Study information

# Mathematics Skills - 2023 entry

MODULE TITLE CREDIT VALUE Mathematics Skills 15 PHY1025 Dr Wolfram Möbius (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 0 0
 Number of Students Taking Module (anticipated) 149
DESCRIPTION - summary of the module content

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.

AIMS - intentions of the module

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 follow-up module PHY1026 Mathematics II will build.

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. Make efficient use of the techniques and concepts of foundation-level mathematics: algebra, trigonometry and calculus
2. Make series expansions of simple functions and determine their asymptotic behaviour
3. Perform basic arithmetic and algebra with complex numbers
4. Perform basic operations on matrices and solve systems of simultaneous linear equations
5. Evaluate single, double and triple integrals in straightforward cases
6. Evaluate partial derivatives

Discipline Specific Skills and Knowledge:
7. Tackle, with facility, mathematically formed problems and their solution

Personal and Key Transferable / Employment Skills and Knowledge:
8. Work co-operatively and use peer group as a learning resource
9. Develop appropriate time-management strategies and meet deadlines for completion of work

SYLLABUS PLAN - summary of the structure and academic content of the module
Foundation Mathematics (Preliminary Self-Study and Self-Evaluation Pack):
1. Algebra
2. Trigonometric functions Binomial theorem
3. Curve sketching

Matrices:
1. Matrix addition, subtraction, multiplication
2. Inversion of matrices
3. Applications to the solution of systems of homogeneous and inhomogeneous linear equations
4. Evaluating numerical determinants
5. Introduction to eigenvalues and eigenvectors

Calculus with a Single Variable:
1. Advanced methods of Differentiation
2. Advanced methods of Integration

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

Sequences, Series, Series Expansions, Limits and Convergence:
1. Sequences and their limits
2. Taylor and Maclaurin series
3. Expansions of standard functions

Complex Numbers:
1. Argand diagram, modulus-argument form, exponential form, de Moivre's theorem
2. Trigonometric functions
3. Hyperbolic functions

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 36 114 0
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 36 hours 9x4-hour problems sets Scheduled learning & teaching activities 11 hours Problems class support Scheduled learning & teaching activities 3 hours Tutorial support Guided independent study 63 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 Practical Exams 10 90 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
9 × Problems sets 20% 36 hours total (Weekly) 1-9 Marked before problems class, then discussed in tutorials
Mid-term test  20% 60 minutes (Week T1:07) 1-9 Marked, then discussed in tutorials
Final examination 60% 120 minutes (January) 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
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:

Reading list for this module:

Type Author Title Edition Publisher Year ISBN
Set Stroud, K.A Engineering Mathematics 7th Palgrave Macmillan 2013 978-1-137-03120-4
Extended Arfken, G.B. and H. J. Weber Mathematical Methods for Physicists 5th edition Academic Press 2001 0-120-59826-4
Extended Riley, K.F. Hobson, M.P., Bence, S.J. Mathematical Methods for Physics and Engineering 3rd Cambridge University Press 2006 978-0521679718
Extended Riley, K. F. and M. P. Hobson Foundation Mathematics for the Physical Sciences Cambridge University Press 2011 978-0-521-19273-6
Extended Spiegel, M.R. Advanced Mathematics for Engineers and Scientists (Schaum Outline Series) McGraw-Hill 1971 0-070-60216-6
Extended Stroud, K.A. and D. J. Booth Advanced Engineering Mathematics 5th edition Palgrave 2011 978-0-23-027548-5
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES None None
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 4 No Thursday 15th December 2011 Friday 2nd June 2023
KEY WORDS SEARCH Physics, Algebra, Calculus, Complex numbers, Differentiation, Equations, Functions, Integration, Matrices, Series

Please note that all modules are subject to change, please get in touch if you have any questions about this module.