# MATHEMATICAL AND COMPUTATIONAL PHYSICS - 2017/8

Module code: PHY1038

Module provider

Physics

Module Leader

DIAZ TORRES A Dr (Physics)

Number of Credits

15

ECT Credits

15

Framework

FHEQ Level 4

JACs code

F340

Module cap (Maximum number of students)

N/A

Module Availability

Semester 2

Overall student workload

Independent Study Hours: 84

Lecture Hours: 44

Laboratory Hours: 22

Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Coursework | COMPUTING SEMESTER 2 COURSEWORK | 30% |

School-timetabled exam/test | MATHEMATICS MID SEMESTER 1HR CLASS TEST | 20% |

Examination | MATHEMATICS END OF SEMESTER 1.5HR EXAMINATION | 50% |

Alternative Assessment

None.

Prerequisites / Co-requisites

The module will assume prior knowledge equivalent to the following module. If you have not taken these modules you should consult the module descriptor Level HE1 (FHEQ Level 4) Essential Mathematics

Module overview

This module builds on the Essential Mathematics module to develop further mathematical and computational skills as an aid to understanding and exploring physics concepts. The mathematics Units of Assessment are taught in lecture-based classes with associated workshop sessions, and cover multi-variable calculus, Fourier Series

The computational part of the course consists of a series of assessed exercises, with classroom support, which develop computational problem solving skills, and link in with the mathematics covered elsewhere in the module and in the prerequisite module.

Module aims

enable students to classify and solve simple first- and second-order ordinary differential equations, including the concepts and appreciation of convergence tests of numerical series.

Enable students to compute the coefficients of Fourier series.

introduce matrices and to define and give practice in the use matrices and of some of the important constructs of introductory linear algebra. To be able to calculate the eigenvalues and eigenvectors of matrices.

provide an understanding of functions of more than one variable, their derivatives, and the location stationary points of functions of two variables, and to be able to classify them as maxima, minima or saddle points.

enable the use multiple integrals to calculate surface and volume properties

develop skills in and experience of developing computational solutions to problems in mathematics and physics.

produce well-structured and well-though-out program solutions to problems, drawing on examples from the mathematical physics part of the module,

present results from the programs in appropriate graphical format.

Learning outcomes

Attributes Developed | |
---|---|

Test numerical and functional series for their convergence properties | KC |

Be able to solve simple first- and second-order ordinary differential equations. | KC |

Be able to compute and manipulate partial derivatives | KC |

Be able to compute Fourier series coefficients | KC |

Be able to use matrices to represent and solve sets of linear equations | K |

Be able to evaluate derivatives and integrals of two- and multi-variable functions and be able to apply these to find maxima and minima and to the calculation of physical quantities such as volume, mass, moments of inertia and centre of gravity of various geometric shapes with both homogeneous and inhomogeneous densities. | KC |

Be able to use computational techniques to solve unseen problems in mathematics and physics, confidently using appropriate syntax and algorithm design, | CT |

Demonstrate skills in debugging and in graphical presentation | T |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

Module content

Indicative content includes:

Mathematical Physics:

Functions of two or more variables. Partial derivative, chain rule, changing variables and Taylor’s theorem. Identifying maxima, minima and saddle points.

First-order differential equations; the method of separation of variables and integrating factors. Exact differential equations. Simple second order equations with constant coefficients. General and particular solutions.

Fourier Series; orthogonal functions, computation of Fourier coefficients.

Laplace transforms and their applications.

Introductory Vector Calculus. Div, grad, curl, Gauss’ law, Lagrange multipliers.

Matrices. Matrix diagonalization, properties of Hermitian Matrices, Normal modes.

Line integrals, multiple integrals; double and triple integrals, changes of variables, the Jacobian; the use of spherical and cylindrical coordinates.

Computational Physics

The Computational Physics part of the module consists of the following 5 assignments:

Newton-Raphson root finding

Finite difference methods

Series computing

Geometric matrix-vector operations

Linear algebra

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

equip students with subject knowledge

develop skills in applying subject knowledge to unseen problems in mathematics, including problems with a direct physical application

ensure that students are able to take problems in

The learning and teaching methods include:

44h of lecture and tutorial classes in mathematics as 4h/week x 11 weeks

22h of supervised computational laboratory sessions as 2h/week x 11 weeks

Total student workload is 150hrs, with the remaining hours consisting of independent study

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

recall of subject knowledge

ability to apply individual components of subject knowledge to basic situations

ability to design and implement computational solutions to given mathematical problems

ability to tackle unseen mathematical problems using known methods

Thus, the summative assessment for this module consists of:

5 computational exercises covering different programming skills, and surveying different areas of the mathematics syllabus with deadlines spread equally throughout semester

a mid-semester mathematics test (1 hr)

a final examination in mathematics (1.5 hrs)

Formative assessment

Verbal feedback is given in tutorial sessions. Continuous feedback given in supervised computational classes. Mid-semester maths test provides feedback as well as contributing to the summative assessment.

Reading list

Reading list for MATHEMATICAL AND COMPUTATIONAL PHYSICS : http://aspire.surrey.ac.uk/modules/phy1038

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.