Partial Differential Equations

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.

• Highlights the importance of studying the equations outside the realm of classical solutions
• Separate chapters on advanced topics such as the Hamilton-Jacobi equation and conservation laws
• Explains the interplay between geometry and analysis in the existence and uniqueness of solutions in the treatment of first order equations