# 2021/22 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 2021/22

### 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
On completion of this module, students should be able to:
- evaluate integrals using the theorems of Green, Stokes and Gauss and be able to apply these theorems to physics problems;
- multiply matrices and evaluate determinants;
- solve a set of linear equations;
- invert matrices and find their eigenvalues and eigenvectors.
- know the properties of Hermitian matrices and be able to use them in physics problems.

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 1.00 11.00 Lecture 22 1.00 22.00 Private study hours 67.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 100.00

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Online Assessment Online Mid-Term Assessment 20.00 Total percentage (Assessment Coursework) 20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Online Time-Limited assessment 2 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

Students will have to complete an online assessment 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. Students are required to pass all assessments for this module in order to pass the module overall.