# Engineering

## ECM1104 - Engineering Mathematics B (2010)

MODULE TITLE CREDIT VALUE Engineering Mathematics B 30 ECM1104 Ms Aileen MacGregor (Coordinator), Dr Khurram Wadee, Dr Krisztian Kohary
DURATION: TERM 1 2 3
DURATION: WEEKS
DESCRIPTION - summary of the module content
AIMS - intentions of the module
The purpose of this module is to extend students' mathematical skills to the level necessary to complete a BEng or MEng engineering degree programme. This module takes students deeper than they are likely to have gone before in mathematics. It covers topics which are fundamental to engineers in their professional careers. In particular a greater emphasis is placed on the direct application of mathematics to engineering problems.
INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
Note: List A comprises core outcomes that will be covered fully in lectures and must be achieved by all students to meet the minimum university requirement for progression. List B comprises outcomes that are EITHER more difficult to achieve OR are to be achieved by private study (or both). All outcomes will be assessed, and coverage of List B outcomes is essential for both BEng and MEng students. A: THRESHOLD LEVEL[ Elementary algebra, evaluation of expressions, brackets, factorising, solving quadratic equations, partial fractions, inequalities, sigma notation, subscripts Matrices: Notation, elementary matrix operations and properties, determinants, the inverse of a matrix, solving linear problems using matrices. Functions: trigonometric, exponential, logarithmic, hyperbolic, inverse functions. Trigonometric identities, limits, series. Differentiation of basic functions, product rule, quotient rule, minima and maxima, function of a function, chain rule, equations of tangents and normals, curve sketching, Maclaurin and Taylor Series. Elementary vector algebra, addition, subtraction, scalar product, vector product, equation of a line. Elementary complex numbers, addition, subtraction, multiplication and division, polar form, de Moivre's theorem, roots of equations, logarithms. Trapezium and Simpson’s Rule. Integration of basic functions. First and second order ordinary differential equations. Initial and boundary conditions. Partial differentiation: Definitions, chain rule, small errors, maxima and minima of functions of two variables. Further integral calculus: Double integrals, repeated integrals, change of order of integration. Probability. Mutually exclusive and independent events. Sum and product rule. Conditional probability, Venn & tree diagrams B: GOOD TO EXCELLENT Differentiation, application to optimisation and maxima and minima and rate of change problems. Further vector algebra, vector equation of a plane. Integration by substitution, integration by parts (not requiring special techniques) applications to centroids, volumes of revolution, centres of mass. Baye’s theorem
SYLLABUS PLAN - summary of the structure and academic content of the module
Algebra and functions. Differential calculus and applications. Vector algebra. Complex numbers. Integration. First and second order ordinary differential equations. Matrices. Partial differentiation. Further integral calculus. Complex variables.
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 50 50
DETAILS OF SUMMATIVE ASSESSMENT
The final module mark awarded will be the better of: 50% of the final examination mark, plus 30% of the end of semester 1 test mark, plus 20% of the total assignments and MathCad marks. or 80% of the final examination mark, plus 20% of the total assignments and MathCad marks.
DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
RE-ASSESSMENT NOTES
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener