2024/25 Undergraduate Module Catalogue

PHYS2370 Maths 3- Matrices and Operators

10 creditsClass 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	2.00	22.00
Lecture	22	1.00	22.00
Private study hours			56.00
Total Contact hours			44.00
Total hours (100hr per 10 credits)			100.00

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	Regular coursework	20.00
Total percentage (Assessment Coursework)		20.00

Resits will be in standard exam format.

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	80.00
Total percentage (Assessment Exams)		80.00

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: 29/04/2024 16:19:13

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