| CODE | PHY2210 | ||||||||||||
| TITLE | Mathematics for Physicists 2 | ||||||||||||
| UM LEVEL | 02 - Years 2, 3 in Modular Undergraduate Course | ||||||||||||
| MQF LEVEL | 5 | ||||||||||||
| ECTS CREDITS | 4 | ||||||||||||
| DEPARTMENT | Physics | ||||||||||||
| DESCRIPTION | This study-unit 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. Study-unit Aims: The objective of this study-unit 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: - An introduction to Integration in multiple dimensions and their application in Physics, Cartesian coordinate system; - Numerical methods for evaluation of double integrals with Continuous Integrands using Python; - A discussion on cylindrical and spherical polar coordinates; - Integration in multiple dimensions; - An introduction to vector transformation, vector operators including the gradient, divergence, curl and Laplace operators together with their uses; - An introduction to vector fields and potential theory including the notion of scalar and vector potentials; - 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 to the property and uses of orthogonal curvilinear coordinates; - An introduction to the use and properties of the Kronecker Delta and the Dirac Delta function; - An introduction to Fourier transforms; - A discussion on Green's function. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit 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 curvilinear coordinates system and cartesian coordinate system; - to be able to use basic double numerical integration Schemes and apply them to their application in Physics. 2. Skills By the end of the study-unit 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: - David J. Griths, Introduction to electrodynamics, third edition (1999), and Edward M. Purcell, Electricity and magnetism. - 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). |
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| ADDITIONAL NOTES | Pre-Requisite qualifications: Follows from: PHY1125 | ||||||||||||
| STUDY-UNIT TYPE | Lecture | ||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Gabriel Farrugia |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date 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 description above applies to study-units available during the academic year 2024/5. It may be subject to change in subsequent years. |
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