Applied Partial Differential Equations

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the sciences. The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains, and applications of PDE's to biology. The text differs from other texts in its brevity; yet it provides coverage of the main topics usually studied in the standard course, as well as an introduction to using computer algebra packages to solve and understand partial differential equations.

This is an accessible book on advanced symmetry methods for partial differential equations. Topics include conservation laws, local symmetries, higher-order symmetries, contact transformations, delete "adjoint symmetries," Noether’s theorem, local mappings, nonlocally related PDE systems, potential symmetries, nonlocal symmetries, nonlocal conservation laws, nonlocal mappings, and the nonclassical method. Graduate students and researchers in mathematics, physics, and engineering will find this book useful.

Drawing on his decade of experience teaching the differential equations course, John Davis offers a refreshing and effective new approach to partial differential equations that is equal parts computational proficiency, visualization, and physical interpretation of the problem at hand.

Numerous significant ideas in applied mathematics have been formulated within the framework of ordinary or partial differential equations, which provides a language for the illustration of these ideas. Through the years, mathematicians and scientists have developed extensions of these methodologies across almost all areas of science and technology. This Special Issue provides an opportunity to showcase recent developments in the many branches of ordinary or partial differential equations in applied mathematics that are related to stochastic, fuzzy, functional, and fractional differential or difference equations in the fields of sciences and engineering.