# Gwybodaeth Modiwlau

Module Identifier
PH06520
Module Title
Introduction to Mathematical Methods for Physicists 2
2021/2022
Co-ordinator
Semester
Semester 2
Co-Requisite
PH06020
Mutually Exclusive
Not available to 3 year BSc or 4 year MPhys
Pre-Requisite
GCSE Maths or equivalent
Other Staff

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 3 Hours   End of semester examination  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. Evaluate basic integrals and derivatives.
2. Construct the gradient of a curve y(x).
3. Calculate arithmetic and geometric series.
4. Apply the binomial theorem.
5. Recognise and manipulate with matrices and determinants.

### Brief description

This second module on theoretical methods introduces the student to 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.

### Content

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. Use of partial fractions.

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

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

Introduction to matrices and determinants.

### Transferable skills

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.

### Notes

This module is at CQFW Level 3