Partial differential equations : classical theory with a modern touch /
A. K. Nandakumaran, P. S. Datti.
- 1 online resource (xix, 356 pages) : digital, PDF file(s).
- Cambridge - IISc series .
- Cambridge - IISc series. .
Title from publisher's bibliographic system (viewed on 20 May 2020).
First-order partial differential equations : method of characteristics -- Hamilton-Jacobi equation -- Conservation laws -- Classification of second-order equations -- Laplace and Poisson equations -- Heat equation -- One-dimensional wave equation -- Wave equation in higher dimensions -- Cauchy-Kovalevsky theorem and its generalization -- A peep into weak derivatives, Sobolev spaces and weak formulation.
Suitable for both senior undergraduate and graduate students, this is a self-contained book dealing with the classical theory of the partial differential equations through a modern approach; requiring minimal previous knowledge. It represents the solutions to three important equations of mathematical physics - Laplace and Poisson equations, Heat or diffusion equation, and wave equations in one and more space dimensions. Keen readers will benefit from more advanced topics and many references cited at the end of each chapter. In addition, the book covers advanced topics such as Conservation Laws and Hamilton-Jacobi Equation. Numerous real-life applications are interspersed throughout the book to retain readers' interest.