Mathematical Methods in Physics

Code	14964
Year	3
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Physics
Entry requirements	None
Learning outcomes	Complement and reinforce mathematics training, notably in areas required for full understanding of classical and modern theoretical physics topics.
Syllabus	1 - Fourier transforms Complex Fourier series. Fourier transform. Inverse transformation. Parseval's Theorems and Convolution Theorem. Fourier integral theorem. Dirac Delta function. 2 - Partial differential equations Cylindrical and spherical coordinates Differential operators Separation of variables Wave equation Laplace and Poisson equations Diffusion equation Green functions 3 - Special Functions Sturm-Liouville problem Legendre, Hermite and Laguerre polynomials Bessel functions.
Main Bibliography	1. Arfken GB, Weber HJ, Harris FE (2012). Mathematical Methods for Physicists, 7th ed. New York: Academic Press 2. Braun M (1993). Differential Equations and Their Applications, 4th ed. New York: Springer 3. Cantrell CD (2000). Modern Mathematical Methods for Physicists and Engineers. New York: Cambridge University Press 4. Ramos M (2011). Curso Elementar de Equações Diferenciais, 3.ª ed. Lisboa: Universidade de Lisboa 5. Riley KF, Hobson MP, Bence JS, Mathematical Methods fpr Physics and Engineering, 3rd ed, New York: Cambridge University Press
Language	Portuguese. Tutorial support is available in English.