EX1001 Engineering Mathematics 1
20 Credits Level HE1
Rationale
Mathematical methods form an indispensable tool of modern Engineering. The module is intended to support
the teaching of engineering modules throughout the programme, to enhance the analytical skills of students
and to highlight relevant engineering applications.
Educational Aims
To support the teaching of engineering modules with strong analytical content.
To enhance the analytical and modelling skills of students.
To motivate the comprehension of advanced analytical concepts which are important in Engineering.
To emphasise the importance of the analytic approach to the solution of engineering problems.
Indicative Content
 Functions of one real variable: definition, domain, range; odd, even, periodic; polynomials, factorisation;
rational functions, partial fractions; exponential and logarithmic functions; circular and hyperbolic
functions; inverse functions, composite functions; limits and continuity.
 Differentiation: definition, chain rule, implicit, parametric, product rule; stationary values, points of
inflection, curve sketching; Cartesian and polar co-ordinates; Maclaurin and Taylor expansions,
polynomial approximation; l'Hopital's rule.
 Functions of two real variables: definition, partial differentiation, total derivative, differential.
 Complex numbers: definition, conjugate, operations with complex numbers; roots of complex numbers,
de Moivre's theorem.
 Matrices and determinants: definition, types of matrices; matrix-operations-I (equality, addition,
subtraction, multiplication by scalar, multiplication by matrix, transposition), determinants (definition,
properties, minors, cofactors); matrix-operations-II (adjoint, inverse, elementary transformations),
solution of system of equations with matrix inversion.
 Vectors in three dimensions: Definition, types of vectors; vector-operations-I (equality, addition,
subtraction, multiplication by scalar), vector components, Cartesian coordinate system (coordinates,
magnitude, direction cosines, unit vectors); vector-operations-II (scalar or dot product, vector or cross
product, scalar triple product); lines and planes, curves, tangents, velocity and acceleration.
 Integration: definition, the indefinite integral, the definite integral, the definite integral as an area and as a
summation, standard integrals, methods of integration (by substitution, of special form, by partial
fractions, by parts, reduction formulae), the definite integral revisited (properties, area under a curve,
length of an arc, surfaces and volumes of revolution), numerical integration (the trapezium rule and
Simpson’s rule).
 Ordinary differential equations: introduction-examples, definitions, first order differential equations
(existence of solutions, initial and boundary value problems, directly integrable, separable, reduced to
separable, exact), first order linear differential equations (integrating factor), second order linear
differential equations (homogeneous and nonhomogeneous differential equations, existence and
uniqueness of solutions), second order differential equations with constant coefficients (solutions of
homogeneous and nonhomogeneous differential equations, the method of undetermined coefficients).
Reading List
1) ENGINEERING MATHEMATICS, K.A. Stroud (PALGRAVE, 5TH EDITION)
2) ADVANCED ENGINEERING MATHEMATICS, K.A. Stroud (PALGRAVE, 4TH EDITION)
3) FURTHER ENGINEERING MATHEMATICS, K.A. Stroud (PALGRAVE, 3RD EDITION)
4) MODERN ENGINEERING MATHEMATICS, G. James (PRENTICE HALL, 3RD EDITION)
5) ENGINEERING MATHEMATICS, A. Croft, R. Davison, M. Hargreaves (PRENTICE HALL, 3RD
EDITION)
6) MATHEMATICS FOR ENGINEERS: A Modern Interactive Approach, A. Croft, R. Davison,
(PRENTICE HALL)
7) MATHEMATICAL TECHNIQUES: W. D. Jordan and P Smith, (OXFORD UNIVERSITY PRESS)
8) ADVANCED MODERN ENGINEERING MATHEMATICS, G. James, (PRENTICE HALL)
9) ADVANCED ENGINEERING MATHEMATICS, E Kreyszing, (WILEY)
10) MATHEMATICAL METHODS FOR SCIENTISTS AND ENGINEERS, D.A. McQuarrie,
(UNIVERSITY SCIENCE BOOKS)
11) Maths for Engineers (CD-ROM)
12) The Open University videos (in Library)
Teaching Pattern
Teaching Component
Lecture
Tutorial
Module Assessment
Assessment Element
Exam (unseen)
Coursework
Contact Hours
40 (+20)
20
Element Pass Mark
40
40
Total Student Learning
Hours
80 (+20)
120
Self Directed Study
Hours
60 (+20)
80
Weighting %
70
30
Module Pass Mark
40