Students will be required to use MATLAB occasionally and should know how to set up vectors, perform mathematical operations on vectors, write simple programmes and plot functions. Demos will be given in examples classes throughout the term and examples given on handouts. Useful MATLAB resources and tutorials can be found on the web, including, HERE. An extensive range of MATLAB manuals are also available at the library.

MATLAB essentials

- Week 0: Classical PDEs (This gives an overview of some of the PDEs you will meet in the course)
- Week 1: Some useful diagrams that illustrate co-ordinate systems
- Week 2: Orthogonal Vectors
- Week 3: Fourier Series
- Week 5-6: Separation of Variables
- Week 7: Bessel functions
- Week 8: Centered Finite Differences for Reaction-Diffusion Equation
- Week 8: Finite Differences for Convection-Diffusion Equation
- Week 9: Explicit Finite Differences for 1D Heat Equation
- Week 10: Implicit Finite Differences for 1D Heat Equation
- Week 10: Vectors and Div,Grad,Curl
- Week 11: Line integrals

The material on solving differential equations via finite differences gives a first taste of numerical analysis. This is a branch of applied mathematics with many important applications in the real world. For more details, and a list of other courses on numerical analysis, see the Numerical Analysis undergraduate student pathway.

- Sheet 1: Introductory material and solutions
- Sheet 2: Orthogonality and solutions.
- Sheet 3: Fourier Series and solutions.
- Sheet 4: Partial Differential Equations and solutions.
- Sheet 5: Separation of Variables A and solutions.
- Sheet 6: Separation of Variables B and solutions.
- Sheet 7: Finite Difference Methods A and solutions.
- Sheet 8: Finite Difference Methods B and solutions.
- Sheet 9: Vectors and Multiple Integrals and solutions.
- Sheet 10: Vector calculus and solutions.

- fourierN_demo.m (illustrates convergence of a Fourier Series - example from Fourier Series notes)
- heateq_demo.m (plots the solution to the Heat Equation - example from Classical PDEs notes)
- trisolve.m
- reac_diff_1d.m
- conv_diff_1d.m
- heat_eq_explicit_fd.m

- James Stewart,
*Calculus, Early Transcendentals*, Thomson, fifth edition (international student edition), 2003.
- (Useful for the first part of the course and vector calculus.)
- R Haberman,
*Elementary Applied Partial Differential Equations with Fourier Series and Boundary Value Problems,*(Third edition) Prentice-Hall, 1998.
- (Useful for the section on Fourier Series and introduction to PDEs.)
- Morton, K.W., Mayers, D.F,
*Numerical solution of partial differential equations,*Cambridge University Press, 2005.
- (Useful for the section of finite difference methods and numerical analysis.)
- Schey, H. M.
*Div, Grad, Curl, and all that : an Informal Text on Vector Calculus*, New York : W. W. Norton, various editions.
- (Useful for the final few weeks of the course when we tackle vector calculus.)

Students who did not collect their scripts during the lectures and examples classes should now go to reception in the Alan Turing building.

Sample exam paper and solutions

Past papers are avaliable from the main School of Mathematics website . Solutions to these exam papers are not provided. Solutions to examples sheets and the sample exam will help you revise for the exam.

Tips and general advice on taking the 20411 exam