# Gwybodaeth Modiwlau

Module Identifier
PH06020
Module Title
Introduction to Mathematical Methods for Physicists 1
2020/2021
Co-ordinator
Semester
Semester 1
Co-Requisite
None
Mutually Exclusive
Not available to students doing 3 year BSc or 4 year MPhys
Pre-Requisite
GCSE Mathematics or Equivalent
Other Staff

#### Assessment

Due to Covid-19 students should refer to the module Blackboard pages for assessment details

Assessment Type Assessment length / details Proportion
Semester Exam 3 Hours   End of semester examinations  70%
Semester Assessment Weekly course work  30%
Supplementary Exam 3 Hours   Written examination.  100%

### Learning Outcomes

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

1. Solve mathematical problems by using algebraic techniques.
2. Identify linear, quadratic, trigonometric, exponential and logarithmic functions and recall fundamental relations between them.
3. Manipulate with vectors.
4. Examine complex numbers and use them to solve simple problems.
5. Solve simple questions on differentiation and recognise 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, complex 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, simultaneous equations. Indicial, exponential and logarithmic equations.

Trigonometry: Sine and cosine rules. Unit circle representation. 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.

### Notes

This module is at CQFW Level 3