Module Identifier PH06020
Module Title INTRODUCTION TO MATHEMATICAL METHODS FOR PHYSICISTS I
Co-ordinator Mrs Glenda Roberts
Semester Semester 1
Pre-Requisite GCSE Mathematics or Equivalent
Co-Requisite None
Mutually Exclusive Not available to students doing 3 year BSc or 4 year MPhys
Course delivery Lecture   40 Hours. Lectures
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam3 Hours End of semester examinations  80%
Semester Assessment 2 Open book assignments  20%
Supplementary Exam3 Hours written examination100%

#### Learning outcomes

After taking this module the student should be able to:
• Use algebraic techniques confidently to solve physical and mathematical problems.
• Demonstrate a knowledge of trigonometrical functions and the relations between them.
• Demonstrate a knowledge of vectors and use them to solve simple problems.
• Demonstrate a knowledge of complex numbers and use them to solve simple problems.
• Demonstrate a knowledge of differentiation and the relation between dy/dx and the gradient of the curve y(x).

#### Brief description

This module introduces the student to some of the basic mathematical tools commonly used in the physical sciences. Topics covered include algabraic techniques, logarithms, trigonometry, an introduction to vectors, comples numbers and differentiation. Particular emphasis is placed on the use of mathematical techniques to solve physical problems.

#### Content

Number: Fractions, decimal system, different bases, indices and logarithms.

Algebraic techniques: linear and quadratic equations, factorisation, transposition of formulae, equations involving fractions, sumultaneous equations. Indicial, exponential and logarithmic equations.

Trigonometry: Sine and cosine rules. Graphs of trigonometrical functions. Trigonometric equations and identities including addition and double angle formulae.

Vectors: Vector representation, unit vectors, position vectors, vector components, vector addition, scalar product.

Complex Numbers: Introduction to complex numbers, multiplication and division in polar form, de Moivre's theorem, powers and roots of complex numbers.

Differentiation and its applications: Gradient of a curve, equation of a straight line, tangents and normals, rates of change, stationary values and turning points, curve sketching.

#### Transferable skills

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