## FOUNDATION MATHEMATICS

 SHE Level 1 SCQF Credit Points 10.00 ECTS Credit Points 5.00 Module Code M1H326751 Module Leader Faridon Amdjadi School School of Computing, Engineering and Built Environment Subject Mechanical Engineering Trimester B (January start)-C (May start)

### Summary of Content

This module aims to prepare GA students to take up level 1 mathematics module, by studying the following mathematical concepts: Basic algebraic manipulation, elementary functions, introduction to trigonometry, and introduction to calculus

### Syllabus

Basic 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 2 by 2 systems, polynomial division. Functions: Definition of a function. understand algebraic functions (linear, parabolic); equations and graphs of straight lines and parabolas; logarithms and its laws, introduction to logarithmic and exponential functions Trigonometry: Angles, radian measure, trigonometric identities, solutions of trigonometric equations, trigonometric functions. Differentiation: Definition of the derivative of a function ; interpretation of the derivative of a function; describe differentiation table; determination of the derivatives of x^n , n integer or fractional; derivatives of standard functions; product, quotient and chain rules. Integration: Introduction to indefinite integration of simple functions; sandard integrals involving algebraic, trigonometric, exponential and logarithmic functions; integration by substitution, evaluation of simple definite integrals

### Learning Outcomes

On successful completion of this module, the student should be able to:1. Algebraically manipulate basic mathematical expressions;2. Solve single and simultaneous linear equations, quadratic equations; 3. Describe the Cartesian co-ordinate system, and use it to represent lines and curves- sketch the graphs of basic algebraic equations including those of the straight line, parabola;4. Understand degree and radian measures (angular measures), trigonometrical ratios and trig identities and solve trigonometrical equations;5. Differentiate simple functions; obtain indefinite and definite integrals of basic functions;

### 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 continuous assessment will be in the form of online tests, using Mobius (Maple TA) and feedback will be given immediately after completion of each test.

-567 Books and articles: CROFT A, AND DAVISON R: Mathematics for Engineers, 4th edition, Addison Wesley, 2014. STROUD: Engineering Mathematics, ISBN 9781352010275, Macmillan Education UK, 8th Edition 2020. CROFT A, AND DAVISON R: Foundation Maths, 7th Edition HOWARD ANTON, IRL C. BIVENS AND STEPHEN DAVIS: Calculus, Wiley & Sons. ISBN: 978-470-39874-6, 2010. -567 Online sources: <http://www.mathcentre.ac.uk/> <http://www.mathtutor.ac.uk/> <http://tutorial.math.lamar.edu/> <https://www.intmath.com/> <https://www.khanacademy.org/math>

### Transferrable Skills

By the end of this module students will have gained competence in the following key areas: D1 Specialist knowledge and application D2 Critical thinking and problem solving D3 Critical analysis D4 Communication skills, written, oral and listening D5 Numeracy D7 Computer literacy D8 Self confidence, self discipline & self reliance (independent working) D9 Awareness of strengths and weaknesses

### Module Structure

Activity Total Hours
Independent Learning (FT) 54.00
Tutorials (FT) 24.00
Lectures (FT) 12.00
Assessment (FT) 10.00

### Assessment Methods

Component Duration Weighting Threshold Description
Course Work 01 n/a 100.00 40% Combination of 4 class tests