Mathematics 1M2


Unit code: MATH19662
Credit Rating: 10
Unit level: Level 1
Teaching period(s): Semester 2
Offered by School of Mathematics
Available as a free choice unit?: N

Requisites

None

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.

Assessment methods

  • Other - 20%
  • Written exam - 80%

Assessment Further Information

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

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

2 hour end of semester 2 examination; Weighting within unit 80%

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.

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

  • Lectures - 24 hours
  • Tutorials - 11 hours
  • Independent study hours - 65 hours

Teaching staff

Colin Steele - Unit coordinator

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