Description

This module covers areas such as differential calculus, complex numbers, and matrices that have wide applicability throughout physics. It emphasises problem solving with examples taken from physical sciences.

Module Aims

All physicists must possess a sound grasp of mathematical methods and a good level of 'fluency' in their application. The aim of this module is to provide a firm foundation on which the follow-up module PHY1026 Mathematics II will build.

Intended Learning Outcomes (ILOs)

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

• Module Specific Skills and Knowledge:
  1. make efficient use of the techniques and concepts of foundation-level mathematics: algebra, trigonometry and calculus;
  2. make series expansions of simple functions and determine their asymptotic behaviour;
  3. perform basic arithmetic and algebra with complex numbers;
  4. perform basic operations on matrices and solve systems of simultaneous linear equations;
  5. evaluate single, double and triple integrals in straightforward cases;
  6. evaluate partial derivatives;
• Discipline Specific Skills and Knowledge:
  7. tackle, with facility, mathematically formed problems and their solution;
• Personal and Key Transferable / Employment Skills and Knowledge:
  8. work co-operatively and use peer group as a learning resource;
  9. develop appropriate time-management strategies and meet deadlines for completion of work.

Syllabus Plan

1. Foundation Mathematics (Preliminary Self-Study and Self-Evaluation Pack)
   1. Algebra
   2. Trigonometric functions
   3. Trigonometry and the binomial theorem
   4. Methods of differentiation and integration
   5. Curve sketching
2. Matrices
   1. Matrix addition, subtraction, multiplication
   2. Inversion of matrices
   3. Applications to the solution of systems of homogeneous and inhomogeneous linear equations
   4. Evaluating numerical determinants
   5. Introduction to eigenvalues and eigenvectors
3. Calculus with a Single Variable
   1. Advanced methods of Differentiation
   2. Advanced methods of Integration
4. Calculus with Several Variables
   1. Partial differentiation, the differential, Reciprocal and Reciprocity Theorems, total derivatives of implicit functions, higher order partial derivatives
   2. Coordinate systems in 2- and 3-dimensional geometries - Cartesian, plane-polar, cylindrical and spherical polar coordinate systems
   3. Two-dimensional and three-dimensional integrals and their application to finding volumes and masses
   4. Line integrals: parametrisation; work as a line integral
5. Series Expansions, Limits and Convergence
   1. Taylor and Maclaurin series, expansions of standard functions
6. Complex Numbers
   1. Argand diagram, modulus-argument form, exponential form, de Moivre's theorem
   2. Trigonometric functions
   3. Hyperbolic functions

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. (2013), Engineering Mathematics (7^th edition), Paulgrave MacMillan, ISBN 978-1-137-03120-4

Supplementary texts:

• Arfken G.B. and Weber H.J. (2001), Mathematical methods for physicists (5^th edition), Academic Press, ISBN 0-120-59826-4
• K.F. Riley, Hobson M.P. and Bence S.J. (2006), Mathematical Methods for Physics and Engineering: A Comprehensive Guide (3^rd edition), Cambridge University Press, ISBN 978-0521679718
• K.F. Riley and Hobson M.P. (2011), Foundation Mathematics for the Physical Sciences, Cambridge University Press, ISBN 978-0-521-19273-6
• Spiegel M.R. (1971), Advanced Mathematics for Engineers and Scientists, Schaum Outline Series, McGraw-Hill, ISBN 0-070-60216-6
• Stroud K.A. and Booth D.J. (2011), Advanced Engineering Mathematics (5^th edition), Paulgrave, ISBN 978-0-23-027548-5

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phy1025

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