PHY1025 - Module Description

MODULE TITLE	Mathematics Skills					CREDIT VALUE	15
MODULE CODE	PHY1025		MODULE CONVENER			Dr W. Moebius

DURATION	TERM	1	2	3	Number Students Taking Module (anticipated)		149
	WEEKS	T1:01-05,07-12

DESCRIPTION – summary of the module content (100 words)

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 – 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)

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:

make efficient use of the techniques and concepts of foundation-level mathematics: algebra, trigonometry and calculus;
make series expansions of simple functions and determine their asymptotic behaviour;
perform basic arithmetic and algebra with complex numbers;
perform basic operations on matrices and solve systems of simultaneous linear equations;
evaluate single, double and triple integrals in straightforward cases;
evaluate partial derivatives;

Discipline Specific Skills and Knowledge:

tackle, with facility, mathematically formed problems and their solution;

Personal and Key Transferable / Employment Skills and Knowledge:

work co-operatively and use peer group as a learning resource;
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
3. Trigonometry and the binomial theorem
4. Methods of differentiation and integration
5. 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
Series Expansions, Limits and Convergence
1. Taylor and Maclaurin series, 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 hours

Guided independent study

114 hours

Placement/study abroad

0 hours

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS