PHY2025 
Mathematics with Physical Applications 
201314 

Dr F.Y. Ogrin 


Delivery Weeks: 
T1:0111, T2:0111


Level: 
5 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
71 students (approx) 

Description
This module will enable the student to build on the knowledge and skills
developed in PHY1026 in order to achieve a deeper understanding of and
greater competence in some central mathematical ideas and techniques
used throughout physics. The emphasis is on practical skills rather than
formal proofs. Students will acquire skills in some key techniques that
relate directly to the advanced modules they will meet in the later
stages of their degree programme, but also have wide applicability
across the mathematical sciences.
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:
 use probability theory to solve problems;
 calculate Fourier transforms and use them to solve problems
 solve partial differential equations by separation of variables;
 calculate eignvalues and eigenvectors and apply the the techniques to physical problems;
 use basis vectors to transform differential operator
equations to matrix form and hence apply eigen equation techniques;
 obtain approximate solutions to differential
equations through the use of perturbation theory;

Discipline Specific Skills and Knowledge:
 apply analytical and numerical skills in mathematics;

Personal and Key Transferable / Employment Skills and Knowledge:
 formulate and tackle problems in a logical and systematic manner;
 present work clearly with justification of techniques and methods;
 work cooperatively with peers and with the demonstrators to solve guided problems.
Syllabus Plan

Probability theory
 Random variables
 Conditional probability
 Probability distributions
 Discrete
 Continuous

The Dirac deltafunction

Fourier transforms including the convolution theorem

Solution of linear partial differential equations
 Simple second order differential equations and common varieties:
Harmonic oscillator, Schrödinger equation, Poisson's equation,
wave equation and diffusion equation.
 Separation of variables: The Laplacian family of equations in physics,
separation of variables, mechanics of the technique, form of solutions,
general solutions in series form, relation to Fourier series,
spatial boundary conditions, time dependence, initial conditions.
 Examples: rectangular drum, classical and quantum harmonic oscillator,
waves at a boundary, temperature distributions, wavepacket/quantum
particle in a box
 Role of symmetry: Cylindrical and spherical polar coordinates, appearance of
special functions. Use of special functions by analogy to sin, cos, sinh, cosh etc.
 Examples: circular drum, hydrogen wave function

Linear Algebra
 Revision: Row and column vectors, matrices, matrix algebra, the
solutions of systems of linear equations.
 Eigenvalue equations I: The matrix equation Ax=ax, solving the
matrix equation, the secular determinant, eigenvalues and
eigenvectors, canonical form, normal modes/harmonics, simple
coupled oscillators.
 Eigenvalue equations II: Properties of eigenvectors:
orthogonality, degeneracy, as basis vectors.
 Eigenvalue equations III: Differential equations as eigenvalue
equations and the matrix representation Ax=ax; choosing the
basis, solving the equation, the secular determinant,
eigenvalues and eigenvectors.
 Examples: classical coupled modes, Schrödinger wave
equation
 Approximate solutions to differential equations (perturbation
theory): use of eigenvectors, first and secondorder through
repeated substitution, problem of degeneracies.
 Examples: quantum particle in a well, a mass on drum, coupled
particles
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
22×1hour lectures 
22 hours

SLT 
8×2hour selfstudy packages 
16 hours

GIS 
10×3hour problems sets 
30 hours

GIS 
Problems class support 
11 hours

SLT 
Tutorial support 
3 hours

SLT 
Reading, private study and revision 
68 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Exercises set by tutor 
6×30minute sets (typical) 
Scheduled by tutor 
110 
Discussion in tutorials

0% 
Guided selfstudy 
8×2hour packages 
Fortnightly 
110 
Discussion in tutorials

20% 
10 × Problems Sets 
3 hours per set 
Fortnightly 
110 
Marked in problems class, then discussed in tutorials

15% 
Midterm Test 1 
30 minutes 
Weeks T1:06 
19 
Marked, then discussed in tutorials

15% 
Midterm Test 2 
30 minutes 
Weeks T2:06 
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:

Constantinescu F. and Magyari E. (1971), Problems in Quantum Mechanics, Pergamon, ISBN 0080190081 (UL: 530.12 CON)

Greiner W. (1994), Quantum Mechanics: An Introduction (3^{rd} edition), SpringerVerlag, ISBN 3540580794 (UL: 530.12 GRE)

James G. (1993), Advanced modern engineering mathematics, AddisonWesley, ISBN 0201565196 (UL: 510.2462 JAM)

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

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 for Physicists (PHY1026) 
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 
 MT07 Solution of linear partial differential equations
 MT12 Fourier series and transforms including the convolution theorem.
 MT13 Probability distributions.

Availability 
unrestricted 
Distance learning 
NO 
Keywords 
Physics; Equation; Differentiation; Eigenvalue; Solution; Eigenvectors; Matrix; Probabilities; Wave; Variables; Differential equations. 
Created 
01Oct10 
Revised 
01Oct11 