Introduction to Mathematical Methods 2

Module Identifier: PH06520
Module Title: Introduction to Mathematical Methods 2
Academic Year: 2027/2028
Semester: Semester 2
Co-ordinator: Dr Balazs Pinter
Reading List: View on Aspire
Pre-Requisite: GCSE Maths or equivalent
Co-Requisite: PH06020
Exclusive (Any Acad Year): Not available to students on a 3-year Bachelor's or on an Integrated Master's scheme
Other Staff: Dr Tom Knight; Dr Balazs Pinter

Assessment

Assessment Type	Assessment details	Proportion
Semester Assessment	Weekly course work:	30%
Semester Exam	End of semester examination: 3 Hours	70%
Supplementary Exam	Supplementary Examination: 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.

Module skills

Skills type	Skills details
Creative Problem Solving	Problem solving skills are developed throughout the module and assessed in coursework and the semester examination.
Professional communication	Presentation of the work by students in coursework and the semester examination develop written communication skills.
Subject Specific Skills	Understanding and application of mathematical techniques are essential to solve problems in the physical sciences.

Notes

This module is at CQFW Level 3