Differential and Integral Equations
This book serves as a guide to undergraduate courses in ordinary and partial differential equations. It contains the basic theory of ordinary differential equations (existence and uniqueness theorems), the variation of parameters method and the correspondence between differential and integral equations. Concerning partial differential equations, the book introduces the reader to first and second order partial differential equations, the reduction of the more general elliptic, parabolic and hyperbolic equations to the Laplace equation, the heat equation and the wave equation, together with classical results on these three basic equations. Some additional methods are then presented (including the Neumann series expansion for integral equations, the power series method, the Fourier transform method and the phase-plane analysis). There is also an introduction to the calculus of variations. The book is very well arranged. Every section is followed by many examples and exercises for better understanding of the topic. Theorems are usually not formulated in the strongest possible form, which increases the comprehensibility of the text. The book is intended not only for students of mathematics but also for students of physics, economics and other fields where differential equations play an important role.