Module Identifier PH06520 Module Title INTRODUCTION TO MATHEMATICAL METHODS FOR PHYSICISTS II Academic Year 2001/2002 Co-ordinator Coleg Ceredigion Staff Semester Semester 2 Other staff Coleg Ceredigion Staff Pre-Requisite GCSE Maths or equivalent Co-Requisite PH06020 Mutually Exclusive Not available to 3 year BSc or 4 year MPhys Assessment Course work 2 Open book assignments 20% Exam 3 Hours end of semester exam 80%

#### Module description

This second module on theoretical methods introduces the student to some more of the basic mathematical tools commonly used in the physical sciences, and develops some of the topics used in the first module. Topics covered include differentiation techniques and applications, integration and some of its applications to physics and rate of change problems, sequences, series and matrices. Particular emphasis is placed on the use of matematical techniques to solve physical problems.

#### Learning outcomes

After taking this module students should be able to:
• Use and apply integration and differentiation with some notion of the relevance of these topics to physics.
• Solve problems on arithmetic and geometric progressions and the Binomial theorem.
• Carry out simple processes using matrices and determinants.

The teaching of this module incorporates a large element of self-paced problem solving for both individual and tutorial work. This is essential to consolidate students understanding of the subject matter of the module.

All sessions are compulsory.

#### Outline syllabus

Differentiation techniques: Standard derivatives, function of a function, products and quotients, logarithmic differentiation, differentiation of implicit and parametric functions.

Applications of differentiation: Small increments and rate of change problems.

Integration techniques: Indefinite integration, integration as summation, definite integration, standard integrals, integration by substitution and by parts.

Applications of Integration: Area under curves, volumes of revolution, lengths of arcs.

Sequences and series: Arithmetic and geometric progressions. Binomial theorem.

Introduction to matrices and determinants.