PHY1026	Mathematics for Physicists	2013-14
	Dr A. Usher
Delivery Weeks:	T2:01-11
Level:	4 (NQF)
Credits:	15 NICATS / 7.5 ECTS
Enrolment:	145 students (approx)

Description

This module aims to consolidate students' skills in foundation topics in mathematics, to introduce students to some of the mathematical techniques that are most frequently used in physics, and to give students experience in their use and application. Emphasis is placed on the use of mathematical techniques rather than their rigorous proof.

Module Aims

This module pre-dates the current template; refer to the description above and the following ILO sections.

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. Complex Numbers
   1. Argand diagram, modulus-argument form, exponential form, de Moivre's theorem
   2. Trigonometric functions
   3. Hyperbolic functions
2. Multi-Variable Calculus
   1. Partial and total derivatives, the differential, reciprocal and reciprocity theorem, total derivatives of implicit functions, higher order partial derivatives
   2. Line integrals and their application to finding arc lengths
   3. Surface integrals and their application to finding surface areas
   4. Evaluation of multiple integrals in different coordinate systems and using parametrisation
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
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

Description	Study time	KIS type
22×1-hour lectures	22 hours	SLT
5×3-hour self-study packages	15 hours	GIS
5×6-hour problems sets	30 hours	GIS
Problems class support	11 hours	SLT
Tutorial support	3 hours	SLT
Reading, private study and revision	69 hours	GIS

Assessment

Weight	Form	Size	When	ILOS assessed	Feedback
0%	Exercises set by tutor	3×1-hour sets (typical)	Scheduled by tutor	1-9	Discussion in tutorials
0%	Guided self-study	5×6-hour packages	Fortnightly	1-9	Discussion in tutorials
20%	5 × Problems Sets	6 hours per set	Fortnightly	1-9	Marked in problems class, then discussed in tutorials
15%	Mid-term Test 1	30 minutes	Weeks T2:04	1-9	Marked, then discussed in tutorials
15%	Mid-term Test 2	30 minutes	Weeks T2:08	1-9	Marked, then discussed in tutorials
50%	Final Examination	120 minutes	May/June assessment period	1-9	Mark via MyExeter, collective feedback via ELE and solutions.

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 (UL: 510.2462 STR)

Supplementary texts:

• Arfken G.B. and Weber H.J. (2001), Mathematical methods for physicists (5^th edition), Academic Press, ISBN 0-120-59826-4 (UL: 510 ARF)
• Spiegel M.R. (1971), Advanced Mathematics for Engineers and Scientists, Schaum Outline Series, McGraw-Hill, ISBN 0-070-60216-6 (UL: 510 SPI)
• 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 (UL: 515.63)
• Stroud K.A. (2007), Engineering Mathematics (6^th edition), Paulgrave, ISBN 1-4039-4246-3 (UL: 510.2462 STR)

ELE:

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

Further Information

Prior Knowledge Requirements

Pre-requisite Modules	Mathematics Skills (PHY1025)
Co-requisite Modules	none

Re-assessment

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

Original form of assessment	Form of re-assessment	ILOs re-assessed	Time scale for re-assessment
Whole module	Written examination (100%)	1-9	August/September assessment period

Notes: See Physics Assessment Conventions.

KIS Data Summary

Learning activities and teaching methods SLT - scheduled learning & teaching activities 36 hrs GIS - guided independent study 114 hrs PLS - placement/study abroad 0 hrs Total 150 hrs

Summative assessment Coursework 20% Written exams 80% Practical exams 0% Total 100%

Miscellaneous

IoP Accreditation Checklist	MT-03 Complex numbers. MT-05 Calculus to the level of multiple integrals. MT-06 Solution of linear ordinary differential equations. MT-08 Three-dimensional trigonometry. MT-09 [Vectors to the level of] div, grad and curl. MT-10 The divergence theorem and Stokes's theorem. MT-12 Fourier series and transforms including the convolution theorem.
Availability	unrestricted
Distance learning	NO
Keywords	Physics; Derrivatives; Differential equations; Functions; Integrals; Linear algebra; Operators; Theorems.
Created	01-Oct-10
Revised	01-Oct-11