Module Description
PHY1026 Mathematics for Physicists 2013-14
Dr A. Usher

Delivery Weeks: T2:01-11
Level: 4 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 145 students (approx)

### Description

This module aims to consolidate students' skills in foundation topics in mathematics, to introduce students to some of the mathematical techniques that are most frequently used in physics, and to give students experience in their use and application. Emphasis is placed on the use of mathematical techniques rather than their rigorous proof.

### Module Aims

This module pre-dates the current template; refer to the description above and the following ILO sections.

### Intended Learning Outcomes (ILOs)

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:
1. tackle, with facility, mathematically formed problems and their solution;
• Personal and Key Transferable / Employment Skills and Knowledge:
1. manage their time effectively in order to meet fortnightly deadlines for the completion of homework and develop appropriate coping strategies;
2. work co-operatively and use one another as a learning resource.

### Syllabus Plan

1. Complex Numbers
1. Argand diagram, modulus-argument form, exponential form, de Moivre's theorem
2. Trigonometric functions
3. Hyperbolic functions
2. Multi-Variable Calculus
1. Partial and total derivatives, the differential, reciprocal and reciprocity theorem, total derivatives of implicit functions, higher order partial derivatives
2. Line integrals and their application to finding arc lengths
3. Surface integrals and their application to finding surface areas
4. Evaluation of multiple integrals in different coordinate systems and using parametrisation
3. 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
4. Fourier series
5. 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

Description Study time KIS type
22×1-hour lectures 22 hours SLT
5×3-hour self-study packages 15 hours GIS
5×6-hour problems sets 30 hours GIS
Problems class support 11 hours SLT
Tutorial support 3 hours SLT
Reading, private study and revision 69 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% 5 × Problems Sets 6 hours per set Fortnightly 1-9 Marked in problems class, then discussed in tutorials
15% Mid-term Test 1 30 minutes Weeks T2:04 1-9 Marked, then discussed in tutorials
15% Mid-term Test 2 30 minutes Weeks T2:08 1-9 Marked, then discussed in tutorials
50% Final Examination 120 minutes May/June assessment period 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:

Supplementary texts:

ELE:

### Further Information

#### Prior Knowledge Requirements

Pre-requisite Modules Mathematics Skills (PHY1025) 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-03 Complex numbers. MT-05 Calculus to the level of multiple integrals. MT-06 Solution of linear ordinary differential equations. MT-08 Three-dimensional trigonometry. MT-09 [Vectors to the level of] div, grad and curl. MT-10 The divergence theorem and Stokes's theorem. MT-12 Fourier series and transforms including the convolution theorem. Availability unrestricted Distance learning NO Keywords Physics; Derrivatives; Differential equations; Functions; Integrals; Linear algebra; Operators; Theorems. Created 01-Oct-10 Revised 01-Oct-11