Study information

Mathematics Skills - 2022 entry

MODULE TITLEMathematics Skills CREDIT VALUE15
MODULE CODEPHY1025 MODULE CONVENERDr Wolfram Möbius (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
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. 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
I. Foundation Mathematics (Preliminary Self-Study and Self-Evaluation Pack)
  1. Algebra
  2. Trigonometric functions
  3. Trigonometry and the binomial theorem
  4. Methods of differentiation and integration
  5. Curve sketching
II. 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
III. Calculus with a Single Variable
  1. Advanced methods of Differentiation
  2. Advanced methods of Integration
IV. 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
V. Series Expansions, Limits and Convergence
  1. Taylor and Maclaurin series, expansions of standard functions
VI. 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 36 Guided Independent Study 114 Placement / Study Abroad
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 15 hours 5×3-hour problems sets
Guided independent study 15 hours 3×5-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 10 Written Exams 90 Practical Exams
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
8 × Problems Sets 10% 30 hours total (scheduled weekly) 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 9) 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
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:
 

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 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) 4 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Thursday 15th December 2011 LAST REVISION DATE Wednesday 26th January 2022
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.