HG1M12 Engineering Mathematics 2 Academic Year: 2009/2010

Total Credits: 10

Level: 1

Teaching semester: Spring 2010 Lecturers:

Dr. K. Harikrishnan Dr. Natanael Karjanto Ms Grace Yap

Module Convenor:

Dr. K. Harikrishnan

Target Students: BEng & MEng at the Faculty of Engineering. Prerequisites: A Study of mathematics which provides fluency in the topics of algebra, geometry, functions-including logarithm and exponential, trigonometry, sequences and series, elementary differential and integral calculus, and vectors as provided by a recent good pass in a GCE A-level Mathematics or pass in the Foundation Year at UNUP, UNMC or UNNc, or equivalent. Corequisites: None Summary of Content: This module introduces the techniques for solving selected first-order and second-order differential equations relevant to the analysis of generic engineering problems. The module also provides mathematical tools in terms of advanced differential calculus and vectors for modeling of generic engineering situations given in terms of multidimensional models: • • • •

vector spaces and their applications; differential calculus of functions of several variables; first-order ordinary-differential equations; second-order linear constant coefficient ordinary equations.

differential

Education Aim: In concert with module HGM11 this module provides a common qualifying year provision to equip students with both the confidence and competence in a range of fundamental elementary mathematical techniques and basis for advance mathematical methods used in the quantitative study and analysis of engineering problems. The module incorporates an increased depth of understanding of mathematical techniques and integrated learning in preparation for follow-on level 2 modules. Module content is coordinated sequentially between HG1M12 and HG1M11.

Method and Frequency of Class: Each week there will normally be two lecture hours and a further hour of worked examples or tutorial problem classes. Method of Assessment: Assessment Type Exam 1 Coursework 1 Inclass Exam 1

Weight (%) 80 10 10

Requirements 2-hour written examination a two-weeks assignment 45 minutes exam (9 MCQs)

Submission of assessed coursework When you submit assessed work, you will normally be asked to fill in an “Assessed Coursework Submission Sheet”, part of which will be detached and given to you as your receipt. Special arrangements may be made for some forms of assessment. This sheet also contains a statement that you have read and understood the guidelines on plagiarism and that the work submitted is your own and does not contain plagiarized material. you might sign this statement in order to receive official credit for your work. Any application (from individual student) for an extension to a mathematics assessed coursework deadline should be made to the appropriate module lecturer, but will only be considered if it is accompanied by a completed Extenuating Circumstances Form (ECF) recording the circumstances giving rise to the request and signed by the student’s tutor. The module lecturer will decide whether or not to grant ant extension and indicate a new dateline (if appropriate) on the coursework script. Calculators and electronic dictionaries The examination rubric only allows the use of calculators with single or dual line display. Graphic calculators will not be permitted. You should therefore familiarize yourself with such a calculator prior to sitting the coursework test and the exam. Graphic calculators may be used in the coursework assignment. Reading Lists 1

James, Glyn. Modern Engineering Mathematics , 4th Edition – August 2007 Pearson – ISB 978-0-13-239144-3.

2

Jordan, D. W. Mathematical techniques: An Introduction for the Engineering, Physical and Mathematical Sciences 3rd Edition, Oxford University Press, 2002.

3

Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, Wiley 2006.

Teaching Plan: Lect 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Topic (approx. timings) Vectors Intro, applications, equality, addition Examples, unit vector, zero vector, multiplication by a scalar, components, position vector Dot product, cross production Triple product, components, equation of a straight line Equation of a plane, angle between planes Moments, differentiation of vectors Calculus of several variables Intro, surfaces, partial derivatives, Notation, second derivatives, examples Taylor Series Stationary points, classification-min/max/sad Least squares, small errors Vector differential, nabla, grad, div Total derivatives, change of variables, chain rule (2&3D) Integration of partial derivatives ODEs Intro, motivation, examples, order, linearity First order ODEs, separable, linear homog First order linear inhomog-Int factor, BCs Exact equations Second order linear homogeneous ODEs with constant coefficients, auxilliary eqn Inhomogeneous case, particular solutions, general solution, boundary conditions, initial conditions Applications Revision

Text- James 4.2.2, 4.2.3, 4.2.1,4.2.2, 4.2.4,

Lecturer

Ms Grace Yap ( 3 weeks )

4.2.7, 4.2.9 4.2.11, 4.3.1 4.3.2 9.5.1 9.6.1, 9.6.2 9.6.7 9.7.1 9.7.2 9.6.9 9.6.3 9.6.5, 9.6.9

10.3.2, 10.3.3, 10.5.3 10.5.9, 10.4.3 9.6.11, 10.5.7 10.9.1 10.9.3

Dr Natanael (4 weeks )

Dr Hari ( 4 weeks )

10.10

2 Courseworks: both around Lecture 14, to cover Secs 1 & 2 of syllabus: (i) take-home assignment– long questions, (ii) in class test - 45 minute MCQ with 9 questions.