MA100 Mathematical Methods

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Course Information for 2009/10

Timetable

Lectures: Tuesday 14.00 and Friday 11.00 in the Peacock Theatre.

Classes: Each student will have one class a week, which will be timetabled towards the end of Week 2.
The classes will begin in Week 3 with Exercise Set 2.

Extra Examples Sessions: These are extra classes designed to reinforce the material covered in the lectures and are entirely optional. There will be no new material presented in these classes. The classes will be held each week:
Thursdays 11.00 - 12.00 in the Old Theatre.

Study Pack

A Study Pack which includes Lecture Notes for the year, all Exercise Sets, the instructions for the Exercise 4 class in Week 5, and past exam papers with solutions will be available at the start of term.

This is a hard copy of some material which will be available on the course Moodle page| on a weekly basis.

The lectures will broadly follow the lecture notes. They will enable you to listen to lectures without having to take down every word; but you will still need to take some notes.

You will be able to purchase the study pack at 13.45 on Tuesday 6th October in the lobby of the Peacock Theatre (just before your first MA100 lecture). The cost, to cover printing, is £4.00 (this is significantly less than printing all the material out from the web). Please have the correct change!

If you don't manage to get a copy, you can buy one from the Maths Dept Office, B401 (4th floor of Columbia House), from 10.30 - 11.30 Monday to Friday.

Course Texts

K. G. Binmore and J. Davies, Calculus, Concepts and Methods;
H. Anton, Elementary Linear Algebra.

It is recommended that you purchase the course texts.

The texts listed below are for reference, and can be found in the library course collection, or on the shelves. (The library references are: \ Calculus QA303, Linear Algebra QA184.)

Reference Texts

D. Lay, Linear Algebra and its Applications
R. Beezer, http://linear.ups.edu/| - this is a (free) online linear algebra text. Download the PDF version to read on-screen. (There's no need to print it out - it can be navigated easily on computer).
L. Johnson, R. Riess and J. Arnold, Introduction to Linear Algebra
G. Strang, Linear Algebra and its Applications
S. L. Salas and E. Hille, Calculus, One and Several Variables
R. Larson and R. Hostetle, Calculus
M. Anthony, N. Biggs, Mathematics for Economics and Finance
Schaum Outline Series: Mathematics for Economists, Linear Algebra, Advanced Calculus, Differential and Integral Calculus.

Teaching Arrangements

There is one calculus lecture (Tuesday) and one algebra lecture (Friday) each week.

There is one set of Exercises for each week.
Solutions of the starred exercises are to be handed in to the class teacher at the end of the following week's class for correction. The classes will be used to discuss the exercises, and students should feel free to bring up any problems arising from the course material. Complete solutions to the exercise sets will be put on the course Moodle page after they have been discussed in the classes.

The mathematics computer program Maple will be used throughout the course to illustrate the material where applicable. Work through the Maple Tutorial| as soon as possible. Classes during week 5 (only) will be held in one of the computer rooms (the room will be listed on your class assignment), where you will use Maple to work parts of Exercise Set 4.

Course description of MA100

Overview

What is this course? This is an introductory level course for those who wish to use mathematics seriously in social science, or in any other context. A range of basic skills and techniques in calculus of one and several variables and in linear algebra are covered and some applications illustrated. The `how to do it' aspects are stressed, rather than their theoretical basis. Hence, the exercises are an important feature of the course. Formal proofs are not attempted; instead, the approach is intuitive using informal arguments to provide the rationale behind the methods. The techniques studied are analytical and not numerical. There is an emphasis in the calculus on graphical visualisation, using the computer software Maple to generate graphs in both two and three dimensions. These provide visual explanation with a view to enhance understanding and develop intuition.

The course is designed to:
provide students with a range of techniques in linear algebra and calculus and to enable them to understand the rationale behind them. provide a foundation in mathematics for students who anticipate taking any mathematically oriented economics options or many further mathematics courses.

After having followed this course, students should:
have the ability to use matrices in solving systems of linear equations, to understand the underlying principle of linearity, to apply matrix diagonalization to the solution of systems of differential and difference equations, and to understand the concept of a vector and use it in studying functions of several variables and interpreting solutions of systems of equations, the ability to optimise functions of one and several variables, to visualise functions, and to solve differential and difference equations.

Course Content of MA100

1. The concept of vectors. Lines and planes in Euclidean spaces.
2. Scalar-valued functions: One-variable and two-variable functions, and functions of several variables.
3. Unconstrained and constrained optimisation of scalar-valued functions, Lagrange multipliers.
4. Vector-valued functions.
5. Techniques of integration of functions.
6. Differential and difference equations.

Applications of the above topics.