MATHEMATICS 2A

 SHE Level 2 SCQF Credit Points 10.00 ECTS Credit Points 5.00 Module Code M2H323566 Module Leader Faridon Amdjadi School School of Computing, Engineering and Built Environment Subject Mechanical Engineering Trimester A (September start)

Summary of Content

This module aims to study the following mathematical topics which are fundamental to the applications of mathematics in engineering problems. Double integrations, Ordinary differential equations through a variety of analytical and numerical techniques , statics (descriptive and inferential).

Syllabus

Double integrations: Double integrals over rectangular regions; double integrals over general region; changing the order of integration; integration in polar coordinates; applications. Ordinary differential equations: First order, separable equations; linear equations; solving the first order linear equations with the use of integrating factors; second order linear ODEs with constant coefficients; homogeneous equations; initial value problems (first order and second order); non-homogeneous equations; the method of undetermined coefficients; numerical solution of ODEs (Euler method). Statistics: Descriptive statistics: Determine the mean and standard deviation of ungrouped and grouped data; probability distribution; density function and normal distribution; Statistical Inference: Populations and samples; sampling distribution of the mean; point and interval estimation of population mean for large/small samples. One sample Hypothesis testing; Simple regression analysis using Excel.

Learning Outcomes

On completion of this module the student should be able to:- evaluate double integrals expressed in Cartesian form;- interchange the order of integration of a double integral;- convert a double integral from Cartesian to polar form;- solve 1st order separable ODE's;- solve 1st linear and 2nd order linear constant coefficient ordinary differential equations analytically;- solve 1st order ordinary differential equations numerically (Euler method) using Excel;- use Matlab to solve mathematical questions;- apply appropriate tabular and graphical methods of data presentation and calculate and interpret appropriate summary statistics;- calculate continues probabilities using the Normal distribution;- conduct a variety of standard statistical hypothesis tests for one sample problems;- use excel to conduct simple regression analysis.

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

Assessment Methods

Component Duration Weighting Threshold Description
Exam (Exams Office) 2.00 70.00 35% Final Exam
Exam (School) 2.00 30.00 35% 3 online tests in weeks 4, 9 and 12