The understanding of more advanced mathematics is important within an engineering curriculum to support and broaden abilities within the applied subjects at the core of all engineering programmes. Students are introduced to additional topics that will be relevant to them as they progress to the next level of their studies, advancing their knowledge of the underpinning mathematics gained in Unit 2: Engineering Maths.

The unit will prepare students to analyse and model engineering situations using mathematical techniques. Among the topics included in this unit are: number theory, complex numbers, matrix theory, linear equations, numerical integration, numerical differentiation, and graphical representations of curves for estimation within an engineering context. Finally, students will expand their knowledge of calculus to discover how to model and solve engineering problems using first and second order differential equations.

On successful completion of this unit students will be able to use applications of number theory in practical engineering situations, solve systems of linear equations relevant to engineering applications using matrix methods, approximate solutions of contextualised examples with graphical and numerical methods, and review models of engineering systems using ordinary differential equations.

Number theory:
Bases of a number (Denary, Binary, Octal, Duodecimal, Hexadecimal) and converting between bases
Types of numbers (Natural, Integer, Rational, Real, Complex)
The modulus, argument and conjugate of complex numbers
Polar and exponential forms of complex numbers
The use of de Moivre’s Theorem in engineering
Complex number applications e.g. electric circuit analysis, information and energy control systems

Matrix methods:
Introduction to matrices and matrix notation
The process for addition, subtraction and multiplication of matrices
Introducing the determinant of a matrix and calculating the determinant for a 2x2 and 3x3 matrix
Using the inverse of a square matrix to solve linear equations
Gaussian elimination to solve systems of linear equations (up to 3x3)

Graphical and numerical methods:
Standard curves of common functions, including quadratic, cubic, logarithm and exponential curves
Systematic curve sketching knowing the equation of the curve
Using sketches to approximate solutions of equations
Numerical analysis using the bisection method and the Newton–Raphson method
Numerical integration using the mid-ordinate rule, the trapezium rule and Simpson’s rule

Differential equations:
Formation and solutions of first-order differential equations
Applications of first-order differential equations e.g. RC and RL electric circuits, Newton’s laws of cooling, charge and discharge of electrical capacitors and complex stresses and strains
Formation and solutions of second-order differential equations
Applications of second-order differential equations e.g. mass-spring-damper systems, information and energy control systems, heat transfer, automatic control systems and beam theory and RLC circuits
Introduction to Laplace transforms for solving linear ordinary differential equations
Applications involving Laplace transforms such as electric circuit theory, load frequency control, harmonic vibrations of beams, and engine governors

A 1500-word problem-based assignment assessing learning outcomes 2 and 3, weighted at 50%.

A 1-hour contextualised examination, assessing learning outcomes 1 and 4, weighted at 50%

Whole group lectures will be used to deliver new material and to consolidate previous material. Small-group tutorials, with activities designed to enhance the understanding of the material delivered in the lectures, will be used to apply the skills and knowledge learned. A mixture of classroom based and practical activities will take place supported by staff. Whole group lectures will be used to deliver new material and to consolidate previous material. Small-group tutorials, with activities designed to enhance the understanding of the material delivered in the lectures, will be used to apply the skills and knowledge learned. A mixture of classroom based and practical activities will take place supported by staff.

Use applications of number theory in practical engineering situations.

Solve systems of linear equations relevant to engineering applications using matrix methods.

Approximate solutions of contextualised examples with graphical and numerical methods.

Review models of engineering systems using ordinary differential equations.

PCs with standard office software, e.g Excel

Scientific Calculators

BIRD, J. (2014) Higher Engineering Mathematics. 7th Ed. London: Routledge.
SINGH, K. (2011) Engineering Mathematics Trough Applications. Basingstoke, Palgrave Macmillan.
STROUD, K.A. and BOOTH, D.J. (2013) Engineering Mathematics. 7th Ed: Basingstoke, Palgrave Macmillan.
Communications on Pure and Applied Mathematics. Wiley.
Journal of Engineering Mathematics. Springer.
Journal of Mathematical Physics. American Institute of Physics.

http://www.mathcentre.ac.uk/ Maths Centre (Tutorials)
http://www.mathtutor.ac.uk/ Maths Tutor (Tutorials)

Must be registered on HNC/D Mechanical Engineering or Electrical and Electronic Engineering provision at South Staffordshire College

The understanding of more advanced mathematics is important within an engineering curriculum to support and broaden abilities within the applied subjects at the core of all engineering programmes. You are introduced to additional topics that will be relevant to you as you progress to the next level of your studies, advancing your knowledge of the underpinning mathematics gained in Unit 2: Engineering Maths.

The unit will prepare you to analyse and model engineering situations using mathematical techniques. Among the topics included in this unit are: number theory, complex numbers, matrix theory, linear equations, numerical integration, numerical differentiation, and graphical representations of curves for estimation within an engineering context. Finally, you will expand your knowledge of calculus to discover how to model and solve engineering problems using first and second order differential equations.

On successful completion of this unit you will be able to use applications of number theory in practical engineering situations, solve systems of linear equations relevant to engineering applications using matrix methods, approximate solutions of contextualised examples with graphical and numerical methods, and review models of engineering systems using ordinary differential equations.