## MATHEMATICS 1B

 SHE Level 1 SCQF Credit Points 10.00 ECTS Credit Points 5.00 Module Code M1H324325 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 1A

### Summary of Content

This module aims to study the following mathematical topics which are fundamental to the applications of mathematics to engineering problems. Basic concepts of vectors , differentiation , integration (indefinite & definite) and Numerical methods

### Syllabus

Vector Algebra: Cartesian forms in 2 and 3 dimension coordinate systems, manipulation of vectors (addition, subtraction, scalar and vector products), unit vectors, polar forms, applications (work done by a force, the moment of a force, angular velocity). Differentiation: Derivatives of standard functions; Product, quotient and chain rules; equations of tangents and normal to a curve; maximum, minimum and points of inflection; curve sketching using the second derivative; optimisation problems. Partial differentiation of 2 variables functions, Del operator. Integrations: Standard integrals involving algebraic, trigonometric, exponential and logarithmic functions; integration by substitution, integration using partial fractions, integration by parts, definite integrals, the link with integration as area, integration as the limit of a sum. Numerical Methods: Newton's approximation, Maclaurin and Taylor series and numerical integrations (Trapezium and Simpson rules) .

### Learning Outcomes

On completion of this module the student should be able to:- describe and manipulate the algebra used for vectors;- differentiate mathematical expressions by using standard rules;- apply differential calculus to rates of change and use it to solve selected optimisation problems from engineering processes;- use differential calculus for sketching the graphs;- perform partial differentiation;- integrate mathematical expressions by using standard rules;- describe and use integral calculus analytically and numerically and apply it to physical expressions;- use power series to approximate functions;- use Newton's method to solve algebraic equations.

### 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
Assessment (FT) 8.00
Tutorials (FT) 24.00
Lectures (FT) 24.00
Independent Learning (FT) 44.00

### Assessment Methods

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