This course contains an introduction to ordinary differential equations. It will cover various kinds of first order equations and then second order equations with constant coefficients.

A knowledge of integration is ESSENTIAL for this course. Please look at your first year and second year notes for reference.

There are 2 lectures per week: Wednesdays at 1pm in Physics Hall and Thursdays at 1pm in Hall F.

The exam is 90 minutes and will take place in January.

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1 A few integrals for you to practice on!

Integrals

2 Lecture 1: What is an ordinary differential equations and what is a solution?

3 Lecture 2: Boundary value solutions, one parameter families of curves and their representation by first order differential equations.

Exercise 1

Diagrams for question 4

4 Lecture 3: First order differential equations of simple and variable separable type.

5 Lecture 4: First order homogeneous equations.

6 Lecture 5: More first order homogeneous ODEs and linear substitutions.

7 Lecture 6: Using linear substitutions to make equations either homogeneous or variable separable. An introduction to linear equations.

Exercise 2.

8 Lecture 7: First order linear equations.

9 Lecture 8: Bernoulli Equations. Simple applications - Newton's laws of motion.

10 Lecture 9: Applications - Radioactive decay and Newton's law of cooling.

Exercise 3

11 Lecture 10: Applications. Newton's Law of Cooling and Kirchoff's Law.

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