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College of Engineering, Mathematics and Physical Sciences Intranet

## ECM1103 - Engineering Mathematics A (2010)

MODULE TITLE | Engineering Mathematics A | CREDIT VALUE | 30 |
---|---|---|---|

MODULE CODE | ECM1103 | MODULE CONVENER | Ms Aileen MacGregor (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
---|---|---|---|

DURATION: WEEKS |

Number of Students Taking Module (anticipated) |
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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 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.
Probability.
The use of Mathcad software.

LEARNING AND TEACHING

LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)

Scheduled Learning & Teaching Activities | Guided Independent Study | Placement / Study Abroad |
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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 | 50 | Written Exams | 50 | Practical Exams |
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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 15% of the total worksheets mark, plus 5% of the MathCad mark.
or
80% of the final examination mark, plus 15% of the total worksheets mark, plus 5% of the MathCad mark.

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

information that you are expected to consult. Further guidance will be provided by the Module Convener

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | Stroud, K A | Advanced Engineering Mathematics | 4th | Macmillan | 2003 | 000-1-403-90312-3 | [Library] |

Set | Stroud, K A | Engineering Mathematics | Macmillan | 2007 | 000-0-333-94790-8 | [Library] |

CREDIT VALUE | 30 | ECTS VALUE | 15 |
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PRE-REQUISITE MODULES | None |
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CO-REQUISITE MODULES | None |

NQF LEVEL (FHEQ) | 1 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Thursday 15 December 2011 | LAST REVISION DATE | Thursday 15 December 2011 |

KEY WORDS SEARCH | None Defined |
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