England.

# 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). You’ll begin by strengthening and consolidating your skills and knowledge in past topics to ensure you have a solid foundation of numeracy and algebra essential for understanding new concepts. Next, you’ll explore the techniques of trigonometry, calculus, complex numbers and matrices in the context of engineering, such as motion, heat transfer and basic statics and electricity. You'll finish with guided revision and exam technique development.

## 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

To begin T194, you must have passed one of the following:

You may enrol on T194 while still studying T193 or MU123. However, if you do not pass T193 or MU123, we must cancel your enrolment on T194.

## 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

You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Ventura or higher.

Any additional software will be provided or is generally freely available.

To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards, and any modern browser is suitable for most activities.

Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.

It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop, as described above.

## Teaching and assessment

• Marking your assignments (TMAs) and providing detailed feedback for you to improve.
• Guiding you to additional learning resources.
• Providing individual guidance, whether that’s for general study skills or specific module content.
• Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part.

### Assessment

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

## 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.