PHY1025 Mathematics Skills 2023-24
Dr W. Moebius

Delivery Weeks: T1:01-05,07-12
Level: 4 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 149 students (approx)

### Description

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.

### Module Aims

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)

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:
1. tackle, with facility, mathematically formed problems and their solution;
• Personal and Key Transferable / Employment Skills and Knowledge:
1. work co-operatively and use peer group as a learning resource;
2. develop appropriate time-management strategies and meet deadlines for completion of work.

### Syllabus Plan

1. 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
2. Matrices
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
3. Calculus with a Single Variable
4. 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
5. Series Expansions, Limits and Convergence
1. Taylor and Maclaurin series, expansions of standard functions
6. 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

Description Study time KIS type
22×1-hour lectures 22 hours SLT
5×3-hour self-study packages 15 hours GIS
9×4-hour problems sets 36 hours GIS
Problems class support 11 hours SLT
Tutorial support 3 hours SLT
Reading, private study and revision 63 hours GIS

#### Assessment

Weight Form Size When ILOS assessed Feedback
0% Exercises set by tutor 3×1-hour sets (typical) Scheduled by tutor 1-9 Discussion in tutorials
0% Guided self-study 5×6-hour packages Fortnightly 1-9 Discussion in tutorials
20% 9 × Problems Sets 36 hours total Weekly 1-9 Marked in problems class, then discussed in tutorials
20% Mid-term Test 60 minutes Weeks T1:07 1-9 Marked, then discussed in tutorials
60% Final Examination 120 minutes January 1-9 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:

• Stroud K.A. and Booth D.J. (2013), Engineering Mathematics (7th edition), Paulgrave MacMillan, ISBN 978-1-137-03120-4

Supplementary texts:

ELE:

### Further Information

#### Prior Knowledge Requirements

Pre-requisite Modules none none

#### Re-assessment

Re-assessment is not available except when 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

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 MT-01 Trigonometric functions. MT-02 Hyperbolic functions. MT-04 Series expansions, limits and convergence. MT-11 Matrices to the level of eigenvalues and eigenvectors. Availability unrestricted Distance learning NO Keywords Physics; Algebra; Calculus; Complex numbers; Differentiation; Equations; Functions; Integration; Matrices; Series. Created 01-Oct-10 Revised 04-Jan-18