2017/18 Undergraduate Module Catalogue
PHYS2370 Maths 3- Matrices and Operators
10 creditsClass Size: 175
Module manager: Dr J. Pachos
Email: j.k.pachos@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2017/18
Pre-requisites
| PHYS1290 | Maths 1- Scalars and Vectors |
| PHYS1300 | Maths 2- Multivariable Calculus |
Module replaces
PHYS2160This module is not approved as a discovery module
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;
- evaluate integrals using the theorems of Green, Stokes and Gauss;
- multiply matrices and evaluate determinants;
- solve a set of linear equations;
- invert matrices and find their eigenvalues and eigenvectors.
Learning outcomes
Manipulate numerical and other quantitative information, and apply manipulative skills to the solution of problems.
Skills outcomes
Basic mathematical methods needed in all branches of science.
Syllabus
Vector calculus:
Cartesian, cylindrical polar and spherical polar coordinate systems.
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.
Integral theorems of Green, Stokes and Gauss.
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.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| Example Class | 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 | ||
Private study
Homework assignments: 15 hours;Reading and assimilation: 32 hours;
Exam preparation: 20 hours.
Opportunities for Formative Feedback
3 x homework assignments.Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| Assignment | 3 marked assignments | 15.00 |
| Total percentage (Assessment Coursework) | 15.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Exams
| Exam type | Exam duration | % of formal assessment |
| Standard exam (closed essays, MCQs etc) | 2 hr 00 mins | 85.00 |
| Total percentage (Assessment Exams) | 85.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 05/09/2017
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- Undergraduate module catalogue
- Taught Postgraduate module catalogue
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