CODE  PHY2210  
TITLE  Mathematics for Physicists 2  
LEVEL  02  Years 2, 3 in Modular Undergraduate Course  
ECTS CREDITS  4  
DEPARTMENT  Physics  
DESCRIPTION  This studyunit discusses a number of important mathematical techniques that are used in a number of physics topics. These include multiple integrals, transformation of coordinates in multiple integrals, Green’s theorem, Gauss’ theorem, Stokes’ theorem and orthogonal curvilinear coordinates. The theoretical framework behind this mathematical techniques is discussed in full. However, the emphasis will be on their applications through the use of various examples. These examples will preferentially be chosen from physical applications creating a link between this topic and the other units where the mathematical techniques are used. Studyunit Aims: The objective of this studyunit is to teach the candidate a number of mathematical techniques that find application in a number of physics topics. This will be carried out by first outlining the theory behind the mathematical methods. Then the techniques will be applied on a number of different examples. The examples will preferentially be derived from physical applications to create a link between the theory and the practical application. This is meant to teach when and how to use these mathematical techniques. More specifically the study will provide:  A discussion on cylindrical and spherical polar coordinates;  An introduction to line integrals, double integrals, triple integrals and multiple integrals;  An introduction to the use and properties of the Kronecker Delta and the Dirac Delta function;  An introduction to Fourier transforms;  A discussion on the use of the Jacobian for the transformation of coordinates in multiple integrals;  An introduction to vector operators including the gradient, divergence, curl and Laplace operators together with their uses;  The statement and use of Green’s theorem;  The statement and use of Gauss’ (Divergence) theorem;  The statement and use of Stokes’ theorem;  An introduction potential theory including the notion of scalar and vector potentials;  An introduction to the property and use of orthogonal curvilinear coordinates;  A discussion on Green's function;  A discussion on series and limits. Learning Outcomes: 1. Knowledge & Understanding By the end of the studyunit the student will be able to:  state an expression for the gradient, divergence, curl and Laplace operators in Cartesian coordinates;  state Green’s theorem;  state Gauss’ (Divergence) theorem;  state Stokes’ theorem;  distinguish between scalar and vector potentials;  distinguish between converging and non converging series. 2. Skills By the end of the studyunit the student will be able to:  evaluate line, surface and volume integrals as well as general double and triple integrals;  determine the Fourier transform and the inverse Fourier transform;  determine the Jacobian of a transformation;  use the Jacobian to transform the integration variables of a double and a triple integrals;  evaluate the gradient, divergence, curl and Laplace operators;  use the Kronecker Delta to solve problems;  use the Dirac Delta function and its properties to evaluate integrals;  use Green’s theorem to solve problems;  use Gauss’ theorem to solve problems;  use Stokes’ theorem to solve problems;  transform coordinates between different orthogonal curvilinear coordinates including Cartesian, cylindrical and spherical polar coordinates;  solve problems involving scalar and vector potentials;  determine the Green's function and use it to find solutions to differential equations. Main Text/s and any supplementary readings: Recommended textbooks:  Arfken, G. ``Mathematical Methods for Physicists'', seventh Edition, Acamedic Press, New York (2003). Supplementary readings:  Riley, K. F., Hobson, M. P. and Bence, S. J. ``Mathematical Methods for Physics and Engineering: A Comprehensive Guide'', third edition, Cambridge University Press (2006) 

ADDITIONAL NOTES  PreRequisite qualifications: Follows from: An advanced level in Mathematics; PHY1125  
STUDYUNIT TYPE  Lecture  
METHOD OF ASSESSMENT 


LECTURER/S  Iman Farhat 

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and StudyUnit information are complete and uptodate at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the studyunit description above applies to the academic year 2019/0, if studyunit is available during this academic year, and may be subject to change in subsequent years. 