PHY1025 
Mathematics Skills 
202223 

Dr W. Moebius 


Delivery Weeks: 
T1:0105,0712 

Level: 
4 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
149 students (approx) 

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 followup 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:
 make efficient use of the techniques and concepts of foundationlevel
mathematics: algebra, trigonometry and calculus;
 make series expansions of simple functions and determine
their asymptotic behaviour;
 perform basic arithmetic and algebra with complex numbers;
 perform basic operations on matrices and solve systems of
simultaneous linear equations;
 evaluate single, double and triple integrals in straightforward cases;
 evaluate partial derivatives;

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

Personal and Key Transferable / Employment Skills and Knowledge:
 work cooperatively and use peer group as a learning resource;
 develop appropriate timemanagement strategies and meet deadlines for completion of work.
Syllabus Plan

Foundation Mathematics (Preliminary SelfStudy and SelfEvaluation Pack)
 Algebra
 Trigonometric functions
 Trigonometry and the binomial theorem
 Methods of differentiation and integration
 Curve sketching

Matrices
 Matrix addition, subtraction, multiplication
 Inversion of matrices
 Applications to the solution of systems of homogeneous and inhomogeneous linear equations
 Evaluating numerical determinants
 Introduction to eigenvalues and eigenvectors

Calculus with a Single Variable
 Advanced methods of Differentiation
 Advanced methods of Integration

Calculus with Several Variables
 Partial differentiation, the differential, Reciprocal and Reciprocity Theorems, total derivatives of implicit functions, higher order partial derivatives
 Coordinate systems in 2 and 3dimensional geometries  Cartesian, planepolar, cylindrical and spherical polar coordinate systems
 Twodimensional and threedimensional integrals and their application to finding volumes and masses
 Line integrals: parametrisation; work as a line integral

Series Expansions, Limits and Convergence
 Taylor and Maclaurin series, expansions of standard functions

Complex Numbers
 Argand diagram, modulusargument form, exponential form, de Moivre's theorem
 Trigonometric functions
 Hyperbolic functions
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 
5×3hour problems sets 
15 hours

GIS 
3×5hour problems sets 
15 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

10% 
8 × Problems Sets 
30 hours total 
Weekly 
19 
Marked in problems class, then discussed in tutorials

15% 
Midterm Test 1 
30 minutes 
Weeks T1:04 
19 
Marked, then discussed in tutorials

15% 
Midterm Test 2 
30 minutes 
Weeks T1:09 
19 
Marked, then discussed in tutorials

60% 
Final Examination 
120 minutes 
January 
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)

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 9780521679718 (UL: eBook)

K.F. Riley and Hobson M.P. (2011), Foundation Mathematics for the Physical Sciences, Cambridge University Press, ISBN 9780521192736 (UL: 500 RIL)

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

Stroud K.A. and Booth D.J. (2011), Advanced Engineering Mathematics (5^{th} edition), Paulgrave, ISBN 9780230275485 (UL: 510.2462 STR)
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
none 
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 
10% 
Written exams 
90% 
Practical exams 
0% 
Total 
100% 

Miscellaneous
IoP Accreditation Checklist 
 MT01 Trigonometric functions.
 MT02 Hyperbolic functions.
 MT04 Series expansions, limits and convergence.
 MT11 Matrices to the level of eigenvalues and eigenvectors.

Availability 
unrestricted 
Distance learning 
NO 
Keywords 
Physics; Algebra; Calculus; Complex numbers; Differentiation; Equations; Functions; Integration; Matrices; Series. 
Created 
01Oct10 
Revised 
04Jan18 