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Engineering: mathematics, modelling, applications

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This module builds on the engineering concepts and basic mathematics in Engineering: origins, methods, context (T192) and Engineering: frameworks, analysis, production (T193). Throughout the initial eight weeks, your study will strengthen and consolidate your skills and knowledge in already visited topics to ensure you have a robust foundation of numeracy and algebra essential for new concepts. Next, you’ll explore the techniques of trigonometry, calculus, complex numbers and matrices in the context of engineering examples such as motion, heat transfer and basic statics and electricity. You’ll finish the module with guided revision and develop exam techniques in preparation for the final examination.

What you will study

Mathematics is an essential component of engineering and forms the foundation of many engineering analysis techniques and concepts. The material you’ll study builds on your earlier study, as well as introducing several completely new mathematical concepts. All new mathematical methods in algebra, geometry, trigonometry, complex numbers, differential and integral calculus and matrices will be introduced and their application within an engineering context demonstrated.

Part 1: The language of mathematics – You’ll develop and cement your knowledge of the fundamentals of mathematics that have been introduced in Engineering: origins, methods, context (T192) and Engineering: frameworks, analysis, production (T193). In addition to learning mathematical concepts, you’ll learn how to correctly write and present mathematical content as well as how to read and interpret mathematical arguments. You’ll study topics including, but not limited to: numerical notation; algebra; logarithms and exponentials; solving simultaneous equations; function notation; sigma notation; graphs; and number series.

Part 2: Describing motion and structures with trigonometry and coordinate systems – Next you’ll study concepts required to model and describe engineering structures and systems, including various coordinate systems, trigonometry and vectors. You’ll learn: about Cartesian and polar co-ordinate systems, how to apply them to engineering problems, and how to convert from one to the other; how to model shapes and structures using trigonometry, and the use of vectors and trigonometry to model bodies in motion.

Part 3: Modelling temperature and change using calculus – In this part, you’ll re-engage with the basic calculus met in Engineering: frameworks, analysis, production (T193) and develop your understanding to a level appropriate for describing thermal conditions in simple engineering examples; other examples such as motion will be used to enrich the topic. You’ll learn: mathematical methods for relating displacement, velocity and time; for finding minima and maxima; and for describing harmonic motion. You’ll also develop an understanding of the fundamentals and standard methods in differentiation and integration.

Part 4: Quantifying electricity and mechanics with complex numbers, calculus and matrices – Complex numbers, more advanced calculus, and matrices will form the basis of what you’ll learn in this part. You’ll be introduced to the topics and learn how they can be applied to engineering and to the mathematical concepts you studied in earlier parts. You’ll learn: how to apply and represent complex numbers; the application of calculus to determining rates of change, including heat and temperature; the concept of matrix algebra and its application to solving simultaneous equations.

Part 5: Revision and exam preparation – Finally, time is set aside for you to revisit and practice each topic, with a focus on preparing for the exam. You’ll also develop exam and revision techniques.

Entry requirements

You must have passed (or be studying) Engineering: frameworks, analysis, production (T193) to study this module – you may not study them at the same time.

You’ll be prepared if you’ve passed Engineering: origins, methods, context (T192) and Engineering: frameworks, analysis, production (T193), normally as part of one of our engineering qualifications.

If you have any doubt about the suitability of the module, please speak to an adviser.

What's included

Four module books, module handbook, module map, assessment guide, access to the module website which includes online study material and activities.

You will need

A scientific calculator, basic drawing equipment.

Computing requirements

A computing device with a browser and broadband internet access is required for this module.  Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

A desktop or laptop computer with either:

  • Windows 7 or higher
  • macOS 10.7 or higher

The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

To participate in our online discussion area you will need both a microphone and speakers/headphones. 

Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students. 

Teaching and assessment

Support from your tutor

You'll have a tutor who will help you with the study material and mark and comment on your written work, and whom you can ask for advice and guidance. You'll also be able to receive support from a wider pool of tutors through specialist forums and study events.

We expect to be able to offer group tutorials or day schools that you are encouraged, but not obliged, to attend. Where your tutorials are held will depend on the distribution of students taking the module. Online study events will also be offered.

Contact us if you want to know more about study with The Open University before you register.


The assessment details for this module can be found in the facts box above.

Throughout the module, weekly interactive quizzes will give you an opportunity to practice the mathematical concepts covered in the module. These provide essential practice and preparation for the interactive computer-marked assignments (iCMAs). Assignment questions will be based on activities in the module material and in the practice quizzes.

You must use the online eTMA system to submit your tutor-marked assignments (TMAs).

You’ll be required to attend an examination at an examination venue.

If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying T194 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

Future availability

Engineering: mathematics, modelling, applications (T194) starts once a year – in October. This page describes the module that will start in October 2018. We expect it to start for the last time in October 2024.

Course work includes:

3 Tutor-marked assignments (TMAs)
5 Interactive computer-marked assignments (iCMAs)
No residential school