Mathematics Skills - 2024 entry
樱花动漫
| MODULE TITLE | Mathematics Skills | CREDIT VALUE | 15 |
|---|---|---|---|
| MODULE CODE | PHY1025 | MODULE CONVENER | Dr Peter Petrov (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 | 36 | Guided Independent Study | 114 | Placement / Study Abroad | 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 | 10 | Written Exams | 90 | Practical Exams | 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
Notes: See .
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
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 | Tuesday 12th March 2024 | LAST REVISION DATE | Tuesday 12th March 2024 |
| 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.