| 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 focuses on a set of important mathematical techniques that are extensively used in a various Physics鈥� topics, such as multiple integrals, transformation of coordinates, Green鈥檚 theorem, Divergence theorem, Stokes鈥� theorem and orthogonal curvilinear coordinates. The theoretical framework is discussed in full, with an emphasis on their applications through the use of various examples chosen from topics in the year of study, primarily focusing on electromagnetism. Study-unit Aims: The objective of this study-unit is for the candidate to be apply to learn and apply various mathematical techniques in a diversity of Physics鈥� topics. This will be achieved by outlining the key principles of the technique, by solving various problems using the technique, and explore its use in a given practical situation in order to construct a stronger link between theory and application. This will help the candidate to better identify when and how to use these analytical methods. More specifically the study-unit will cover the following topics: - An introduction to Integration in multiple dimensions (Cartesian and Polar Coordinates) and their application in Physics; - A discussion on cylindrical and spherical polar coordinates; - An introduction to scalar and vector fields, 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鈥檚 theorem; - The statement and use of the Divergence theorem; - The statement and use of Stokes鈥� theorem; - A brief introduction to the use and properties of the Dirac Delta function; - An overview of Fourier transforms. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - To be able to carry out double and triple integration and apply them to their application in Physics; - State an expression for the gradient, divergence, curl and Laplace operators in Cartesian coordinates; - Distinguish between scalar and vector potentials; - State and use Green鈥檚 theorem and its application to circulation and flux; - State and use the Divergence theorem and its application to flux and amount of a conserved quantity; - State and use Stokes鈥� theorem and its application to circulation and flux; - Define the Fourier and inverse Fourier transform. 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 Jacobian of a transformation; - Use the Jacobian to transform the integration variables of double and triple integrals; - Evaluate the gradient, divergence, curl and Laplace operators and apply them in various physical applications; - Solve problems involving scalar and vector potentials; - Evaluate line integrals and its relation to work done of a particle along a path; - Distinguish between conservative and non-conservative vector fields, and its relation to obtaining scalar potentials; - Use Green鈥檚 theorem to solve problems; - Use the Divergence theorem to solve problems; - Use Stokes鈥� theorem to solve problems; - Determine the Fourier transform and the inverse Fourier transform; - Use the Dirac Delta function and its properties to evaluate integrals. Main Text/s and any supplementary readings: Main Texts: - 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 2025/6. It may be subject to change in subsequent years. |
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