In this module, you will learn a wide range of mathematical methods and techniques that will enable you to think analytically and solve engineering problems. The topics included are:

Basic mathematics: indices, exponentials, logarithms, transposition of formulae, algebraic fractions, partial fractions, vectors in 2D and 3D, and vector operations.

Trigonometry: trigonometric ratios, their graphs, polar form, combining waveforms.

Complex numbers: polar and exponential form, complex number operations, powers and roots.

Matrices: Introduction, operations on matrices, determinants, solving linear equations including complex coefficients.

Basic probability: rules of probability, conditional probability, prob. distributions- binomial, Poisson and normal.

Basic calculus: theory of differentiation, derivatives of simple functions, applications.

Advanced calculus: theory of integrals, integrals as areas, numerical methods, partial differentiation, stationary points.

A 2-hour Examination (Exam 1) weighted at 50%, assessing learning outcomes 1¿and 2. Meeting AHEP 4 Outcome C1.

A 2-hour Examination (Exam 2) weighted at 50%, assessing Learning Outcomes 3 and 4. Meeting AHEP 4 Outcome C1.

Professional Body requirements mean that a minimum overall score of 40% is required to pass a module, with each element of assessment requiring a minimum mark of 30% unless otherwise stated.

The module will be taught through lectures, small group tutorials, and practical sessions on software to underpin knowledge and illustrate graphical solutions when mathematical techniques are introduced and applied.

A total of 48 hours of contact time will be used. The contact time allocated for this module emphasises an intensive and focused approach to experiential learning. This extended engagement allows you to immerse deeply in the subject matter.

You are expected to engage in 152 hours of independent study where you will prepare for your taught sessions and your assessments. This will also allow you to reflect on your current learning and practices, acquire a deeper knowledge of key mathematical techniques, and start developing ideas generated during the taught sessions.

1. Apply algebraic and trigonometric techniques to solve a wide variety of mathematical problems. (AHEP 4: C1)

Knowledge and Understanding,

Analysis,

Problem Solving

2. Manipulate complex numbers and perform matrix operations. (AHEP 4: C1)

Knowledge and Understanding,

Analysis,

Problem Solving,

Application

3. Learn the use of different probability rules and apply binomial, Poisson and normal probability laws. (AHEP 4: C1)

Knowledge and Understanding,

Analysis,

Problem Solving

4. Use differentiation and integration techniques in mathematical and engineering problems including partial differentiation techniques. (AHEP 4: C1)

Knowledge and Understanding,

Analysis,

Problem Solving,

Application

Blackboard VLE¿

Formula book

Scientific Calculator¿

Bird, J. (2017) Basic Engineering Mathematics, 7th Edition, Routledge, Abingdon.

Singh, K., (2011) Engineering Mathematics through Applications, 2nd Edition, Palgrave Macmillan.

Stroud, K.A. & Booth, D.J. (2020) Foundation Mathematics, 8th Edition, Macmillan Publishers Ltd., Basingstoke.

Mathematical tools play a crucial role in engineering to solve real-world problems. As an engineer, you are expected to have extensive problem-solving skills for the design, innovation, optimisation, precision, and accuracy of systems. In this module, you will encounter a wide variety of mathematical techniques including algebra, trigonometry, complex numbers, matrices, probability theory, and basic and advanced calculus techniques to develop your analytical ability and problem-solving skills essential for engineering study.