MATHEMATICS 1A

 SHE Level 1 SCQF Credit Points 10.00 ECTS Credit Points 5.00 Module Code M1H323910 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. Basic algebraic manipulation, partial fractions, functions, trigonometry, engineering waves, complex numbers and matrices

Syllabus

Algebra: Application of algebraic techniques to the manipulation of mathematical expressions including indices, arithmetic of algebraic fractions, simplifying algebraic fractions, factorisation, completing the square, linear equations, quadratic equations, simultaneous linear equations, polynomial division and partial fractions. Functions: Linear, parabolic, exponential and logarithmic functions including their graphs, application of exponential functions, logarithms and their laws, solving equations involving logarithms and exponents, linear and logarithmic scales. Trigonometry: Angles, radian measure, trigonometric identities, solutions of trigonometric equations, trigonometric functions, engineering waves, angular frequency, amplitude, period and frequency, adding waves of the same frequency, phase angle, phase-shift of a wave, Asin ( x+a ) form and the oscilloscope trace . Complex Numbers : R ectangle form, addition, subtraction, multiplication, division of complex numbers, graphical representation (the Argand diagram), polar form (multiplication and division), De Moivre's theorem, roots, exponential forms, phasors. Matrix Algebra: Manipulation including addition, subtraction, multiplication, transpose, inverse of a matrix, determinants.

Learning Outcomes

On completion of this module the student should be able to:- manipulate mathematical expressions, formulae and equations by applying the basic rules of algebra.- solve linear, quadratic and simultaneous equations.- describe and manipulate the algebra used for partial fraction expansions- understand algebraic functions (linear, parabolic, exponential) and logarithmic with their applications in engineering problems.- solve trigonometrical equations with the aid of reference angle and CAST rule.- describe and manipulate engineering waves.- describe and manipulate complex numbers in Cartesian and polar forms, phasors.- describe and manipulate matrices, determinant of 2 by 2 and 3 by 3 matrices, inverse of matrices.

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, 3 rd edition, Addison Wesley, 2010. HOWARD ANTON, IRL C. BIVENS AND STEPHEN DAVIS: Calculus, Wiley & Sons. ISBN: 978-470-39874-6, 2010. 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 (FT) 24.00
Independent Learning (PT) 44.00
Lectures (PT) 24.00
Independent Learning (FT) 44.00
Tutorials (PT) 24.00
Lectures (FT) 24.00
Assessment (FT) 8.00
Assessment (PT) 8.00

Assessment Methods

Component Duration Weighting Threshold Description
Exam (School) n/a 40.00 35% time limited online test week 12
Exam (School) n/a 30.00 35% time limited online test week 4
Exam (School) n/a 30.00 35% time limited online test week 8