Partial Differential Equations

eman ta zabal zazu	The University of the Basque Country			Theoretical Physics
2008-2009		Partial Differential Equations

Function spaces and expansions in orthogonal functions. Boundary condition problems. Sturm-Liouville theory.
Fourier series and Fourier transforms.
Introduction to Partial Differential Equations. Boundary problems and separation of variables. Solution of boundary problems by integral transforms.
Classification and the method of characteristics. First order equations.
Green's functions and perturbation methods.
Asymptotic methods. Asymptotic series. Saddle-point method. Steepest descent. Stationary phase method. WKB approximations.
Probability and statistics Introduction to probability. Basic discrete distributions. Probability distributions. Moments. Functions of a random variable. Characteristic function. Introduction to statistics and hypothesis testing.

BIBLIOGRAPHY (common to all groups)

Textbooks:

K. F. Riley, M. P. Hobson, and S.J. Bence Mathematical Methods for Physics and Engineering Cambridge University Press (2nd ed. 2002))
M. D. Greenberg Foundations of applied mathematics Prentice-Hall (1978)
J. Mathews and R.L. Walker Mathematical methods of physics Benjamin (1970)
H.F. Weinberger Ecuaciones diferenciales en derivadas parciales Reverté (1986)
J. M. Aguirregabiria Fisika ikasleentzako ekuazio diferentzial arruntak UPV/EHU (2000)
W. E. Boyce y R. C. DiPrima Ecuaciones diferenciales y problemas con valores en la frontera 4[tm] Ed., Limusa (1998)
L. Elsgoltz Ecuaciones diferenciales y calculo variacional URSS (1994)
P. Z. Peebles Probability, random variables, and random signal principles McGraw-Hill (1987)

Tables

M. R. Spiegel y L. Abellanas Fórmulas y Tablas de Matemática Aplicada Schaum McGraw-Hill (1999)
I. Bronshtein y K. Semendiaev Manual de Matemáticas Mir (1993). Handbook of Mathematics Springer (1997)