## MATHEMATICS 2B

 SHE Level 2 SCQF Credit Points 10.00 ECTS Credit Points 5.00 Module Code M2H324340 Module Leader Faridon Amdjadi School School of Computing, Engineering and Built Environment Subject Mechanical Engineering Trimesters B (January start) A (September start) C (May start)

### Pre-Requisite Knowledge

Expected: Maths 2A

### Summary of Content

This module aims to study the following mathematical topics which are fundamental to the applications of mathematics to engineering problems. Laplace transforms , linear first and second order systems of differential equations, Fourier series.

### Syllabus

Laplace transform: Definition, linear property; inverse Laplace transform; the first shifting theorem; transformation of derivatives; application to solve 1 st and 2 nd ODE's; unit step function and its Laplace transform; second shifting theorem; Dirac delta function and its Laplace transform; convolution. Linear systems of ODE's: Real eigenvalues and eigenvectors of the matrices up to 3 rd order; repeated eigenvalues, complex eigenvalues; digonalisation of the matrices; solving the linear systems of 1 st and 2 nd order ODE's using diagonalisation method. Fourier series: Piecewise periodic functions; determination using analytical and numerical techniques; frequency spectrum.

### Learning Outcomes

On completion of this module the student should be able to:- use table to determine Laplace Transforms and inverse Laplace Transforms;- manipulate unit step function;- apply Laplace Transforms to solve 1st and 2nd order linear constant coefficient ordinary differential equations, possibly containing unit step or Dirac delta functions;- determine the (real, complex) eigenvalues and eigenvectors of a matrix up to order 3;- determine the solution to systems of ordinary differential equations using diagonalisation (matrix) methods;- use Matlab in solving mathematical questions;- define the Fourier series of a piecewise periodic function;- determine Fourier coefficients;- determine frequency spectrum.

### Teaching / Learning Strategy

Traditional lectures will be supported by tutorials . Lectures will deliver the module syllabus and tutorials used for developing mathematical manipulation skills for exploring applications (which can be expected to continue into private study) . Directed study will require the undertaking of specified tutorial material; the completion or extension of the exercises covered in tutorials; and the opportunity for the student to dig deeper through identified 'advanced' topics. The continuous assessment will be in the form of online tests, using GCU learn and feedback will be given immediately. The lectures delivery will be enhanced by using the new technology such as surface with a stylus pen.

CROFT A AND DAVISON R: Mathematics for Engineers, 3rd edition, Addison Wesley, 2010. K.A. STROUD, DEXTER J. BOOTH: Advanced Engineering Mathematics, Palgrave Macmillan, ISBN 978-0-8311-3449-5, 2011. MUSTOE L R AND BARRY M D J: Mathematics in Engineering & Science, Wiley, ISBN 047 197 093X, 1998. BIRD J O: Engineering Mathematics, Newnes, 2nd edition, 1996.

### Transferrable Skills

D2 Critical thinking and problem solving; D3 Critical analysis; D5 Numeracy; D8 Self confidence, self discipline & self reliance (independent working); D9 Awareness of strengths and weaknesses

### Module Structure

Activity Total Hours
Independent Learning (FT) 43.00
Assessment (FT) 8.00
Practicals (FT) 1.00
Tutorials (PT) 24.00
Lectures (PT) 24.00
Independent Learning (PT) 44.00
Lectures (FT) 24.00
Tutorials (FT) 24.00
Assessment (PT) 8.00

### Assessment Methods

Component Duration Weighting Threshold Description
Exam (School) 2.00 30.00 35% 2 time limited online tests (each test 2 hours)-week 6 and week 10
Exam (Exams Office) 2.00 70.00 35% Final Exam