PHY1025 Mathematics Skills

2011-2012

Code: PHY1025
Level: 1
Title: Mathematics Skills
Instructors: Dr P.G. Petrov
CATS Credit Value: 15
ECTS Credit Value: 7.5
Pre-requisites: N/A
Co-requisites: N/A
Duration: T1:01-11
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

All physicists must possess a sound grasp of mathematical methods and a good level of 'fluency' in their application. This module covers areas such as differential calculus, complex numbers, and matrices that have wide applicability throughout physics. It provides a firm foundation on which the follow-up module PHY1026 will build, and emphasises problem solving with examples taken from physical sciences.

Intended Learning Outcomes

Students will be able to:

1. Module Specific Skills:
   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.
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 PHY1025), 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 T1:04
15%	Mid-term Test 2	30 minutes	Week T1:08
50%	Final examination	120 minutes	Week T2:00
Formative	Guided self-study	5×3-hour packages	Fortnightly

Syllabus Plan and Content

1. Foundation Mathematics (Self-Study Pack)
   1. Algebra
   2. Trigonometric functions
   3. Trigonometry and the binomial theorem
2. 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
3. Calculus with a Single Variable
   1. Differentiation
   2. Integration I
   3. Integration II
4. Calculus with Several Variables
   1. Partial differentiation
   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
5. Series Expansions, Limits and Convergence
   1. Taylor and Maclaurin series, expansions of standard functions
6. Curve Sketching

Core Text

Stroud K.A. (2007), Engineering Mathematics (6^th edition), Paulgrave, ISBN 1-4039-4246-3 (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. and Booth D.J. (2003), Advanced Engineering Mathematics (4^th edition), Paulgrave, ISBN 1-4039-0312-3 (UL: 510.2462 STR)

IOP Accreditation Compliance 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.

Formative Mechanisms

Students monitor their own progress by attempting the problem sets which will be discussed in classes. Students who need additional guidance are encouraged to discuss the matter with the lecturer or their tutor.

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.