# 2023/24 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** 2023/24

### Pre-requisite qualifications

PHYS 1290 MATHS 1PHYS 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 Stokesâ€™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 websiteLast updated: 28/04/2023 14:55:13

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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