Mathematical Techniques 2 (MT2 | SPA4122)

Year: 1 | Semester: B | Level: 4 | Credits: 15

Course organiser: Dr Marcella Bona | Course deputy: Dr Jeanne Wilson

Synopsis:

Further techniques of mathematics needed in the physical sciences. Complex numbers and hyperbolic functions. Polar and spherical coordinates and coordinate transformations. Multiple integrals. Line and surface integrals. Vector algebra. Vector calculus. The theorems of Gauss, Green and Stokes. Matrices. Determinants. Eigenvalues and eigenvectors. Fourier series and transforms including the convolution theorem. Differential equations. Computer algebra (Mathematica) is used in the practical classes to enable the students to learn a professional physicists approach to real problem-solving.

Aims:

The aim of this course is to teach essential mathematical skills which are necessary for a wide range of work in physics

Outcomes:

By the end of this course, a student would be expected to be able to: understand and use basic complex analysis, in particular the symbol 'i', multiplication, graphical representation, polar form, exponential form and roots; have a familiarity with hyperbolic functions and their relationship with trigonometric functions; have a familiarity with double and triple integrals, polar and spherical coordinates, line and surface integrals and coordinate transformations; use and understand the meaning of scalar and vector quantities, vector components, addition, direction cosines, scalar and vector products, angle between vectors, vector differential operators, div, grad and curl and properties; comprehend matrices, their order and type, operations, inverse and transpose, symmetry, orthogonality, Hermiticity and unitarity, determinants, eigenvalues and eigenvectors, use in solving linear systems of equations; know the elements of Fourier expansions, coefficient formulae, applications and the convolution theorem; be able to solve simple, linear first and second order differential equations; have a working knowledge of the use of the Mathematica package for solving mathematical problems, basic syntax and techniques, sources of error, cross-checking, simple applications, use in more complicated problems arising in all the above subjects.

Recommended books:

Stroud, K.A.
Engineering Mathematics 7th Ed.
Palgrave, (2007)
ISBN 978-1-4039-4246-3
&
Stroud, K.A.
Advanced Engineering Mathematics 4th Ed.
Palgrave,
ISBN 1-4039-0312-3
&
Riley, K.F.; Hobson, M.P.; Bence, S.J.
Mathematical Methods for Physics and Engineering; Cam Uni Press (2006) 
ISBN 0-521-67971-0