Students are assessed by two 40-minute class test, held during each semester circa week 9, and by a formal three hour examination at the end of the spring semester. In addition, an online assessment during the first weeks in January will be available forming the remainder of the assessment of this module.

\n\n\tThe 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.

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

\n"}, {"rank" : 113, "descriptionName" : {"welshDescName" : "Sut y caiff y modiwl ei gyflwyno", "descriptionCode" : "MAV_DELM", "descriptionName" : "How the module will be delivered"}, "descriptionDetail" : "\n\tLectures, illustrated by formal examples, are used to explain the basic principles and applications (three hours per week).

\n\n\tFormal example / tutorial classes are used to help students apply the knowledge and understanding gained from the lectures (two hours per week).

\n\n\tStudents 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.

\n"}, {"rank" : 111, "descriptionName" : {"welshDescName" : "Disgrifiad Amlinellol or Modiwl", "descriptionCode" : "MAV_DESC", "descriptionName" : "Outline Description of Module"}, "descriptionDetail" : "- \n\t
- \n\t\tTo 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 and to provide an introduction to numerical methods as a tool for solving engineering problems. \n

- \n\t
- \n\t\tDemonstrate knowledge and understanding of differential and integral calculus \n\t
- \n\t\tDisplay an understanding of matrices and matrix algebra \n\t
- \n\t\tUnderstand the concept of series expansions and convergence \n\t
- \n\t\tUnderstand basic complex numbers and their applications \n\t
- \n\t\tUnderstand elementary statistical analysis and probability, via the interpretation, formulation and solution of mathematical and engineering problems. \n\t
- \n\t\tDemonstrate the ability to apply integration to solve a variety of engineering problems \n\t
- \n\t\tUnderstand the concepts and techniques required for solving differential equations \n\t
- \n\t\tUnderstand the concept and application of Fourier series \n\t
- \n\t\tUnderstand the scope offered by numerical techniques for the solution of engineering problems \n

\n\tMathematical Methods for Science Students

\n\tG Stephenson (Longman))

\n\tEngineering Mathematics

\n\tK A Stroud (Macmillan)

\n\tEngineering Mathematics

\n\tC W Evans (Chapman & Hall)

\n\tMathematics for Engineers and Scientists

\n\tA Jeffrey (Van Nostrand Rheinhold)

\n\tEngineering Mathematics

\n\tA Croft, R Davidson, M Hargreaves (Addison-Wesley)

\n\tModern Engineering Mathematics

\n\tG James et al (Addison-Wesley)

\n\tFoundation Mathematics

\n\tD J Booth (Addison-Wesley)

\n\tEngineering Mathematics Exposed

\n\tM Attenborough (McGraw Hill)

- \n\t
- \n\t\tApply the basic principles of differential and integral calculus in the solution of mathematical and engineering problems. \n\t
- \n\t\tApply matrix algebra in the solution of simultaneous equations \n\t
- \n\t\tDetermine the series expansions of mathematical functions and the conditions under which they converge. \n\t
- \n\t\tApply basic complex numbers in the solution of numerical problems \n\t
- \n\t\tApply the basic principles of probability theory and statistical analysis in an engineering context. \n\t
- \n\t\tApplication of integration in solving variety of numerical/engineering problems \n\t
- \n\t\tApply partial differentiation to find stationary values of functions with more than one variable \n\t
- \n\t\tSolve first and second order differential equations \n\t
- \n\t\tCalculate Fourier series representation of standard waveforms \n\t
- \n\t\tApply basic numerical methods to solve engineering problems

\n\t\t \n

\n\tFundamentals of Algebra, Vectors & Function

\n\tExpansion and simplification of algebraic expressions. Introduction to vector addition and multiplication. Review of single and multivariable functions such as polynomials, trigonometry and inverse functions.

\n\tDifferentiation

\n\tDefinition as a limit; product, quotient and chain rules; differentiation of algebraic, trigonometric, exponential, hyperbolic, logarithmic, inverse, implicit and parametric functions; higher derivatives.

\n\tIntegration

\n\tDefinition of indefinite integral; standard forms, integration by substitution and by parts; rational and irrational functions; algebraic, trigonometric and hyperbolic substitutions; definite and improper integrals.

\n\tMatrices

\n\tIntroduction to matrices and matrix algebra. Solving simultaneous equations using matrix algebra.

\n\tInfinite series and expansion of functions

\n\tDefinition of series and simple concepts of convergence; ratio test for general series; power series and expansion of functions; Maclaurin`s and Taylor`s series; series for trigonometric, logarithmic and exponential functions; evaluation of functions.

\n\tComplex Numbers

\n\tComplex numbers, rectangular and polar forms, Argand diagrams, principal values, conjugates, exp(jq) = cos q + j sinq, De Moivre`s theorem, roots of complex numbers.

\n\tProbability and Statistics

\n\tGraphical 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.

\n\tApplication of integration

\n\tMultiple 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.

\n\tHyperbolic Functions

\n\tHyperbolic functions, inverse hyperbolic functions and their properties.

\n\tOrdinary differential equations

\n\tOrdinary 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.

\n\tPartial differentiation

\n\tFunctions 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.

\n\tFourier series

\n\tPeriodic Functions

\n\tThe Euler formulas and alternative formulas for Fourier coefficients.

\n\tHalf-Range expansions and simple applications of Fourier series.

\n\tNumerical Methods

\n\tLinear simultaneous equations - Gauss, Siedel, Jacobi