20411 Online Resources (2014-2015)
Lecturer: Dr. Catherine Powell
Email: c_dot_powell_at_manchester_dot_ac_dot_uk
Office: 1.124, Alan Turing Building.
Office Hours: Monday 3-4, Tuesday 4-5.
At the above times, I am guaranteed to be in my office. Students may see me at those times to discuss MATH20411 without an appointment. If you want to meet me at another time, send me an email to arrange it.
Syllabus
The course syllabus is available from the School of Mathematics web site.
Lectures and Examples Classes
Lectures will take place on Monday at 12:00 (Zochonis, Theatre A) and Tuesday at 17:00 (Simon Building, Theatre C). Students are allocated ONE examples class that will take place in the Alan Turing building (G.207) on either Monday at 13:00 or Tuesday at 12:00. It is important that you attend the examples class that you are allocated.
Online Lecture Notes
Students are required to take their own notes in the lectures. Additional material in the form of handouts that students are expected to read between lectures will be made available online below. I will usually also give out paper copies of these at the end of lectures.
- Week 0: Classical PDEs (This gives an overview of some of the PDEs you will meet in the course)
- 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 (revision)
Summaries of lecture notes will be provided online for revision, but only after a topic has been fully covered in the lectures.
- Section 1: Introductary Material
- Section 2: Fourier Series
- Section 3: Introduction to PDEs
- Section 4: Separation of Variables
- Section 5: Finite Difference Methods
- Section 6: Vector Calculus
Numerical Analysis
The material in Section 5 on finite difference methods will give students their first taste of numerical analysis. This is a branch of applied mathematics with many important practical applications in the real world. For more details, and a list of other numerical analysis courses, see the Numerical Analysis undergraduate student pathway.
Example Sheets
On average, there is one example sheet per week. However, questions are grouped according to topics. Therefore, the numbering of the examples sheets will not necessarily correspond to the week number. This is no reason to panic (or complain). Below, I will indicate which questions you should attempt in which weeks.
Some sheets will certainly have more questions than you will be able to do in one week, but these can be used for revision later. Example classes start in week 2. There will be many students in the examples class, so you will get the most benefit out if the class of 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.
- Sheet 1: Introductory material (Attempt as much as possible before the week 2 class)
- Sheet 2: Orthogonality
- Sheet 3: Fourier Series
- Sheet 4: Partial Differential Equations
- Sheet 5: Separation of Variables A
- Sheet 6: Separation of Variables B
- Sheet 7: Finite Difference Methods A
- Sheet 8: Finite Difference Methods B
- Sheet 9: Vectors and Multiple Integrals
- Sheet 10: Vector Calculus
MATLAB
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.
A useful summary of basic commands is given here: MATLAB essentials
For certain lectures (e.g. the ones 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.
Textbooks
You do not need to buy any textbooks for this course . We will study several basic topics in calculus and applied mathematics, which are covered in hundreds of available texts in the library. 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 sections 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).
Coursework
The coursework component of the course (worth 20%) will take the form on an in-class test in Reading Week .
Exam Revision Resources
Past papers are avaliable from the main School of Mathematics website . Apart from the sample paper, solutions to exam papers are not provided. Solutions to examples sheets and the sample exam will help you revise.
The following documents provide feedback on general performance on past exam papers and common mistakes.