PHY1026 
Mathematics for Physicists 
201314 

Dr A. Usher 


Delivery Weeks: 
T2:0111 

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 predates 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:
 calculate and manipulate partial and total derivatives of functions of more than one variable;
 evaluate single, double and triple integrals using commonly occurring coordinate systems;
 apply differential operators to vector functions;
 apply Stokes's and Gauss's theorems;
 solve simple firstorder differential equations and secondorder differential
equations with constant coefficients;
 calculate Fourier series and use them to solve simple problems;

Discipline Specific Skills and Knowledge:
 tackle, with facility, mathematically formed problems and their solution;

Personal and Key Transferable / Employment Skills and Knowledge:
 manage their time effectively in order to meet fortnightly deadlines for the completion of
homework and develop appropriate coping strategies;
 work cooperatively and use one another as a learning resource.
Syllabus Plan

Complex Numbers
 Argand diagram, modulusargument form, exponential form, de Moivre's theorem
 Trigonometric functions
 Hyperbolic functions

MultiVariable Calculus
 Partial and total derivatives, the differential, reciprocal and reciprocity theorem, total
derivatives of implicit functions, higher order partial derivatives
 Line integrals and their application to finding arc lengths
 Surface integrals and their application to finding surface areas
 Evaluation of multiple integrals in different coordinate systems
and using parametrisation

Vector Calculus
 The grad operator and its interpretation as a slope
 The divergence operator and its physical interpretation
 The divergence theorem
 The curl operator and its physical interpretation
 Stokes's theorem

Fourier series

Solution of linear ordinary differential equations
 Firstorder separable, homogeneous, exact and integratingfactor types
 Linear secondorder equations with constant coefficients; damped harmonic motion
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
22×1hour lectures 
22 hours

SLT 
5×3hour selfstudy packages 
15 hours

GIS 
5×6hour 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 
3×1hour sets (typical) 
Scheduled by tutor 
19 
Discussion in tutorials

0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
19 
Discussion in tutorials

20% 
5 × Problems Sets 
6 hours per set 
Fortnightly 
19 
Marked in problems class, then discussed in tutorials

15% 
Midterm Test 1 
30 minutes 
Weeks T2:04 
19 
Marked, then discussed in tutorials

15% 
Midterm Test 2 
30 minutes 
Weeks T2:08 
19 
Marked, then discussed in tutorials

50% 
Final Examination 
120 minutes 
May/June assessment period 
19 
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:
Supplementary texts:

Arfken G.B. and Weber H.J. (2001), Mathematical methods for physicists (5^{th} edition), Academic Press, ISBN 0120598264 (UL: 510 ARF)

Spiegel M.R. (1971), Advanced Mathematics for Engineers and Scientists, Schaum Outline Series, McGrawHill, ISBN 0070602166 (UL: 510 SPI)

Spiegel M.R. and Lipschutz S. (2009), Schaum's Outline of Vector Analysis (2^{nd} edition), McGrawHill, ISBN 9780071615457 (UL: 515.63)

Stroud K.A. (2007), Engineering Mathematics (6^{th} edition), Paulgrave, ISBN 1403942463 (UL: 510.2462 STR)
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
Mathematics Skills (PHY1025) 
Corequisite Modules 
none 
Reassessment
Reassessment is not available except when required by referral or deferral.
Original form of assessment 
Form of reassessment 
ILOs reassessed 
Time scale for reassessment 
Whole module 
Written examination (100%) 
19 
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 
 MT03 Complex numbers.
 MT05 Calculus to the level of multiple integrals.
 MT06 Solution of linear ordinary differential equations.
 MT08 Threedimensional trigonometry.
 MT09 [Vectors to the level of] div, grad and curl.
 MT10 The divergence theorem and Stokes's theorem.
 MT12 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 
01Oct10 
Revised 
01Oct11 