Study information

Mathematics for Physicists - 2023 entry

MODULE TITLE CREDIT VALUE Mathematics for Physicists 15 PHY1026 Unknown
DURATION: TERM 1 2 3
DURATION: WEEKS 11
DESCRIPTION - summary of the module content
This module introduces students to some of the mathematical techniques that are most frequently used in physics. Emphasis is placed on the use of mathematical techniques rather than their rigorous proof.

AIMS - intentions of the module

This module aims to consolidate students' skills in foundation topics in mathematics and to give students experience in their use and application.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
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 - summary of the structure and academic content of the module
I. Multi-Variable Calculus
1. Green's Theorem in the plane
2. Surface integrals and their application to finding surface areas
3. Evaluation of multiple integrals in different coordinate systems and using parameterisation
II. The Dirac delta-function

III. 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
IV. Fourier series, Fourier transforms including the convolution theorem

V. 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 (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 36 114
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning & teaching activities 22 hours 22×1-hour lectures Guided independent study 15 hours 5×3-hour self-study packages Guided independent study 30 hours 5×6-hour problems sets Scheduled learning & teaching activities 11 hours Problems class support Scheduled learning & teaching activities 3 hours Tutorial support Guided independent study 69 hours Reading, private study and revision

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Exercises set by tutor (0%) 3×1-hour sets (typical) (Scheduled by tutor) 1-9 Discussion in tutorials
Guided self-study (0%) 5×6-hour packages (Fortnightly) 1-9 Discussion in tutorials

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 10 90
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
5 × Problems Sets 10% 6 hours per set (Fortnightly) 1-9 Marked in problems class, then discussed in tutorials
Mid-term Test 1 15% 30 minutes (Week 4) 1-9 Marked, then discussed in tutorials
Mid-term Test 2 15% 30 minutes (Week 8) 1-9 Marked, then discussed in tutorials
Final Examination 60% 120 minutes (May/June assessment period) 1-9 Mark via MyExeter, collective feedback via ELE and solutions

DETAILS OF RE-ASSESSMENT (where 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

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

RE-ASSESSMENT NOTES
An original assessment that is based on both examination and coursework, tests, etc., is considered as a single element for the purpose of referral; i.e., the referred mark is based on the referred examination only, discounting all previous marks. In the event that the mark for a referred assessment is lower than that of the original assessment, the original higher mark will be retained.

Physics Modules with PHY Codes
Referred examinations will only be available in PHY3064, PHYM004 and those other modules for which the original assessment includes an examination component - this information is given in individual module descriptors.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
ELE:

Type Author Title Edition Publisher Year ISBN
Set Stroud, K.A. and D. J. Booth Advanced Engineering Mathematics 5th edition Palgrave 2011 978-0-23-027548-5
Extended Riley, K. F. and M. P. Hobson Foundation Mathematics for the Physical Sciences Cambridge University Press 2011 978-0-521-19273-6
Extended Riley, K. F. and M. P. Hobson Essential Mathematical Methods for the Physical Science Cambridge University Press 2011 978-0-521-76114-7
Extended Spiegel, M.R. Advanced Mathematics for Engineers and Scientists (Schaum Outline Series) McGraw-Hill 1971 0-070-60216-6
Extended Spiegel, M.R. and S. Lipschutz Schaum's Outline of Vector Analysis 2nd edition McGraw-Hill 2009 978-0-07-1615-45-
Extended Stroud, K.A Engineering Mathematics 7th Palgrave Macmillan 2013 978-1-137-03120-4
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES PHY1025
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 4 No Thursday 15th December 2011 Thursday 26th January 2023
KEY WORDS SEARCH Physics; Derrivatives; Differential equations; Functions; Integrals; Linear algebra; Operators; Theorems.