Autumn Semester

Unit(s) of Assessment	Weighting Towards Module Mark( %)
Written examination	50%
Coursework	50%
Qualifying Condition(s)   A weighted aggregate mark of 40% is required to pass the module

Engineers rely heavily on mathematical models to solve engineering problems and must have knowledge of a range of techniques to solve these. This is a first level engineering mathematics module designed for students in need of greater assistance than normal (e.g. as identified by initial diagnostic test, or with entry qualifications not quite at full A level Maths standard).The module starts at a lower level than the standard ENG1001, but with higher contact hours and greater staff support brings students to the same level as ENG1001 on completion of the module.

Special entry requirements for Engineering degree – e.g. AS Maths grade A/B or equivalent, or normal entry requirement to degree course in Engineering but poor maths diagnostic test result.

For students starting from an AS level base in Mathematics, to consolidate and extend students' knowledge of basic mathematical concepts and techniques relevant to the solution of engineering problems, to make students aware of possible pitfalls, to enable students to select appropriate methods of solution, to bring students up to standard required to rejoin main cohort on ENG1002.

On successful completion of the module , you should developed competence and confidence in:

·                   Algebraic and trigonometric manipulation

·                   manipulating and graphing standard functions

·                   using complex numbers

·                   using the techniques of differential and integral calculus for functions of one variable

·                   applying integration to determine physical engineering properties (e.g. in mechanics)

·                   manipulation of simple series.

·                   presenting & summarising simple statistical data graphically and numerically

• evaluating simple probabilities

Arithmetic, Algebra and Simple Trigonometry: 

·                   Revision of number systems and arithmetic operation

·                   Basic algebra, power laws . Algebraic manipulation, simplification of rational expressions, the Remainder Theorem,  algebraic division; Partial fractions

·               Solution of linear, quadratic equations and simultaneous linear       equations

·                   Revision of basic trigonometry, trigonometric identities. Double angle formulae and formulae for sin (A+B) etc.

Functions:

·                   Functions, domain, range, graph sketching, incl. straight line, circle

·                   Composition of functions. Piecewise defined functions. Odd, even and periodic functions.

·                    Inverse functions

·                   The exponential and logarithm functions

·                   The trigonometric functions and inverse trigonometric functions. Solution of trig equations

·                   Hyperbolic functions

Sequences and Series:

·                   Binomial expansions and factorial notation

·                   Arithmetic sequences and series. Geometric sequences and series

Complex Numbers:

·                   Definition and use of j and complex conjugate 

·                   Arithmetic operations with complex numbers 

·                   Fundamental Theorem of Algebra 

·                   Modulus and argument of a complex number and their properties. Polar and exponential representations of a complex number . Relationship between trigonometric and hyperbolic functions 

·                   De Moivre’s Theorem

Differentiation: 

·                   Limits 

·                   Definition of a derivative 

·                   Techniques of differentiation such as the product rule, the quotient rule, the chain rule 

·                   Differentiation of a range of functions e.g trigonometric, exponential and logarithmic  

·                   Implicit,  parametric and logarithmic differentiation 

·                   Higher derivatives 

·                   Applications of differentiation to equations of the tangent, local maxima, minima and points of inflection, rates of change and related rates of change 

·                   Maclaurin and Taylor series, 

·                   L’Hopitals’ rule 

·                   Newton Raphson method

Integration: 

·                   Indefinite integration as the reverse of differentiation 

·                   Definite integration interpreted as the area under a curve 

·                   Techniques of integration incl. substitution, integration by parts & using partial fractions 

·                   Applications of integration to the area between curves.

·                   Numerical integration using the Trapezium rule

·                   Application of integration to curve lengths, surfaces and volumes of revolution, first moments and centroids, second moments and radii of gyration.

Probability and statistics:

·                   Descriptive statistics: numerical and graphical summaries. 

• Basic Probability: elementary laws, random variables, mean and variance. 

48 hours lectures, 24 hours supervised tutorial sessions, and 26hours independent learning; 2 hour written examination. Coursework assessment will involve 3 class tests and assessment of tutorial work and progress.

James G, Modern Engineering Mathematics, 4th edition (or earlier), Prentice-Hall, 2008 (ISBN 978-0-13-239144-3)

Stroud KA and Booth D.J., Engineering Mathematics, 6^th edition (or earlier), Palgrave Macmillan, 2007. (ISBN 978-1-4039-4246-3)

Attenborough MP, Engineering Mathematics Exposed, McGraw-Hill, 1994. (ISBN 00770 79752)