Introduction to partial differential equations, its degree and order. Classification of partial differential equations to canonical form, parabolic, hyperbolic and elliptic, heat equation, wave equation and Laplaces equation. Separation of variables, Legendre and Bessel equations. Homogeneous and non-homogeneous equations. Canonical forms of the first and second order.



Laplace transformation, Fourier series.



Initial-Boundary value problems.



Fourier transforms and Greens functions.



References:

1. Boyce, W.E., & DiPrima, R.C. (2005). Elementary Differential Equations and Boundary Value Problems (8th Edition). Wiley & Sons.

2. Zauderer, E. (2006). Partial Differential Equations of Applied Mathematics (3rd Edition). Wiley & Sons.

3. DuChateau, P., & Zachmann, D. (2002). Applied Partial Differential Equations. Dover Publications.