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MM311: Mathematics 4B
by Martin Grant
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MM311: Mathematics 4B

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0. Probability and Statistics

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53.202 Materials

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Presentation and Summarisation of Data

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RandomVariables

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Basic Laws

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Probability Theory

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Measures of Spread

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Measures of Locaion

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Z-test, samples and confidence

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Coursework (Semester 2)

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Sheet 1

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Sheet 2

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Sheet 3

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1. Fourier Series

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Periodic Functions

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Extended Functions

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Sketching Functions

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Odd and Even Functions

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Half Range Fourier Series

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Continuous Fourier Series

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Term-by-Term Differentiation

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Complex Exponential Form

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Tutorials

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Worked Examples

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2. Partial Differential Equations

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Solving Simple PDE's

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Change of Variables

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Real Examples of PDE's

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Linearity, Homogeneity and Superposition

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Constant Coefficient ODE's

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Separation of Variables

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Tutorials

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Worked Examples

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3. Complex Analysis

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Complex Numbers

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Points in the Complex Plane

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Complex Functions

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Continuity

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Analytic Functions

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The Cauchy-Riemann Equations

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Harmonic Functions

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Functions of Complex Variables

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Line Integrals in the Complex Plane

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Parameterising Curves

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Cauchy's Integral Theorem

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Cauchy's Integral Formula

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Tutorials

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4. Techniques of Complex Integration

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Taylor and Laurent Series

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Residue Integration

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Real Integration using Residue Theorem

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Tutorials

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5. Fourier Transforms

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The Fourier Transform

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The Fourier Sine and Cosine Transforms

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Properties of the Fourier Transform

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Parseval's Identity

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Dirac Delta Function

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Generalised Fourier Transforms

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Application of Residue Integration to Fourier Transforms

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Tutorials

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Sample Papers

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Sample Paper 1

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Sample Paper 2

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