Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. You'll learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavors involving reasonably smooth, predictable changes of measurable quantities. Basis partial differential equations enable you not only to find solution of many PDEs, but also to interpret and use these solutions. If offers 600 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Over 280 examples are worked out in detail. Applications include heat conduction, wave propagation fluid flow, electrostatics, quantum mechanics, minimal surfaces, gravitation, and vibrations of strings, square drums, round drums and spheres. This book should be of interest to undergraduate and postgraduate students taking mathematics courses.