2024/25 Undergraduate Module Catalogue

PHYS2370 Maths 3- Matrices and Operators

10 Credits Class Size: 250

Module manager: Prof. Jiannis Pachos
Email: J.K.Pachos@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

Pre-requisite qualifications

PHYS 1290 MATHS 1 PHYS 1300 MATHS 2

Pre-requisites

PHYS1290 Maths 1- Scalars and Vectors
PHYS1300 Maths 2- Multivariable Calculus

Module replaces

PHYS2160

This module is not approved as a discovery module

Module summary

Fluency in mathematical techniques is essential for solving physics problems. This module introduces vector calculus and linear algebra concepts and techniques indispensable for modern physics, including electromagnetism and quantum mechanics. Exercises that allow practicing actual calculations are an integral and important part of the module.

Objectives

Manipulate numerical and other quantitative information, and apply manipulative skills to the solution of problems.

Learning outcomes

Students will be able to demonstrate knowledge, understanding and application of:
1. Vector calculus
2. Integrals with vectors, including Stokes’s theorem and Divergence theorem
3. Algebra, trace and determinant of matrices
4. Solve linear equations with matrices
5. Diagonalisation of matrices with eigenvalues and eigenvectors

Skills outcomes

Basic mathematical methods needed in all branches of science.

Syllabus

Vector calculus:
Line, surface and volume integrals, i.e integration along curves, over areas and volumes. Use of spherical and cylindrical polar coordinates.
Integral theorems of Green, Stokes and Gauss. Application of these concepts to physics problems.
Matrices:
Multiplication of matrices, inverses and linear transformations. Determinants and the solution of linear equations, eigenvalues and eigenvectors.
Diagonalisation of matrices, real symmetric matrices, Hermitian matrices, their eigenvalues and eigenvectors, and physics applications.

Teaching Methods

Delivery type Number Length hours Student hours
Workshop 11 2 22
Lecture 22 1 22
Private study hours 56
Total Contact hours 44
Total hours (100hr per 10 credits) 100

Methods of Assessment

Coursework
Assessment type Notes % of formal assessment
In-course Assessment Regular coursework 20
Total percentage (Assessment Coursework) 20

Resits will be in standard exam format.

Exams
Exam type Exam duration % of formal assessment
Standard exam (closed essays, MCQs etc) 2.0 Hrs 30 Mins 80
Total percentage (Assessment Exams) 80

Students will have to complete an in-person exam at the end of the module. This will take place during the examinations period at the end of the semester and will be time bound.

Reading List

The reading list is available from the Library website

Last updated: 4/29/2024

Errors, omissions, failed links etc should be notified to the Catalogue Team