Module code: PHY2064

Module Overview

The module will introduce the physical significance and the mathematical methods (and selected theorems) of the operators of vector calculus: div, grad and curl in different co-ordinate systems.

The module will introduce the partial differential equations of mathematical physics and their solution for selected physical systems involving different co-ordinate systems and involving time.

The module will introduce the foundations of electromagnetism, up to Gauss’ Law and Laplace’s equation, as a major application of the vector calculus and partial differential equations techniques.

Module provider

Mathematics & Physics

Module Leader

SEAR Richard (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 5

Module cap (Maximum number of students): N/A

Overall student workload

Independent Learning Hours: 63

Lecture Hours: 22

Tutorial Hours: 11

Laboratory Hours: 22

Guided Learning: 10

Captured Content: 22

Module Availability

Semester 1

Prerequisites / Co-requisites


Module content

Introduction to vectors and their properties, to vector and scalar fields, and the physical significance and mathematical properties and identities of the gradient, divergence and curl and Laplacian operators. Introduction to the application of these mathematical concepts, notations and techniques in Electromagnetism.

Introduction to differential equations involving more than one dynamical variable. The equations of mathematical physics: Laplace’s equation, the wave equation, the diffusion equation, Schrodinger’s equation for the hydrogen atom.  The use of appropriate coordinate systems. The Laplacian operator in different coordinate systems coordinates. Simple boundary conditions. Discussion of the method of separable solutions: introduction to separable solutions involving spatial coordinates and involving time.

The basic principles of electrostatics are discussed, including electric charge, Coulomb's Law, the electric vector field E, the Principle of Superposition, the electrostatic scalar potential V, the conservative nature of E. The concepts of equipotentials, flux, and the properties and use of Gauss's Law and Stokes’ Theorem.


The student will perform a selection experiments with the general theme of electromagnetism. Typical experiments include: measurement of e/m for the electron, Coulomb's Law, Current balance, Magnetic Field Gradients, Transmission Lines or Paths of charged particles.

An Equality, Diversity and Inclusion Awareness workshop.

Assessment pattern

Assessment type Unit of assessment Weighting
Examination End of semester examination - 2 hours 60
Practical based assessment EDI Awareness Engagement Pass/Fail

Alternative Assessment

Alternative assessment: For the laboratory coursework the written reports may be assessed by a condensed programme of laboratory work, with written report.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their knowledge of vector calculus, partial differential equations, and practical laboratory skills.

Thus, the summative assessment for this module consists of:

A short quiz in alternate weeks to test learning and provide feedback on progress during the semester.

The laboratory coursework is assessed through a combination of interviews, written reports and a poster presentation.

The Laboratory unit of assessment has a qualifying mark of 40%.

A 2 hour final examination.

The assessment of engagement with the EDI Awareness Workshop will be by an open book quiz with unlimited re-attempts, but it must be passed in order to pass the module.

Formative assessment

Problem sets are provided weekly on vector calculus and electromagnetism, together with model answers to these questions, which allow the students to test their understanding of course material. Formative assessment during the laboratory classes is provided by an online quiz for each experiment carried out each week by the students to prepare for the forthcoming laboratory experiment.



Verbal feedback is provided at tutorial sessions throughout the semester. Model solutions are provided for the questions on the problem sets to provide students with feedback on their problem-solving ability. The quizzes in alternate weeks provide feedback on progress. Feedback during the laboratory classes is provided by demonstrators and staff giving verbal feedback and support during the class.


Module aims

  • Vector calculus: To review vector properties and vector products and introduce both the physical significance and properties of the gradient, divergence and curl operators in scalar and vector fields. To develop the Laplacian operator in different coordinate systems for use in applications of the wave, diffusion, and Laplace equations of mathematical physics.
  • Partial differential equations: To develop use of the method of separable solutions and to discuss separable solutions in Cartesian and polar co-coordinates and in time - with emphasis on problems involving scalar fields and involving Fourier series and the Schrodinger's equation for the hydrogen atom
  • Electromagnetism. To introduce the principles of electromagnetism, from Coulomb's Law, to give an overview of electrostatics and scalar and vector fields. To develop theorems and applications of the use of vector calculus methods, including Stokes¿ Theorem and the use of Gauss¿ Law.
  • The laboratory classes will build on the foundation of earlier practical classes. Several classical electromagnetism experiments will be carried out to underpin theoretical knowledge and improve understanding.
  • To explore the concepts from electromagnetism in the laboratory, while developing practical skills.

Learning outcomes

Attributes Developed
002 Demonstrate competence with using the notation and methods of partial differential equations and vector calculus. KCT
003 Solve, partial differential equations in different coordinate systems and involving time, and be able to appraise the forms of the solutions in physically interesting cases. KCT
004 Appreciate and be able to calculate the gradient, divergence and curl of scalar and/or vector fields and be able to manipulate and evaluate integral and differential vector equations involving div, grad and curl. KCT
005 Describe and use the underlying concepts of electrostatics and calculate and use the field equations in simple problems in electrostatics. KCT
006 Demonstrate practical skills through experimentation in areas related to electromagnetic phenomena KCPT
007 Be able to communicate results effectively using laboratory write-ups. CPT
001 Recognise benefits of equality, diversity and inclusion and identify causes and effects of unconscious bias KPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• Develop the skills required to analyse and solve problems that require vector calculus and/or partial differential equations, especially as applied to electromagnetism

• Develop problem-solving skills in mathematics by showing worked examples and challenging students to attempt problem-solving on their own.

• Apply knowledge and develop skills by tailored EM laboratory experiments.


The learning and teaching methods include:

Lectures and tutorials.

Experiments throughout semester  (laboratory work)


Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list

Upon accessing the reading list, please search for the module using the module code: PHY2064

Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Employability, Digital Capabilities, Global and Cultural Capabilities, Sustainability, and Resourcefulness and Resilience. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

Digital Capabilities: The students will use computers to plot and fit data, and write up reports, as an integral part of the laboratory component of this module.

Employability: The module introduces learners to experimental equipment and techniques used in both industry and academia, as well as preparing and giving presentations.

Resourcefulness and Resilience: students must develop strategies to solve both problems in the experimental labs, as well as to solve the mathematical equations.

Global and Cultural Capabilities The module includes an Equality, Diversity and Inclusivity (EDI) workshop which aims to increase awareness of cultural, religious, or racial differences while delivering information about how a person can change their behaviour to be more inclusive. Through this training, students are encouraged to diversify their knowledge and reflect upon their experiences as a physicist and in education.

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics with Astronomy BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Nuclear Astrophysics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Nuclear Astrophysics MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Astronomy MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Computing BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Computing MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module

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 2024/5 academic year.