Instructions on how to study for the resit exam in September 2016 are the same as for the May 2016 exam.

## Wednesday, 20 July 2016

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## Lecture notes

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Chapter 0 - Introduction

Chapter 1 - Contractions

Chapter 2 - Existence and uniqueness

Chapter 3 - Linear autonomous ODEs

Chapter 4 -The flow near an equilibrium

Chapter 5 - Poincare-Bendixson Theorem (+ appendix)

Chapter 6 - Biological applications

Chapter 7 - Calculus of Variations (Liquid mirror example)

Chapter 1 - Contractions

Chapter 2 - Existence and uniqueness

Chapter 3 - Linear autonomous ODEs

Chapter 4 -The flow near an equilibrium

Chapter 5 - Poincare-Bendixson Theorem (+ appendix)

Chapter 6 - Biological applications

Chapter 7 - Calculus of Variations (Liquid mirror example)

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Inverse Function Theorem in R: proof + proof of formula for derivative

Higher dimensional derivatives

Implicit Function Theorem in R^n: proof + proof of formula for derivative

Proof of Lemma 4.1.1 (notes)

Higher dimensional derivatives

Implicit Function Theorem in R^n: proof + proof of formula for derivative

Proof of Lemma 4.1.1 (notes)

Nr 1 (Solns )

Nr 2 (Solns )

Nr 3 (Solns )

Nr 4 (Solns )

Nr 5 (Solns )

Nr 6 (Solns )

Nr 7 (Solns )

Nr 8 (Solns )

Nr 2 (Solns )

Nr 3 (Solns )

Nr 4 (Solns )

Nr 5 (Solns )

Nr 6 (Solns )

Nr 7 (Solns )

Nr 8 (Solns )

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