MATH10232 Course Materials - 2011/2012

MATH 10232: Calculus and Applications

This page contains notes, links and exercises for the course MATH 10232

Course Description (Outline)

This course unit aims to introduce students to ordinary differential equations, primarily covering methods of solution and applications to physical situations. The unit will cover first and second order ordinary differential equations including classification and standard solution methods. Applications will be drawn from the field of classical mechanics, but no prior experience in mechanics is expected or required. The computer package MATLAB will be used to illustrate many of the ideas and methods. The code in the lecture notes and example sheets has been tested with MATLAB.

Examples Sheets and Solutions

Example Sheet 0 (pdf) Solutions (pdf)
Example Sheet 1 (pdf) Solutions (pdf)
Example Sheet 2 (pdf) Solutions (pdf)
Example Sheet 3 (pdf) Solutions (pdf)
Example Sheet 4 (pdf) Solutions (pdf)
Example Sheet 5 (pdf) Solutions (pdf)
Example Sheet 6 (pdf) Solutions (pdf)
Example Sheet 7 (pdf) Solutions (pdf)
Example Sheet 8 (pdf) Solutions (pdf)
Example Sheet 9 (pdf) Solutions (pdf)
Example Sheet 10 (pdf) Solutions (pdf)
Example Sheet 11 (pdf) Solutions (pdf)

Lecture Notes

The notes below extend and supplement the material delivered in lectures. The notes are provided as is and may contain typos (if you find any please let me know). These notes are not a substitute for writing your own notes in the lectures and I would encourage you all to attend the lectures and take your own written notes.

The only exception is Chapter 0, which contains a summary of material that you should already know from previous courses and a brief introduction to MATLAB commands that you might find useful. The material in Chapter 0 will not be covered in depth in the lectures and you should take a little time to read it over and check that you understand it.

Chapter 0: Preliminaries with a brief Introduction to MATLAB (pdf)
Chapter 1: Introduction (pdf)
Chapter 2: First-order ODEs (pdf)
Chapter 3: Higher-order ODEs (pdf)
Chapter 4: (Classical) Mechanics (pdf)

In-class test

In-class test 2011/2012 (pdf) and solution (pdf)

In-class test 2012/2013 (pdf) and solution (pdf)

Past papers

2011/2012 (Tests for years prior to 2011 were given by a different lecturer and are not needed.)

Reading List

It is not necessary to buy any books. Your lecture notes will be completely sufficient. That said, you may find the alternative perspectives in books helpful. If you are interested, have a look in the library in the calculus and mechanics sections. Possible choices are

Calculus, Early Transcendentals by James Stewart.
Elementary differential equations with boundary value problems by C. H. Edwards.
Schaum's Outlines: Differential Equations by Richard Bronson & Gabriel Costa.
Classical Mechanics by R. Douglas Gregory.