Term	Michaelmas Term 2008  (6 lectures)

Overview

These lectures are designed to give students a gentle introduction to applied mathematics in their first term at Oxford, allowing time for both students and tutors to work on developing and polishing the skills necessary for the course. It will have an `A-level' feel to it, helping in the transition from school to university. The emphasis will be on developing skills and familiarity with ideas using straightforward examples.

Background reading:

D. W. Jordan & P. Smith, Mathematical Techniques (OUP, 3rd Edition, 2003), Chapters 1–4, 14–17.

 

Learning outcomes

At the end of the course students will be able to solve a range of ODEs and linear systems of first order ODEs.

Synopsis

Standard integrals, integration by parts.
Definition of order of an ODE - example of separation of variables. General linear homogeneous ODEs: integrating factor for first order linear ODEs, second solution when one solution known for second order linear ODEs. First and second order linear ODEs with constant coefficients. General solution of linear inhomogeneous ODE as particular solution plus solution of homogeneous equation. Simple examples of finding particular integrals by guesswork.
(Jordan & Smith, Chapters 18, 19, 22; Kreyszig, Sections 1.1–1.3, 1.6, 2.1–2.3, 2.8.)

Systems of linear coupled first order ODEs. Calculation of determinants, eigenvalues and eigenvectors and their use in the solution of linear coupled first order ODEs.
(Kreyszig, Sections 3.0–3.3.)

Reading list

1. D.W. Jordan & P. Smith, Mathematical Techniques (OUP, 3rd Edition, 2003).
2. Erwin Kreyszig, Advanced Engineering Mathematics (Wiley, 8th Edition, 1999).

Taking our courses

This form is not to be used by students studying for a degree in the Department of Computer Science, or for Visiting Students who are registered for Computer Science courses

Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.