PHY1026 Mathematics for Physicists

2010-2011

Code: PHY1026
Level: 1
Title: Mathematics for Physicists
Instructors: Dr A. Usher
CATS Credit Value: 15
ECTS Credit Value: 7.5
Pre-requisites: N/A
Co-requisites: N/A
Duration: L1-L11
Availability: unrestricted
Background Assumed: -

Total Student Study Time

150 hours, to include: 22×1-hour lectures; 45 hours directed self-study; 11 hours of problems class support; 3 hours of tutorial support; 69 hours private study.

Aims

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.

Intended Learning Outcomes

Students will be able to:

1. Module Specific Skills:
   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;
2. Discipline Specific Skills:
   1. tackle, with facility, mathematically formed problems and their solution.
3. Personal Transferable Skills:
   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.

Learning / Teaching Methods

Lectures, e-Learning resources (ELE PHY1026), and problems classes.

Assessment and Assignments

Contribution	Assessment/Assignment	Size (duration/length)	When
20%	Problem Sets	5×6-hour sets	Fortnightly
15%	Mid-term Test 1	30 minutes	Week L4
15%	Mid-term Test 2	30 minutes	Week L8
50%	Final examination	120 minutes	Term 3
Formative	Guided self-study	5×3-hour packages	Fortnightly

Syllabus Plan and Content

1. Complex Numbers
   1. Argand diagram, modulus-argument form, exponential form, de Moivre's theorem
   2. Trigonometric functions
   3. Hyperbolic functions
2. Three-dimensional trigonometry
   1. Coordinate Systems in 2- and 3-Dimensional Geometries - Cartesian, plane-polar, cylindrical and spherical polar coordinate systems
3. 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
4. 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
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

Core Text

Stroud K.A. and Booth D.J. (2003), Advanced Engineering Mathematics (4^th edition), Paulgrave, ISBN 1-4039-0312-3 (UL: 510.2462 STR)

Supplementary Text(s)

Arfken G.B. and Weber H.J. (2001), Mathematical methods for physicists (5^th edition), Academic Press, ISBN 0-120-59826-4 (UL: 510 ARF)
Spiegel M.R. (1971), Advanced Mathematics for Engineers and Scientists, Schaum Outline Series, McGraw-Hill, ISBN 0-070-60216-6 (UL: 510 SPI)
Stroud K.A. (2007), Engineering Mathematics (6^th edition), Paulgrave, ISBN 1-4039-4246-3 (UL: 510.2462 STR)

IOP Accreditation Compliance 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.

Formative Mechanisms

Students monitor their own progress by attempting the problems set which will be discussed in class. Students who need additional guidance are encouraged to discuss the matter with the lecturer.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.