MATH20411 Online Course Materials
Lecturer: Dr. C. Powell
Office: 1.124, Alan Turing Building.
Office Hours: Monday, 4-5pm, Tuesday, 4-5pm.
Lectures: Monday, 5pm Schuster Building, Rutherford Lecture Theatre. Tuesday, 5pm Chemistry Building, G.51.
Example Classes: Students are allocated ONE of the following classes: Monday 1pm or Tuesday 12pm, Alan Turing G.209.
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.
Lecture NotesStudents are required to take notes in the lectures. Supplementary lecture notes are available below. I will usually give out paper copies of these in lectures.
Online Lecture Notes
- Classical PDEs
- Orthogonal Vectors
- Fourier Series
- Separation of Variables
- Bessel functions
- Centered Finite Differences for Reaction-Diffusion Equation
- Finite Differences for Convection-Diffusion Equation
- Explicit Finite Differences for 1D Heat Equation
- Implicit Finite Differences for 1D Heat Equation
- Vectors and Div,Grad,Curl
- Line integrals
Example SheetsOn average, there is one example sheet per week. Some sheets have more questions than you will be able to do in one week but can be used for revision later. Example classes start in week 2, so you should aim to have done most of sheet 1 for week 2. You will get the most out of the example classes if you try the questions beforehand. You can then ask questions about the problems you are unable to do. You should attend ONE example class per week (not both).
Solutions will be posted here a short while after the corresponding examples classes have taken place.
Please do not email to ask for solutions!
- 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 (Revision sheet) and solutions
- Sheet 10: Vector calculus and solutions
For the lectures on finite difference methods (in weeks 9 and 10) students will need the following MATLAB codes. Download the files and save to your P-drive. Open them in the MATLAB editor and read the instructions. Students should try and reproduce the examples from the handouts on this topic using these codes and attempt all of the questions on examples sheets 7 and 8.
TextbooksYou do not need to buy any textbooks for this course. We cover several topics in calculus and applied mathematics. However, the following books all contain some material you will meet in the course.
- 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.)
CourseworkUnclaimed coursework can be collected from reception in the Alan Turing building.
Past papers are avaliable from main School of Math website. Note that this course began in 2006. Solutions to these exam papers are not provided. Solutions to examples sheets will help you revise for the exam.