This self-contained text offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, and also providing some perspective on nonlinear equations. The classical treatment is mathematically rigorous with a generally theoretical layout, though indications to some of the physical origins of PDEs are made throughout. Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, to correct errors and to improve clarity. The exposition is replete with examples, problems and solutions that complement the material to enhance understanding and solidify comprehension. The only prerequisites are advanced differential calculus and some basic Lp theory. The work functions as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists.

Klappentext

This book offers a self-contained introduction to partial differential equations (PDEs), primarily focusing on linear equations, and also providing perspective on nonlinear equations. The treatment is mathematically rigorous with a generally theoretical layout, with indications to some of the physical origins of PDEs. The Second Edition is rewritten to incorporate years of classroom feedback, to correct errors and to improve clarity. The exposition offers many examples, problems and solutions to enhance understanding. Requiring only advanced differential calculus and some basic Lp theory, the book will appeal to advanced undergraduates and graduate students, and to applied mathematicians and mathematical physicists.