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Mathematical, Computational & Professional Skills 2 - PHY00033C

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  • Department: Physics
  • Module co-ordinator: Dr. Chris Murphy
  • Credit value: 20 credits
  • Credit level: C
  • Academic year of delivery: 2024-25
    • See module specification for other years: 2023-24

Module summary

This module aims to extend your understanding of differentiation and integration in order to understand concepts such as Fourier transforms and vector calculus. This will lead you to appreciate how such concepts can be used to solve problems in physics as diverse as optics, quantum mechanics and electromagnetism. In much the same way, this module will also help develop your computational and professional skills allowing you to hone new skills in problem solving and communication.

Related modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Additional information

Pre-requisite: Mathematical, Computational & Professional Skills 1 - PHY00031C

Module will run

Occurrence Teaching period
A Semester 2 2024-25

Module aims

Mathematics is a fundamental tool for the study of Physics. Computational and other professional skills must be gained to become a successful modern physicist. This module aims to introduce the concepts of calculus, complex numbers, vectors, linear algebra and statistics by making links back to A-Level Mathematics and forward to areas of Physics to be studied. This module aims to develop your skills in programming such that you can solve physics problems computationally. The module also aims to develop your professional skills which will help you in your study of physics but can also be transferred to challenges in other fields.

Module learning outcomes


  • Understand the physical meaning of double and triple integrals and be able to compute them in Cartesian, spherical and cylindrical coordinate systems in order to solve a physical problem.

  • Define a Fourier series of any periodic function and use it to derive the Fourier transform

  • Solve second-order partial differential equations that describe a range of physical phenomena

  • Describe the rate at which scalar and vector fields change in an arbitrary direction and use this concept to calculate the flux of fields through and around regions of space.


  • Be able to apply Python to problems such as modelling and data analysis.

Professional Skills

  • Use commercial office software applications confidently for scientific presentation.

  • Demonstrate an ability to effectively communicate physics ideas and personal development by written and oral means.

  • Demonstrate an ability to work independently and as part of a collaborative team.

Module content

Further Integration: Standard integrals, integration by substitution, integration by parts. Double and triple integrals and changing the order of integration. Polar coordinates (2D), spherical and cylindrical coordinates (3D).

Scalar and Vector Fields: Rate of change of a scalar field, conservative fields, work done along a vector field, flux of a vector field, divergence theorem. Curl of a vector field, circulation, Stokes’ theorem, Laplace operator, div, grad and curl in different coordinate systems. Surface integrals of vector fields.

Further Differential Equations: Second order PDEs, separation of variables.

Fourier Series: Fourier theorem and Fourier series, boundary conditions, Fourier coefficients, waveforms, Fourier transforms, reciprocal broadening.

Computational Skills; Introduction to numerical methods, using python libraries, fitting and plotting data.

Professional Skills: Electronic document presentation, record keeping, accessibility, effective communication, self-awareness, teamwork, scientific report structures and styles, referencing.


Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Mathematical, Computational & Professional Skills 2
2.5 hours 60
Computational Assignments
3 hours 15
Physics Practice Questions
2 hours 15
Professional Skills Assignments
2 hours 10

Special assessment rules




Module feedback

'Feedback’ at a university level can be understood as any part of the learning process which is designed to guide your progress through your degree programme. We aim to help you reflect on your own learning and help you feel more clear about your progress through clarifying what is expected of you in both formative and summative assessments.

A comprehensive guide to feedback and to forms of feedback is available in the Guide to Assessment Standards, Marking and Feedback. This can be found at:

The School of Physics, Engineering & Technology aims to provide some form of feedback on all formative and summative assessments that are carried out during the degree programme. In general, feedback on any written work/assignments undertaken will be sufficient so as to indicate the nature of the changes needed in order to improve the work. Students are provided with their examination results within 25 working days of the end of any given examination period. The School will also endeavour to return all coursework feedback within 25 working days of the submission deadline. The School would normally expect to adhere to the times given, however, it is possible that exceptional circumstances may delay feedback. The School will endeavour to keep such delays to a minimum. Please note that any marks released are subject to ratification by the Board of Examiners and Senate. Meetings at the start/end of each semester provide you with an opportunity to discuss and reflect with your supervisor on your overall performance to date.

Our policy on how you receive feedback for formative and summative purposes is contained in our Physics at York Taught Student Handbook.

Indicative reading


  1. Vector Calculus Book by P. C. Matthews

  2. Mathematical Methods in the Physical Sciences Textbook by Mary L. Boas

  3. A Student's Guide to Fourier Transforms: With Applications in Physics and Engineering Book

Professional Skills:

John M. Lannon & Laura J. Gurak: Technical Communication, Global Edition. 15th Ed 2021 (Pearson)

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.