## ENGINEERING MATHEMATICS

 SHE Level 1 SCQF Credit Points 10.00 ECTS Credit Points 5.00 Module Code M1H323563 Module Leader Faridon Amdjadi School School of Computing, Engineering and Built Environment Subject Mechanical Engineering Trimester B (January 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, complex numbers, matrices, differentiation and integration.

### 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 equation , quadratic equations, simultaneous linear equations and partial fractions. Functions: Linear, parabolic, exponential and logarithmic functions including their graphs, application of logarithms and their laws, solving equations involving logarithms and exponents. Complex Numbers : R ectangle form, addition, subtraction, multiplication, division, of complex numbers, graphical representation (the Argand diagram), polar form (multiplication and division). Matrix Algebra: Manipulation including addition, subtraction, multiplication, transpose, determinants. Differentiation: Derivatives of standard functions; Product, quotient and chain rules; Integrations: Standard integrals involving algebraic, trigonometric, exponential and logarithmic functions; integration by substitution, integration using partial fractions, integration by parts, definite integrals.

### 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;- describe and manipulate complex numbers in Cartesian and polar forms;- describe and manipulate matrices, determinant of 2 by 2 and 3 by 3 matrices;- differentiate mathematical expressions by using standard rules;- integrate mathematical expressions by using standard rules.

### 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. 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
Assessment (PT) 8.00
Independent Learning (PT) 44.00
Lectures (PT) 24.00

### Assessment Methods

Component Duration Weighting Threshold Description
Exam (School) 2.00 30.00 35% A time limited online tests-week 6
Exam (Exams Office) 2.00 70.00 35% Final Exam