Undergraduate Teaching 2025-26

2025-26

2025-26

Not logged in. More information may be available... Login via Raven / direct.

Engineering Tripos Part IB, 2P8: Civil and Structural Engineering, 2025-26

Course Leader

Dr J Hambleton

Lecturers

Dr J Hambleton, Dr S Selvakumaran,

Timing and Structure

Weeks 1-4 Easter Term. 16 lectures / design workshops, 4 classes/week

Prerequisites

Engineering Part I

Aims

The aims of the course are to:

  • Act as a shop window for the techniques and technologies of civil engineering seen as a practical and scientific discipline.
  • Create interest in the design, construction and maintenance of the built environment, using floating offshore wind turbines as an example.
  • Provide illustrations from real life schemes, and in combining theory in context with real life examples, highlight the role of the professional.
  • Introduce the topics of structural materials (with more detailed introduction to structural concrete), structural stability, geotechnical engineering, and using data for smart infrastructure and construction.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Introduce students to the range of disciplines within civil engineering;
  • Develop awareness of the integrated civil engineering projects that they might work on as professional engineers;
  • Learn to use Part I theory in simple integrated design applications;
  • Recognise limitations with Part I theory; and
  • Develop an awareness of potential courses of study that will address these limitation in Part II.

Content

The course focuses on a Civil Engineering mega-project - in this case the design of Floating Offshore Wind Turbines (FOWT). This will illustrate how the knowledge you have gained in Part I knowledge might be used immediately. Their enormous scale makes FOWTs a very exciting prospect for making a major contribution to tackllng the world's energy demand in a sustainable manner.

The course will also highlight a wide spectrum of Division D Part II module offerings that will provide extensions to specialist knowledge in specifc areas. 

There will be four sub-topics, and these will be covered by lectures in the first half of the course.

- Concrete Design

- Hydrostatic Stability

- Geotechnical Engineering (Ground anchor design)

- Smart Infrastructure & Construction (Systems thinking and Digital Twins)

The second half of the course will be informal workshop sessions with the lecturers, where students can undertake their own research into these issues and prepare coursework for submission.

Students should attend all lectures but only need to submit coursework on TWO of the four topics. 

 

Integrated Civil Engineering Introduction

The course will begin with an introductory lecture, explaining how the course works. It will also give a background to the wider topic of Floating Offshore Wind Turbines (FOWTs). This will be given by Ari Liddell, an alumna of the department, who now works on the design of FOWTs and associated green energy infrastructure in the Celtic Sea.

Structural Materials (2L + 2 Design Workshops)

  • Lectures: overview of structural aspects related to FOWT design (steel for turbine, and an introduction to concrete for base design); development of simple analysis techniques from Part I material, highlighting limitations and scope for knowledge extension in Part II through the design of reinforced concrete sections; 
  • Design classes: two hours of interactive design classes to help students work through producing a design for the FOWT base.

Hydrostatic Stability (2L + 2 Design Workshops)

  • Lectures: an introduction to ship stability and the buoyancy considerations related to FOWT design, extending basic stability from Part I to how a FOWT floats and how it can be moved safely into place; 
  • Design classes: two hours of interactive design classes to help students work through to determine the stabilty of various shapes, to better  understand the design for the FOWT main section.

Geotechnical Engineering (2L + 2 Design Workshops)

  • Lectures: overview of geotechnical aspects related to FOWT design (seabed); development of simple analysis techniques from Part I material, highlighting limitations and scope for knowledge extension in Part II; 
  • Design classes: two hours of interactive design classes to help students work through producing a design for the FOWT cables and anchor to the seabed.

Smart Infrastructure and Construction (2L + 2 Design Workshops)

  • Lectures: overview of sensing and data aspects related to FOWT design (Big Data, smart sensing, data-driven approaches and systems thinking, digital twins); developing an understanding of how we can derive value from data, rather than simply collecting it.
  • Design classes: two hours of interactive design classes talking with an industry guest speaker to work out why they want to measure followed by a design exercise and the option to analyse real data collected from a FOWT.

 

Examples papers

Example papers will not be issued as part of this course, and there will be no examination. Students will work through design workshops and hand in their completed assignments for assessment over the 4-week period.

Coursework

There is no examination for this course. Assessment is via coursework submitted in the duration of the course.

Coursework exercises will be delivered during the design workshops, where students will have time and support in working on their designs. There will be 4 possible exercises, one for each lecture topic:

  1. Structural Materials
  2. Hydrostatic Stability
  3. Geotechnical Engineering
  4. Smart Infrastructure and Construction

Students are asked to submit two coursework assignments on Moodle (and are encouraged to come to the design classes and try out each of the activities!).

 

Booklists

Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

 
Last modified: 05/06/2025 11:18

Engineering Tripos Part IB, 2P8: Mechanical Engineering, 2025-26

Course Leader

Prof M Sutcliffe

Lecturers

Prof H Hunt, Prof M Sutcliffe, Dr S Mandre, Dr S Goetz, Prof J Cullen

Timing and Structure

Lent Term: 14 lectures + 2 examples classes, 4 lectures/week. Lectures will be recorded.

Aims

The aims of the course are to:

  • Describe systematic methods for assessing the sustainability of wind energy and other renewable energy systems.
  • Analyse the aerodynamics and structural loading of wind turbine blades, the choice of materials, and the effect of scale.
  • Analyse the mechanical and electrical aspects of wind turbine machinery.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Summarise the technical, social, environmental and economic challenges to consider in assessment of the sustainability of renewable energy systems.
  • Make quantitative estimates relating to materials, energy and environmental aspects of a renewable energy technology.
  • Analyse the aerodynamic loads on a wind turbine blade.
  • Calculate the energy capture potential of a wind turbine.
  • Follow an appropriate methodology for preliminary structural design and material selection for wind turbine blades.
  • Make a realistic fatigue lifetime prediction for blade structures.
  • Select materials and perform structural optimisation for towers and turbine blades.
  • Analyse epicyclic and parallel gearboxes as applied to wind turbine generators.
  • Undertake a simple modal analysis of a wind turbine.
  • Outline principle sources of noise generation in wind turbines.
  • Understand how the electrical power generator rating is chosen and the implication for turbine/generator control,annual energy production and system payback period.
  • Know the main electrical technologies that are used, their advantages and disadvantages, with reference to the implications for the need for a gearbox, fixed vs variable speed operation and power electronic convertors for interfacing to the 3-phase grid.
  • Understand how the induction motor theory taught in the Lent Term may be extended to induction generators.

Content

Overview of renewable energy systems (1L, Prof HEM Hunt)

  • Renewable energy technologies: wind, hydro, solar, tidal; development status in UK, EU, worldwide. (2) Chap. 5 
     

Sustainable development: materials and renewable energy systems (1L, Prof J Cullen)

  • Five-step methodology for assessment of sustainability of a technological development
  • Application to wind turbines, focussing on materials supply, energy payback and environmental issues.

Fundamentals of wind turbine design (1L, Prof HEM Hunt)

  • Fundamental fluid mechanics limits to energy generating potential, including derivation of Betz limit, influence of size and height, estimates of wind loading, capacity factor.

Wind turbine loading (3L, Dr S D Mandre)

  • Aerofoil aerodynamics
  • Blade element momentum theory
  • Centrifugal loading
  • Self weight loading

Structural design and material selection for wind turbines (3L, Prof MPF Sutcliffe)

  • Scaling effects
  • Material performance indices
  • Shape optimization
  • Composite blades

Mechanics of wind turbines (2L, Prof MPF Sutcliffe)

  • Gearbox design: epicyclic and parallel drives, velocity ratios and tooth force calculations
  • Vibration modelling and modal analysis.
  • Noise and vibration.

Power generation in wind turbines (2L, Dr S Goetz)

  • Electrical challenges of generating electricity from wind energy- contrast with conventional fossil fuel generation met in the Lent Term
  • Generator rating in terms of volume and rotational speed.
  • Need for gearbox - the electrical perspective.
  • Choice of generator rating by considering output electrical power vs wind speed, annual energy production, payback period.
  • Generator technologies and their advantages and disadvantages
  • (i) Implications for gearbox.
  • (ii) Implications for fixed or variable speed operation.(iii) Implications for power electronic convertors and interfacing to the 3-phase grid.
  • Extension of induction motor theory met in the Lent Term to induction generators.
  • Simple output power and reactive power calculations.
  • Slip energy recovery and variable speed operation.

Guest lecture (1L, Prof Shaun Fitzgerald)

  • Climate repair

Examples papers

  1. Global warming and carbon footprints. Sustainability of wind energy. Wind power fundamentals. Wind turbine aerodynamics and loading.
  2. Manufacturing. Materials. Fatigue. Mechanics. Electrical Power

Booklists

Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

D2

Understand customer and user needs and the importance of considerations such as aesthetics.

D3

Identify and manage cost drivers.

S1

The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.

S3

Understanding of the requirement for engineering activities to promote sustainable development.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

P5

Awareness of nature of intellectual property and contractual issues.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 09/06/2025 22:25

Engineering Tripos Part IB, 2P8: Aerothermal Engineering, 2025-26

Course Leader

Dr C Clark

Lecturers

Dr I Dedoussi

Lecturer

Dr C Clark

Timing and Structure

Easter Term: 14 lectures + 2 examples classes, 4 lectures/week.

Aims

The aims of the course are to:

  • Understand why current engines on large airliners look as they do, how they work and how they are specified.
  • Determine what is needed to propel a new large airliner.
  • Appreciate the mixture of physical modelling and empirical input necessary to make the decisions to allow a design to proceed, as well as the need for compromises.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Calculate the major parameters of the engine (this will be carried out in the form of exercise questions throughout the course).
  • Make appropriate design choices for engine components.
  • Sketch a cross-section of the engine showing principal components with appropriate parameters.
  • Calculate the effect of speed and altitude on engine performance.

Content

Modern jet engines are amongst the most expensive mechanical engineering devices to design and develop; a new engine is expected to cost several billion pounds. Why is it so expensive? Why do they look the way they do?

Many of the most important decisions are taken at an early stage of design using fairly simple procedures, similar to those that can be used in lectures and example classes. The constraints, especially those associated with material properties, need to be known or specified, together with estimates for the likely level of aerodynamic performance. From these the desirable type of engine configuration can be specified, preliminary choices for the main components (compressor and turbine) can be made and a sketch of the engine layout can be drawn.

Introduction to Aircraft Propulsion

  • Operating principles,key aircraft parameters, nacelle/wing arrangements
  • Design constraints, environmental issues and fuel burn.

Aircraft performance

  • Basic aircraft aerodynamics, sizing the wing, lift-drag relationships.
  • Breguet range equation, estimation of aircraft fuel burn and emissions.
  • Thrust requirements, trade-offs between weight and performance.

Generation of thrust

  • Momentum analysis, propulsive efficiency, overall efficiency.
  • Choice of engine type for given duty; high subsonic cruise compared with supersonic operation.

Thermodynamic Analysis of Gas Turbine

  • Power generation: effect of pressure ratio, temperature ratio and component efficiency.Relationship between thermal efficiency and cycle efficiency.
  • Jet propulsion as a means for utilisation of power.

Choice of Engine

  • Selection of bypass ratio and calculation of corresponding engine mass flow.
  • Turbine inlet temperature and blade cooling.
  • Calculation of fuel consumption in determining fan diameter.

High Speed Flow of Gas

  • Subsonic and supersonic flow, nozzle flow, choking.

Dimensional Analysis

  • Dynamic scaling of jet engine.
  • Start-of cruise is the design condition - estimating thrust and fuel consumption at off-design conditions, such as take off.
  • To consider requirements for thrust in case of engine failure at take off or cruise.

Turbomachinery Principles

  • General introduction to operation of compressors and turbines.
  • Selection of number of stages in compressor and turbine.

Appraisal of Design

  • Having specified overall size, bypass ratio, turbine inlet temperature, sketch engine layout and compare with existing designs.

Booklists

Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

D2

Understand customer and user needs and the importance of considerations such as aesthetics.

D3

Identify and manage cost drivers.

S1

The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.

S3

Understanding of the requirement for engineering activities to promote sustainable development.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

P5

Awareness of nature of intellectual property and contractual issues.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 05/06/2025 11:18

Engineering Tripos Part IB, 2P8: The Engineer in Business (Compulsory), 2025-26

Lecturer

Dr S Lu

Lecturer

Dr C Coleridge

Lecturer

Prof M Polltt

Timing and Structure

Weeks 1-8, Lent Term. 8 x 1-hour sessions including: 3 x 1-hour sessions on economics, 2 x 1-hour sessions on strategy, 3 x 1-hour sessions on marketing. The first three lectures will be delivered live on Zoom.

Aims

The aims of the course are to:

  • provide students with a basic understanding of how businesses work, and to give them the language to work effectively with those who work in non-technical roles within a business.

Objectives

As specific objectives, by the end of the course students should be able to:

  • gain a preliminary, concise and multi-faceted understanding of issues in running businesses.

Content

The module is structured around three major fields of studies that complement each other, namely economics, marketing, and strategy.

  • The sessions on economics aim to introduce the economic nature of the firm, why and how firms grow or contract, and the nature of economic regulation facing firms.
  • The sessions on strategy aim to examine how firms develop and maintain competitive advantage; and to help students to develop skills that will allow them to make robust strategic business decisions in the face of uncertainty and complexity.
  • The sessions on marketing aim to help students understand core questions in marketing and how marketing contributes to business strategy and firm performance; and to help students to develop strategic and analytical skills in planning and evaluating marketing decisions in the business world.

 

The Engineer in Business

Sessions on economics (3 x 1-hour sessions):

The economic nature of the firm (1 session)

The theory of the firm (1 session)

The regulation of the firm (1 session)

 

Sessions on strategy (2 x 1-hour sessions):

What is strategy and how to analyse industries? (1 session)

Types of competitive advantage: Cost leadership and differentiation strategies (1 session)

 

Sessions on marketing (3 x 1-hour sessions):

Demystifying marketing (1 session)

Strategic brand management (1 session)

Marketing communication in the digital age (1 session)

Further notes

Assessment

A set of multiple-choice questions to be completed over 30 minutes of examination time.

Examples papers

 

See VLE.

 

Booklists

Please refer to the Booklist for Part IB Courses for complete references to this module, this can be found on the associated Moodle course.

Helpful reference for Economics Sessions: 

Sloman, J., Garrett, D., Guest, J. and Jones, E. (2023)

Economics for Business, 8th, 9th Editions, Pearson.

Chapters 3 (Business Organisations), 13 (Alternative Theories of the Firm), 15 (Growth Strategy), 20 (Reasons for Government Intervention in the Market) and 21 (Government and the Firm).

E-book via:

iDiscover

Helpful reference for Strategy Sessions: 

 

 

Clegg, S.R. 

Pitelis, C. 

Schweltzer, J. 

Whittle, A. (2022)

Strategy: Theory and Practice 2nd, 3rd, 4th Editions, SAGE.

Available:

UL: 425:1.b.201.51  

 

 

Helpful reference for Marketing Sessions: 

Kotler, P. et al. (2019)

Marketing Management. 3rd / 4th European ed. Harlow: Prentice Hall/Pearson Education

‘Defining marketing for new realities/Introduction to Marketing.’

‘The changing marketing environment and information management.’

‘Managing digital technology in marketing.’

‘Digital and global brand management strategies.’

E-book via 

iDiscover

 

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

KU3

Appreciate the social, environmental, ethical, economic and commercial considerations affecting the exercise of their engineering judgement.

D2

Understand customer and user needs and the importance of considerations such as aesthetics.

D3

Identify and manage cost drivers.

S1

The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.

S2

Extensive knowledge and understanding of management and business practices, and their limitations, and how these may be applied appropriately to strategic and tactical issues.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

 
Last modified: 05/06/2025 11:18

Engineering Tripos Part IB, 2P7: Linear Algebra, 2025-26

Lecturer

Dr J.P. Jarrett

Timing and Structure

Weeks 4 & 8 Lent Term 1 lecture/week; weeks 5-7 Lent Term 2 lectures/week. 8 lectures

Aims

The aims of the course are to:

  • Introduce the ideas and techniques of Linear Algebra, and illustrate some of their applications in engineering.

Objectives

As specific objectives, by the end of the course students should be able to:

  • For all objectives, complete calculations by hand for small problems, or by using Matlab for larger problems (the IB Computing Course deals with this in detail).
  • Solve a set of linear equations using Gaussian elimination, and complete the LU factorisation of a matrix.
  • Understand, and be able to calculate bases for the four fundamental subspaces of a matrix.
  • Calculate the least squares solution of a set of linear equations.
  • Orthogonalize a set of vectors, complete the QR factorisation of a matrix, and be able to use this to find the least squares solution of a set of linear equations.
  • Find the eigenvalues and eigenvectors of a matrix, and complete the A = SL S-1 or A = QL QT factorisations as appropriate.
  • Find the SVD of a matrix, and to understand how this can be used to calculate the rank of the matrix, and to provide a basis for the each of its fundamental subspaces.

Content

  • Solution of the matrix equation Ax = b: Gaussian elimination, LU factorization, the four fundamental subspaces of a matrix.
  • Least squares solution of Ax = b for an m x n matrix with n independent columns: Gram-Schmidt orthogonalization, QR decomposition.
  • Solution of Ax = l x, eigenvectors and eigenvalues.
  • Singular Value Decomposition.

Booklists

Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P8

Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

 
Last modified: 05/06/2025 11:17

Engineering Tripos Part IB, 2P7: Vector Calculus, 2025-26

Lecturer

Prof G Pullan

Timing and Structure

Weeks 1-3 and 6-8 Michaelmas term, 2 lectures/week; weeks 4-5 Michaelmas term, 1 lecture/week. 14 lectures

Aims

The aims of the course are to:

  • Provide the necessary background mathematics to ensure that students are confident in handling partial differential equations in vector form while maintaining a tangible physical appreciation of the manipulations involved.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Differentiate and integrate scalar functions of two or more variables including transformations to other co-ordinate systems.
  • Manipulate vector differential equations including the gradient, divergence and curl operators while retaining a physical appreciation of the mathematical operations involved.
  • Perform line, surface and volume integrals and understand their various physical interpretations.
  • Set up conservation statements in both differential and integral form and be able to transform from one to the other using Gauss's theorem.
  • Appreciate the physical significance of curl and its relationship to circulation via Stokes's theorem in simple examples.
  • Solve common PDE's (particularly the Laplace, Poisson, heat conduction and wave equations) with simple boundary conditions by the method of separation of variables.
  • Solve the diffusion (heat conduction) equation using the self-similar solutions method.

Content

The course provides an introduction to vector calculus and aims to familiarise the student with the ideas of the differential calculus (the vector gradient, divergence and curl) and the integral calculus (line, surface and volume integrals and the theorems of Gauss and Stokes). The physical interpretation of the mathematical ideas will be stressed throughout via applications which centre on the derivation and manipulation of the common partial differential equations of engineering. The analytical solution of simple partial differential equations by the method of separation of variables will also be discussed.

A knowledge of the following Part IA lecture material on functions of more than one variable will be assumed: representation of curves and surfaces (including parametric representation); partial differentiation; total and perfect differentials; Taylor series; maxima and minima.

The course will then consist of lectures on the following topics:

Vector functions and fields; field lines.

Vector differentiation; differentiation formulae.

The vector gradient and its physical interpretation;

Cylindrical and spherical polar co-ordinate systems.

The divergence and its physical interpretation; solenoidal fields; conservation statements;

Surface integrals; volume integrals; Gauss's divergence theorem; integral-differential transformations. Stokes's theorem.

The curl and its physical interpretation; irrotational fields; scalar potential; line integrals; conservative fields.

Types of PDE and boundary conditions; solution by separation of variables; examples of some common PDE's (Laplace, Poisson, heat conduction, wave equation). Solution of the diffusion (heat conduction) equation by the self-similar solution method.

Booklists

Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

 
Last modified: 05/06/2025 11:17

Engineering Tripos Part IB, 2P6: Fourier Transforms & Signal and Data Analysis, 2025-26

Course Leader

Prof I Lestas

Lecturer

Dr F Mancini

Timing and Structure

Lent Term: 7 lectures Weeks 1-3, 2 lectures, week 4, 1 lecture

Aims

The aims of the course are to:

  • Introduce the Fourier Transform as an extension of Fourier techniques on periodic functions and to see how the Fourier Transform is applied to real problems
  • Introduce discrete Fourier methods and to develop skills in analysing discrete data.

Objectives

As specific objectives, by the end of the course students should be able to:

  • develop the ability to discuss and manipulate signals in terms of their frequency content.
  • relate properties of signals in the time domain to those in the frequency domain.
  • be familiar with the difference in behaviour/properties of continuous signals compared to sampled signals, and the basic rules that apply to the latter.

Content

Introduction and preliminaries

  • Motivation for signal analysis. Examples of typical datasets.
  • Power and energy
  • Revision and extension of delta functions
  • Revision of Fourier series

The Fourier Transform (FT)

  • Mathematical formulation of the FT
  • Interpretation of the FT
  • The inverse Fourier transform (IFT)
  • Some important Fourier transforms

Properties of the Fourier Transform

  • Linearity and scaling
  • Time and frequency shifts (modulation)
  • Duality, Parseval's Theorem, convolution
  • Relationship to Laplace transforms

Sampling Theory

  • The sampling theorem and aliasing
  • The discrete time Fourier transform
  • Signal reconstruction and the Nyquist frequency

The Discrete Fourier Transform

  • Derivation of DFT and inverse DFT
  • Examples of using the DFT
  • The spectrogram

Booklists

Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 05/06/2025 11:17

Engineering Tripos Part IB, 2P6: Communications, 2025-26

Course Leader

Prof I Lestas

Lecturer

Prof Ramji Venkataramanan

Timing and Structure

7 lectures: 1 in week 5, 2 per week in weeks 6-8

Aims

The aims of the course are to:

  • Introduce the basic elements of typical communication systems.
  • Provide an understanding of bandwidth, as it applies to signals and transmission channels.
  • Discuss digitisation of signals and how it affects their properties.
  • Understand the basic elements of analogue and digital modulation schemes.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Describe the key elements of a communication system.
  • Understand analogue modulation, and discuss the merits of amplitude and frequency modulation, and their power and bandwidth requirements.
  • Understand how digitisation affects the characteristics of a signal; in particular, the separate effects of sampling (in time) and quantisation (in amplitude).
  • Analyse the trade-off between quantisation rate and the quality of digital representation.
  • Understand the basic principles of digital modulation, be familiar with the design choices involved, and analyse the performance of modulation schemes in terms of error probability and data rates.
  • Understand the need for coding, and encode and decode bits using simple error-correcting codes such as repetition and Hamming codes

Content

Signals and Channels

  • Key signal properties (Energy, Power, Bandwidth)
  • Communication channels and some simple channel models

Analogue Modulation

  • Amplitude modulation
  • Frequency modulation

Digitisation of Analogue Signals

  • Digitisation of signals (sampling, quantisation)

Digital Communication

  • Basics of Baseband modulation, Passband modulation
  • Data rate, probability of detection error
  • Introduction to coding: Repetition codes and Hamming codes

Multiple Access

  • Frequency-division, Time-division, and Code-division multiple access

Booklists

Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 05/06/2025 11:17

Engineering Tripos Part IB, 2P6: Linear Systems and Control, 2025-26

Course Leader

Prof I Lestas

Lecturer

Prof I Lestas

Timing and Structure

Weeks 1-4 and 7-8, 2 lectures/week. Weeks 5-6, 1 lecture/week. 14 lectures.

Aims

The aims of the course are to:

  • Introduce and motivate the use of feedback control systems.
  • Introduce analysis techniques for linear systems which are used in control, signal processing, communications, and other branches of engineering.
  • Introduce the specification, analysis and design of feedback control systems.
  • Extend the ideas and techniques learnt in the IA Mechanical Vibrations course.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Develop and interpret block diagrams and transfer functions for simple systems.
  • Relate the time response of a system to its transfer function and/or its poles.
  • Understand the term 'stability', its definition, and its relation to the poles of a system.
  • Understand the term 'frequency response' (or 'harmonic response'), and its relation to the transfer function of a system.
  • Interpret Bode and Nyquist diagrams, and to sketch them for simple systems.
  • Understand the purpose of, and operation of, feedback systems.
  • Understand the purpose of proportional, integral, and derivative controller elements, and of velocity feedback.
  • Possess a basic knowledge of how controller elements may be implemented using operational amplifiers, software, or mechanical devices.
  • Apply Nyquist's stability theorem, to predict closed-loop stability from open-loop Nyquist or Bode diagrams.
  • Assess the quality of a given feedback system, as regards stability margins and attenuation of uncertainty, using open-loop Bode and Nyquist diagrams.

Content

 

Section numbers in books

 

(1)

(2)

(3)

Examples of feedback control systems. Use of block diagrams. Differential equation models. Meaning of 'Linear System'.

1.1-1.11, 2.2-2.3

1.1-1.3, 2.1-2.6.1

1.1-1.8, 3.1-3.5, 3.18

Review of Laplace transforms. Transfer functions. Poles (characteristic roots) and zeros. Impulse and step responses. Convolution integral. Block diagrams of complex systems.

2.4-2.6

3.1-3.2

3.8-3.14, 4.1-4.8, 6.1-6.2, 7.1-7.8

Definition of stability. Pole locations and stability. Pole locations and transient characteristics.

5.6, 6.1

3.3-3.4, 4.4.1

5.1-5.2, 6.4

Frequency response (harmonic response). Nyquist (polar) and Bode diagrams.

8.1-8.3

6.1

6.5, 11.2, 11.5, 15.1-15.5

Terminology of feedback systems. Use of feedback to reduce sensitivity. Disturbances and steady-state errors in feedback systems. Final value theorem.

4.1-4.2, 4.4-4.5

4.1

9.2, 9.5

Proportional, integral, and derivative control. Velocity (rate) feedback. Implementation of controllers in various technologies.

10.6, 12.6

4.2

 

Nyquist's stability theorem. Predicting closed-loop stability from open-loop Nyquist and Bode plots.

 9.1-9.3

 6.3

 11.10

Performance of feedback systems: Stability margins, speed of response, sensitivity reduction.

6.3,8.5, 9.4, 9.6, 12.5, 12.8-12.9

6.4, 6.6, 6.9

10.4, 11.11, 13.2, 15.6-15.7

 

REFERENCES

(1) DISTEFANO, J.J., STUBBERUD, A.R. & WILLIAMS, I.J. FEEDBACK AND CONTROL SYSTEMS
(2) FRANKLIN, G.F., POWELL; J.D. & EMAMI-NAEINI, A. FEEDBACK CONTROL OF DYNAMIC SYSTEMS
(3) OPPENHEIM, A.V., WILLSKY, A.S. & NAWAB, S.H. SIGNALS AND SYSTEMS
(4) ÅSTRÖM, K.J. & MURRAY, R.M. FEEDBACK SYSTEMS: AN INTRODUCTION FOR SCIENTISTS AND ENGINEERS
(5) DORF, R.C. & BISHOP, R.H. MODERN CONTROL SYSTEMS

Booklists

Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 05/06/2025 11:17

Engineering Tripos Part IB, 2P5: Electromagnetic Fields and Waves, 2025-26

Course Leader

Prof A Flewitt

Lecturer

Prof A Flewitt

Timing and Structure

Weeks 5-8 Lent term. 8 lectures, 2 lectures/week

Aims

The aims of the course are to:

  • To understand what a transmission line is, and how by analysing an equivalent circuit for a short length of the line allows us to understand wave propagaion along the line.
  • To understand the Maxwell Equations of Electric and Magnetic Fields which allow us to understand the propagation of electromagnetic waves through free space and how such waves interact with other conducting and insulating materials.
  • To understand how antennas can be used to both transmit and receive free space electromagnetic waves.
  • To appreciate how we can engineer the propagation of waves in free space and along transmission lines with a focus on communications applications.

Objectives

As specific objectives, by the end of the course students should be able to:

  • To be able to create and solve a wave equation for an ideal transmission line from an equivalent circuit and appreciate how this differs in a lossy transmission line.
  • To understand the characteristic impedance of a transmission line, and be able to use this to solve problems involving reflection and transmission of waves along transmission lines.
  • To understand the physical significance of the Maxwell Equations and how the differential (vector calculus) form can be produced from the integral form.
  • To use the Maxwell Equations to produce a wave equation for the free-space propagation of electromagnetic waves and deduce their behaviour (e.g. direction of propagation relative to the E and H field, the Poynting vector).
  • To understand the basic operation of antennas, how to calculate the field around a sinple antenna, antenna figures of merit and how to use these to design simple transmitted and receiver circuits..
  • To use the intrinsic impedance to understand how electromagnetic waves are reflected and transmitted at interfaces with dielectics
  • To understand how electromagnetic waves interact with conductors.

Content

Transmission Lines

  • What is a transmission line?
  • Ideal transmission line equivalent circuit
  • The Telegrapher's Equations
  • The wave equation solution to the Telegrapher's Equations
  • Expressions for current and voltage waves
  • Description of how waves propagate along transmission lines.
  • Importance of the wavelength in considering whether wave effects on a line need to be considered
  • The 'lossy' transmission line equivalent circuit and how this affects wave propagation
  • Characteristic impedance
  • Reflections from a load impedance
  • Input impedance of a terminated line
  • Ringing

 

The Maxwell Equations in Integral and Differential (Vector Calculus) Form

  • The Gauss Law of Electric Fields
  • The Gauss Law of Magnetic Fields
  • The Faraday Law of Magnetic Fields
  • The Ampère-Maxwell Law

Electromagnetic Waves in Dielectrics

  • Derivation of wave equation for electric and magnetic fields from the Maxwell Equations
  • Expressions for the electric and magnetic fields in plane electromagnetic waves
  • Intrinsic impedance
  • The power in an electromagnetic wave and the Poynting Vector

Antennas

  • What is an antenna and a description of how they work
  • How to calculate the field around a simple dipole antenna
  • Figures of merit for antennas including the Antenna Gain, Radiation Resistance and Effective Area

Electromagnetic Waves at Interfaces

  • Boundary conditions: the conservation of E, D, H and B at interfaces
  • Polarised plane electromagnetic waves
  • Reflection and refraction of plane waves
  • Polarisation by reflection and the Brewster Angle
  • Anti-reflection coatings

Electromagnetic Waves in Conducting Media

  • Derivation of wave equation for electric and magnetic fields from the Maxwell Equations
  • Expressions for the electric and magnetic fields in plane electromagnetic waves
  • The Skin Effect
  • Intrinsic impedance of a conducting medium
  • Waves at conducting interfaces

Booklists

Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

 
Last modified: 05/06/2025 11:17

Pages

Subscribe to 2025-26