## PHYS2160 Matrices and Vector Calculus

### 10 creditsClass Size: 100

Module manager: Professor G J Morgan
Email: g.j.morgan@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2005/06

### Pre-requisites

PHYS1150 (Basic Mathematical Methods) PHYS1160 (Differential Calculus and Infinite Series) or equivalents

This module is not approved as an Elective

### Objectives

On completion of this module, students should be able to:
- evaluate the gradient of a scalar function, the divergence of a vector function and the curl of a vector function;
- Evaluate line, surface and volume integrals which may include changing the order of integration and using Cartesian, cylindrical polar or spherical polar coordinates;
- multiply matrices and evaluate determinants;
- solve a set of linear equations; using Kramer's rule;
- invert matrices and find eigenvalues and eigenstates;
- use the properties of delta-functions.

Skills outcomes
Basic mathematical methods needed in all branches of science.Basic mathematical methods needed in all branches of science.

### Syllabus

Integration:
Gradient of a scalar function or field, divergence and curl of a vector function or field. Use of these operators in fluid mechanics and electromagnetism.
Line,surface and volume integrals, i.e integration along curves, over areas and volumes. Use of spherical and cylindrical polar coordinates.
Matrices:
Multiplication of matrices, inverses and linear transformations. Determinants and the solution of linear equations, eigenvalues and eigenvectors.
Diagonalisation of matrices, real symmetric matrices and diagonalisation of quadratic forms. Hermitian matrices and forms, including real eigenvalue property.
Properties of delta-functions.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures: 22 x 1 hour;

Example classes: 6 x 1 hour.

### Private study

Homework and tutorials: 50 hours;
Reading and revision: 22 hours .

### Opportunities for Formative Feedback

5 x marked assignments.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

1 x 2 hour examination at the end of the semester: 85%;
5 marked assignments: 15%.