|Unit level:||Level 1|
|Teaching period(s):||Semester 2|
|Offered by||School of Mathematics|
|Available as a free choice unit?:||N
To provide a second-semester course in calculus and algebra to students with A-level mathematics or equivalent in school of MACE.
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.
- 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%
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.
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)
- Lectures - 24 hours
- Tutorials - 11 hours
- Independent study hours - 65 hours