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.
Bibliography of reference
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.