# Engineering Mathematics 2

## Module summary

Module code: MATH1145
Level: 5
Credits: 15
School: Engineering and Science
Department: Engineering
Module Coordinator(s): ENG & SCI TBA

## Specification

MATH1143

### Aims

To build on skills developed at level 4, strengthen and extend students’ mathematical skills and enable them to appreciate the use of mathematics as a tool to solving engineering problems.

### Learning outcomes

On successful completion of this module a student will be able to:
1 Demonstrate understanding of relevant mathematical concepts
2 Identify relevant mathematical tools for the solution of s specific problem
3 Apply mathematical tools and numerical techniques to the solution of engineering problems

### Indicative content

Vector Calculus: addition, subtraction, multiplication, dot product, cross product, divergence of vectors, vector projection on a plane, vector equations of lines and planes, complex numbers’ algebra, Loci problem, (properties, De Moivre’s theorem, vectors amplitude and phase)
Matrix algebra: addition, subtraction, multiplication, trace, determinant, linear equations, linear transformations, decompositions, eigenvalues and eigenvectors, the polynomial method, the power method and inverse power method, application to vibration problems, introduction to tensors (with applications to stress and strain tensors)
Series expansion around a point- Taylor’s series
Integration applications: volumes of solids of revolution, moment of inertia, parallel axis theorem, centre of pressure, multiple integrals
Numerical Methods for Ordinary Differential Equations: first order ODEs (linear ODEs, integral factor method, initial value problem, exponential decay, Newton’s cooling law, Bernoulli’s equation, second order ODEs, (homogenous equations, non-homogeneous equations, order reduction, state-space formulation, undamped and damped oscillations), Euler’s method, the mid-point method, modified Euler’s method, and the 4th order Runge-Kutta method, step size and accuracy, finite difference method for solving higher order ordinary differential equations.
Numerical Method for Partial Differential Equations: partial differentiation, application of separation of variable method to first order and second order PDEs, finite difference method, truncation errors.
Laplace transform: definition, examples, transfer functions, stability of systems, application to solution of ODEs and PDEs
Fourier transform: Fourier series (discrete domain), definition, examples, link to Laplace transform, frequency domain, applications to SDOF
Computer Modelling Techniques: Application of MATLAB for engineers and scientific problems.
Statistics and Probability

### Teaching and learning activity

Concepts and methods will be introduced and demonstrated in lectures. Students will build up their understanding and competence by applying the methods they have learnt in tutorials. Take home exercises will form part of the assessment through regular submissions of a logbook. Timed assessment will be used at regular intervals to ascertain students’ progress, provide feedback and extra support if needed.

### Assessment

Logbook - 30%
LO - 1, 2, 3.
Pass mark - 40%
1500words.
Solved exercises.

Exam - 70%
LO - 1, 2, 3.
Pass mark - 40%
2 hours.
Closed book exam.

All elements of summative assessment must be passed to pass the module.

Nature of FORMATIVE assessment supporting student learning:
Timed assessment will be used to gauge students’ progress and provide feedback.