Mathematics is an essential engineering component and forms the foundation of many engineering analysis techniques and concepts. The material you’ll study builds on your earlier study and introduces 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 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 and 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 coordinate 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 how to use 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 use 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, focusing on preparing for the exam. You’ll also develop exam and revision techniques.
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Course work includes:
You’ll have access to a module website, which includes:
We also provide physical:
You can study this module on its own or use the credits you gain towards an Open University qualification.
T194 is a compulsory module in our:
T194 is an option module in our:
Engineering: mathematics, modelling, applications (T194) starts once a year – in October.
It will next start in October 2026.
We expect it to start for the last time in October 2029.
As a student of The Open University, you should be aware of the content of the academic regulations, which are available on our Student Policies and Regulations website.
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