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School of Mathematics

# 2M2 Course Materials

## Resources by Dr Cotter

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• Lecture notes: Week 1, week 2, week 3, and weeks 4-6(vector calculus). DISCLAIMER: These notes are liable to be full of mistakes, typos, crossings out and terrible handwriting. They were not designed to be published, but am happy to do so following a request. I strongly urge students to continue to take notes in the lectures if they are able.
• Course Information (first half)
• Fourier Series Notes
• Introductory slides
• Problem sheet on Fourier Analysis
• Scanned answers to FS problems Q1 Q2-6
• Mathematica notebook of Fourier answers and pdf file of notebook
• First problem sheet on Vector Calculus
• Scanned handwritten answers. Answers as a pdf of a mathematica notebook.
• Second problem sheet on Vector Calculus
• Scanned handwritten answers
• Answers to second problem sheet on vector calculus as a Mathematica notebook, and as a pdf of the mathematica notebook
• Coursework on Fourier series and vector calculus download. Due Friday week 7 at 4pm.
• A skeleton outline of the course, with links to the relevant HELM modules, will appear here shortly.
• ## Resources by Dr Thomas

Resources by Dr Thomas are now on the MATH29662 Blackboard area

## HELM Modules

Download and print the HELM modules on topics relevant to 2M2.

Differential Vector Calculus
Background to Vector Calculus
Differential Vector Calculus
Orthogonal Curvilinear Coordinates
Integral Vector Calculus
Line Integrals Involving Vectors
Surface and Volume Integrals
Integral Vector Theorems
Fourier Series:
Periodic Functions
Representation of Periodic Functions by Fourier Series
Even and Odd Functions
Convergence
Half Range Series
The Complex Form
Applications of Fourier Series
Eigenvalues and Eigenvectors:
Basic Concepts
Applications of Eigenvalues and Eigenvectors
Repeated Eigenvalues and Symmetric Matrices
Numerical Determination of Eigenvalues and Eigenvectors

### Formula Tables

Download, print and get used to looking up information in these Formula Tables. Your lecturer will be able to confirm if these tables will be provided in exams.

## Past exam papers

Download and print exam papers from previous years. Be aware that the syllabus may have changed, making some questions no longer relevant to the course you are taking. The number of questions may also have changed.

A Mock paper to service the 2011 paper can be constructed from questions 2, 3 and 4 from the 2010 paper together with question 4 from the 2002 paper. Please also note that in 2011, each question will be marked out of 20.

Solutions will NOT be available for these exams.