complex Plane

Parameterising Curves

Cauchy's Integral Theorem

Cauchy's Integral Formula


4. Techniques of Complex Integration

Taylor and Laurent Series

Residue Integration

Real Integration using Residue Theorem


5. Fourier Transforms

The Fourier Transform

The Fourier Sine and Cosine Transforms

Properties of the Fourier Transform

Parseval's Identity

Dirac Delta Function

Generalised Fourier Transforms

Application of Residue Integration to Fourier Transforms


Sample Papers

Sample Paper 1

Sample Paper 2