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MEng Mechanical Engineering with Industrial Experience

Year of entry: 2021

Course unit details:
Mathematics 1M2

Unit code MATH19662
Credit rating 10
Unit level Level 1
Teaching period(s) Semester 2
Offered by Department of Mathematics
Available as a free choice unit? No

Aims

To provide a second-semester course in calculus and algebra to students with A-level mathematics or equivalent in school of MACE.

Learning outcomes

Knowledge and understanding: Be familiar with second order ordinary differential equations, partial differentiation, series and limits, partial differential equations and matrices.

Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.

Transferable skills and personal qualities: Have a set of tools and methods that can be applied in the courses given in the host school or in subsequent years.

Syllabus

5 Lectures: Second-order Ordinary Differential Equations. Linear Equations with constant coefficients; homogeneous and non-homogeneous cases; complementary functions and particular integrals, Special cases with non-constant coefficients.

3 Lectures: Partial Differentiation. Chain rule for partial differentiation. Total derivatives. Theory of errors. Coordinate Systems (Cartesian, Cylindrical, Spherical), change of variables.

3 Lectures: Series and Limits. Definition of Limits. L'Hopital's Rule. Sequences and Series; convergence; Power Series, Taylor and Maclaurin Series.

3 Lectures: Functions of Two Variables. Maxima, minima and saddle points. Taylor Series in Two variables.

3 Lectures: Second-order partial differential equations (wave, heat/diffusion, Laplace/Poisson. Solution by separation of variables.

4 Lectures: Matrices and Determinants: Definition of an m x n matrix. Matrix addition, subtraction, multiplication by a scalar, matrix multiplication; square matrices, determinants and properties; Solution of equations; inverse matrices.

3 Lectures: LinearAlgebra: LU Decomposition; solution of simultaneous equations; Gaussian Elimination; Cholesky's method.

Assessment methods

Method Weight
Other 20%
Written exam 80%

Coursework 1 (week 5); Weighting within unit 10%

    Coursework 2 (week 10); Weighting within unit 10%

    End of semester 2 examination; Weighting within unit 80%

Recommended reading

KA Stroud, Engineering Mathematics, Palgrave

E Kreyszig, Advanced Engineering Mathematics, Wiley

A Croft and R Davison, Mathematics for Engineers, Prentice Hall

HELM (Helping Engineers Learn Mathematics)

Study hours

Scheduled activity hours
Lectures 24
Tutorials 11
Independent study hours
Independent study 65

Teaching staff

Staff member Role
Colin Steele Unit coordinator

Additional notes

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  

Please see Blackboard / course unit related emails for any further updates

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