Clearing 2022

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# BEng Mechanical Engineering with Management

Year of entry: 2022

## Course unit details:Mathematics 1M2

Unit code MATH19662 10 Level 1 Semester 2 Department of Mathematics 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%

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