EN1090: Engineering Analysis
|School||Cardiff School of Engineering|
|External Subject Code||H100|
|Number of Credits||20|
|Language of Delivery||English|
|Module Leader||Dr Emmanuel Brousseau|
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
- Demonstrate knowledge and understanding of differential and integral calculus
- Display an understanding of matrices and matrix algebra
- Understand basic complex numbers and their applications
- Understand elementary statistical analysis and probability, via the interpretation, formulation and solution of mathematical and engineering problems.
- Demonstrate the ability to apply integration to solve a variety of engineering problems
- Understand the concepts and techniques required for solving differential equations
- Understand the concept and application of Fourier series
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
- Apply the basic principles of differential and integral calculus in the solution of mathematical and engineering problems.
- Apply matrix algebra in the solution of simultaneous equations
- Apply basic complex numbers in the solution of numerical problems
- Apply the basic principles of probability theory and statistical analysis in an engineering context.
- Application of integration in solving variety of numerical/engineering problems
- Apply partial differentiation to find stationary values of functions with more than one variable
- Solve first and second order differential equations
- Calculate Fourier series representation of standard waveforms
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 five optional questions, covering all the material taught.
There is a potential for re-assessment in this module which may result in a 100% written assessment during the August Resit period.
|Class Test||10||Engineering Analysis Test||N/A|
|Examination - Spring Semester||90||Engineering Analysis||3|
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.
Definition as a limit; product, quotient and chain rules; differentiation of algebraic, trigonometric, exponential, hyperbolic, logarithmic, inverse, implicit and parametric functions; higher derivatives.
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.
Introduction to matrices and matrix algebra. Solving simultaneous equations using matrix algebra.
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, 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.
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.
The Euler formulas and alternative formulas for Fourier coefficients.
Half-Range expansions and simple applications of Fourier series.
Essential Reading and Resource List
Engineering Mathematics from K A Stroud and D J Booth
Background Reading and Resource List
Mathematical Methods for Science Students
G Stephenson (Longman))
K A Stroud (Macmillan)
C W Evans (Chapman & Hall)
Mathematics for Engineers and Scientists
A Jeffrey (Van Nostrand Rheinhold)
A Croft, R Davidson, M Hargreaves (Addison-Wesley)
Modern Engineering Mathematics
G James et al (Addison-Wesley)
D J Booth (Addison-Wesley)
Engineering Mathematics Exposed
M Attenborough (McGraw Hill)