Mathematical Methods of Physics

Year
3
Academic year
2019-2020
Code
01002815
Subject Area
Physics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Elective
Level
1st Cycle Studies

Recommended Prerequisites

Modern Physics, General Physics I and II, Real Analysis I, II and III, Linear Algebra and Analytical Geometry.

Teaching Methods

Topics of the syllabus are developed in lectures; participation of students is  encouraged to develop their critical thinking and ability to understand and relate concepts. Students will be asked to solve proposed problems during practical classes, aiming at clarifying their ideas and uncertainties through the dialogue with colleagues and with the teacher.

Learning Outcomes

Deepening of the knowledge in an essential field for physics: mathematical methods of physics.
Ability to search and use bibliography, organizing a consistent amount of information regarding the mentioned field.
Ability to solve problems, including the development of mathematical competences appropriate for this purpose.
Ability to implement simple simulations concerning the contents of the curricular unit.

Generic competences:

Competences in analysis and summary.
Competences in organization and planning.
Competences in oral and written communication.
Competences in group work.
Competences in critical thinking.
Competences to communicate with people who are not specialists in this field.
Adaptability to new situations.
Concern with quality.
Competences to apply the theoretical knowledge in pratice.

Work Placement(s)

No

Syllabus

1. Introduction to Group Theory
Symmetry and invariance transformations. Discrete and continuous groups. Homomorphisms and isomorphisms. Irreducible and reducible representations. Generators of continuous groups. Structure constants. SO(2), SO(3) e SU(2), Lorentz and Poincaré groups.
2. Complex Analysis
Cauchy-Riemann equations. Cauchy's integral theorem. Taylor and Laurent series. Singularities, poles and branch points. Residue theorem. Cauchy's principal value.
4. Differential equations
Separation of variables and series expansion methods.
5. Dirac's delta functional
Sequences and integral representations. Interpretation and properties.
6. Green's Functions
Definition, physical interpretation and properties.
7. Fourier Series
Convergence, differentiation and integration.
8. Integral Transforms
Fourier and Laplace transforms: properties and usage.
9. Special  Functions
Legendre's functions. Hermite's polynomials. Laguerre's polynomials and  Laguerre's functions.

Head Lecturer(s)

Alexandre Carlos Morgado Correia

Assessment Methods

Assessment
Frequency: 40.0%
Exam: 60.0%

Bibliography

Mathemathical Methods for Physicists, G. Arfken and H. J. Weber, Academic Press, New York, 1995.
Mathematical Methods of Physics, J. Mathews and R. L. Walker, W. A. Benjamin, Menlo Park, California, 1965.