Description

This module introduces students to some of the mathematical techniques that are most frequently used in physics. Emphasis is placed on the use of mathematical techniques rather than their rigorous proof.

Module Aims

This module aims to consolidate students' skills in foundation topics in mathematics and to give students experience in their use and application.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. calculate and manipulate partial and total derivatives of functions of more than one variable;
  2. evaluate single, double and triple integrals using commonly occurring coordinate systems;
  3. apply differential operators to vector functions;
  4. apply Stokes's and Gauss's theorems;
  5. solve simple first-order differential equations and second-order differential equations with constant coefficients;
  6. calculate Fourier series and use them to solve simple problems;
• Discipline Specific Skills and Knowledge:
  7. tackle, with facility, mathematically formed problems and their solution;
• Personal and Key Transferable / Employment Skills and Knowledge:
  8. manage their time effectively in order to meet fortnightly deadlines for the completion of homework and develop appropriate coping strategies;
  9. work co-operatively and use one another as a learning resource.

Syllabus Plan

1. Multi-Variable Calculus
   1. Green's Theorem in the plane
   2. Surface integrals and their application to finding surface areas
   3. Evaluation of multiple integrals in different coordinate systems and using parameterisation
2. The Dirac delta-function
3. Vector Calculus
   1. The grad operator and its interpretation as a slope
   2. The divergence operator and its physical interpretation
   3. The divergence theorem
   4. The curl operator and its physical interpretation
   5. Stokes's theorem
4. Fourier series, Fourier transforms including the convolution theorem
5. Solution of linear ordinary differential equations
   1. First-order separable, homogeneous, exact and integrating-factor types
   2. Linear second-order equations with constant coefficients; damped harmonic motion

Learning and Teaching

Learning Activities and Teaching Methods

Assessment

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Stroud K.A. and Booth D.J. (2011), Advanced Engineering Mathematics (5^th edition), Paulgrave, ISBN 978-0-23-027548-5

Supplementary texts:

• K.F. Riley and Hobson M.P. (2011), Foundation Mathematics for the Physical Sciences, Cambridge University Press, ISBN 978-0-521-19273-6
• K.F. Riley and Hobson M.P. (2011), Essential Mathematical Methods for the Physical Sciences, Cambridge University Press, ISBN 978-0-521-76114-7
• Spiegel M.R. (1971), Advanced Mathematics for Engineers and Scientists, Schaum Outline Series, McGraw-Hill, ISBN 0-070-60216-6
• Spiegel M.R. and Lipschutz S. (2009), Schaum's Outline of Vector Analysis (2^nd edition), McGraw-Hill, ISBN 978-0-07-1615-45-7
• Stroud K.A. and Booth D.J. (2013), Engineering Mathematics (7^th edition), Paulgrave MacMillan, ISBN 978-1-137-03120-4

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phy1026

Further Information

Prior Knowledge Requirements

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Notes: See Physics Assessment Conventions.

KIS Data Summary

Miscellaneous