Mathematics 0D2

Requisites

Aims

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

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.

Assessment methods

• Other - 20%
• Written exam - 80%

Assessment Further Information

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

Mathematica Test (week 10 unless the project is submitted in week 10, in which case, the 0D2 coursework would be submitted in week 11.) Weighting within unit 10%

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

Syllabus

2: Numerical Interpolation: Linear Interpolation, Quadratic Interpolation.

1: Numerical Differentiation

2: Numerical Integration: The Trapezoidal Rule, Simpson's Rule.

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

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

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

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

5: Mathematica: General introduction, application to topics in syllabus.

Recommended reading

CROFT, A & DAVISON, R. 2010. Foundation Maths (5th ed.) Pearson Education, Harlow. (ISBN9780273730767)

BOSTOCK, L., & CHANDLER, S. 1981. Mathematics - the core course for A-level. Thornes, Cheltenham. (ISBN0859503062)

BOSTOCK, L., & CHANDLER, S. 1994. Core Maths for A-level (2nd ed.). Thornes, Cheltenham. (ISBN9780748717798)

STROUD, K.A, 2007. Engineering mathematics (6th ed.) Palgrave Macmillan, Baisingstoke. (ISBN9781403942463 / ISBN1403942463)

JAMES, G. 2001. Modern engineering mathematics (3rd ed.). Prentice Hall, Harlow. (ISBN0130183199 / ISBN9780130183194)

COOMBES, K. 1998. The Mathematica primer. Cambridge University Press, Cambridge. (ISBN0521631300 / ISBN0521637155  / ISBN9780521631303 / ISBN9780521637152)

Study hours

• Lectures - 24 hours
• Tutorials - 11 hours
• Independent study hours - 65 hours

Teaching staff

Simon Pearce - Unit coordinator