# 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 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**

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.

### Reading list

The reading list is available from the Library websiteLast updated: 19/07/2021 11:31:03

## Browse Other Catalogues

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

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