EN1090 - Engineering Analysis

SchoolCardiff School of Engineering
Department CodeENGIN0
Module CodeEN1090
External Subject CodeH100
Number of Credits20
LevelL4
Language of DeliveryEnglish
Module Leader Dr Emmanuel Brousseau
SemesterDouble Semester
Academic Year2016/7

Outline Description of Module

To develop the basic mathematical knowledge and intellectual skills appropriate for a modern engineering degree scheme, and the ability to apply such knowledge and skills in an engineering context.

On completion of the module a student should be able to

How the module will be delivered

Lectures, illustrated by formal examples and tutorials, are used to explain the basic principles and applications (three hours per week).

Students are expected to devote a minimum of three hours per week to private study and attempting a comprehensive set of tutorial problems, which form the basis of the example / tutorial classes.

Skills that will be practised and developed

How the module will be assessed

Students are assessed by a 60-minute class test, held during the Autumn semester circa week 11, and by a formal three hour examination at the end of the spring semester.

The class test takes the form of several compulsory questions, covering the material taught to date, and is designed to enable students to evaluate their progress in relation to the specified learning outcomes. Feedback is provided during subsequent example / tutorial classes.

The formal examination consists of one compulsory question and three from six optional questions, covering all the material taught.

Assessment Breakdown

Type % Title Duration(hrs) Period Week
Class Test 10
Engineering Analysis Test
N/A 1 N/A
Examination - Spring Semester 90
Engineering Analysis
3 1 N/A

Syllabus content

Fundamentals of Algebra, Vectors & Functions
Expansion and simplification of algebraic expressions. Introduction to vector addition and multiplication. Review of single and multivariable functions such as polynomials, trigonometry and inverse functions.
Differentiation
Definition as a limit; product, quotient and chain rules; differentiation of algebraic, trigonometric, exponential, hyperbolic, logarithmic, inverse, implicit and parametric functions; higher derivatives.
Integration
Definition of indefinite integral; standard forms, integration by substitution and by parts; rational and irrational functions; algebraic, trigonometric and hyperbolic substitutions; definite and improper integrals.
Matrices
Introduction to matrices and matrix algebra. Solving simultaneous equations using matrix algebra.
Complex Numbers
Complex numbers, rectangular and polar forms, Argand diagrams, principal values, conjugates, exp(jq) = cos q + j sinq, De Moivre`s theorem, roots of complex numbers.

Probability and Statistics
Graphical representation of data; measures of location and dispersion; discrete and continuous frequency distributions; probability and probability distributions; Binomial, Poisson and Normal distributions; basic ideas of significance and confidence limits.
Application of integration
Multiple integrals; areas and moments of area, centroid, radius of gyration; parallel and perpendicular axes theorems; polar co-ordinates; lengths and moments of arcs; surface and volumes of revolution; theorems of Pappus; moments of inertia.
Hyperbolic Functions
Hyperbolic functions, inverse hyperbolic functions and their properties.

Ordinary differential equations
Ordinary differential equations, directly integrable, variable separable, homogeneous and linear equations of first order and degree. Integrating factors. Linear differential equations with constant coefficients, complementary functions and particular integrals.

Partial differentiation
Functions of several variables; partial differentiation, the total derivative, partial differentiation of a function of functions, chain rule, higher partial derivatives. Stationary values of a function of several variables.

Fourier series
Periodic Functions
The Euler formulas and alternative formulas for Fourier coefficients.
Half-Range expansions and simple applications of Fourier series.

Background Reading and Resource List

Mathematical Methods for Science Students
G Stephenson (Longman))         1972/2nd ed.

Engineering Mathematics
K A Stroud (Macmillan)              2013/7th ed.

Engineering Mathematics
C W Evans (Chapman & Hall)     1997/2rd ed.

Mathematics for Engineers and Scientists
A Jeffrey (Van Nostrand Rheinhold) 2005/6th ed.

Engineering Mathematics
A Croft, R Davidson, M Hargreaves (Addison-Wesley) 1996/2nd ed.

Modern Engineering Mathematics
G James et al (Addison-Wesley)  2015/5th ed.

Foundation Mathematics
D J Booth (Addison-Wesley)        1998/3rd ed.

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