0D2

 

Unit specification

Aims

The programme unit aims to provide a basic course in various mathematical topics to students in Foundation Year.

Brief description

3-4 : Polar Coordinates : Polar coordinates of points. Polar coordinates of lines and curves. Points of intersection of polar curves

2 : Numerical Interpolation : Linear Interpolation, Quadratic Interpolation.

3 : Numerical Solution of Equations : Bisection Method, Rule of False Position, Newton-Raphson method

3 : Areas, lengths and volums : Area inside a polar Curve, Volume of Solid of Revolution, Arc Length, Surface Area of Solid of Revolution

1 : Numerical Differentiation

2-3 : Numerical Integration : The Trapezoidal Rule, Simpson's Rule. Inspired in part by integrals for arc length and surface areas of solids of revolution.

3 : Recurrence Relations and Reduction Formulae : Recurrance relatons, Reduction formulae [f(x)]^n with limits, reduction formulae x^n * f(x) with limits, reduction formulae without limits.

4 : Mathematica : General introduction, solution of equations, numerical integration.

Textbooks

A Croft et. al., Foundation Maths, Pearson Education

Bostock and Chandler, Mathematics, The core course for A-level, Stanley Thornes

Bostock and Chandler, Core Mathematics for A-level, Stanley Thornes

KA Stroud, Engineering Mathematics, Palgrave

G James et. al., Modern Engineering Mathematics, Pearson

KR Coombes et. al., The Mathematica Primer, Cambridge University Press

Intended learning outcomes

Knowledge and understanding: Be familiar with reduction formulae, numerical methods, polar coordinates and geometrical applications of integration.

Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.

Practical Skills: Be able to use the package Mathematica.

Transferable skills and personal qualities: Have a set of tools and methods that can be applied in the courses given in the host department or in subsequent years.

Learning and teaching processes

Two lectures per week. One tutorial (in small groups) in weeks 2-5 and 7-12.

Lectures : 22

Tutorials : 10

Hours of private study : 68

Assessment

Coursework (Computerised Assignment) (week 7) Weighting within unit 10%

Mathematica Test (week 12) Weighting within unit 10%

2 hour examination (semester 1) Weighting within unit 80%

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Arrangements

This is a second semester course with two lectures and one tutorial per week.

The lectures for course 0D2 (MATH19872) for 2012-13 are as follows

• Lecture : Monday 11 am in Renold/C2
• Lecture : Tuesday 3 pm in Renold/C2
• Lectures given by Dr Jack Williams
• Tutorial time Tuesday 2 pm

Several lectures will take place in computer clusters and will concern the computer programme mathematica.

Several lectures will take place in computer clusters and will concern the computer programme mathematica.