Andrei D. Polyanin, Valentin F. Zaitsev
Handbook of Nonlinear Partial Differential Equations
The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering–many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions.
A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity.
Thomas Hillen, I. Ed Leonard, Henry van Roessel
Partial Differential Equations: Theory and Completely Solved Problems
Uniquely provides fully solved problems for linear partial differential equations and boundary value problems
Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences.
The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including:
• Classification of second-order linear PDEs
• Derivation of heat, wave, and Laplace’s equations
• Fourier series
• Separation of variables
• Sturm-Liouville theory
• Fourier transforms
Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources.
Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.
Pavel Drabek, Gabriela Holubova
Elements of Partial Differential Equations
This textbook presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. – An elementary introduction to the basic principles of partial differential equations. – Many illustrations. – Addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics.
Partial Differential Equations: Modelling and Numerical Simulation
For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development.
Andrei D. Polyanin, Valentin F. Zaitsev, Alain Moussiaux
Handbook of First-Order Partial Differential Equations
This handbook is presented in chapters, sections and subsections to aid the reader. Within each subsection the equations are arranged in order of increasing complexity. The book pays special attention to equations of the general form, showing their dependence on arbitrary functions.
It presents equations and their applications; these include differential geometry, nonlinear mechanics, gas dynamics, heat and mass transfer, wave theory and much more.