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# A Comprehensive Guide to Partial Differential Equations by Evans: Second Edition PDF.RAR Mega Download

## Partial Differential Equations by Lawrence C. Evans: A Review

If you are looking for a comprehensive, modern, and clear text on partial differential equations (PDE), you should definitely check out Partial Differential Equations by Lawrence C. Evans. This is the second edition of the now definitive text on PDE, which offers a survey of various techniques and methods in the theoretical study of PDE, with a particular emphasis on nonlinear equations. In this article, I will review this book and explain why it is a great resource for anyone interested in learning more about PDE.

## What is this book about?

PDE are equations that involve partial derivatives of unknown functions with respect to several variables. They arise naturally in many fields of mathematics, physics, engineering, biology, economics, and more, as they can model various phenomena such as heat, sound, waves, fluid flow, electromagnetism, quantum mechanics, etc. PDE are also very challenging to analyze and solve, as they often require sophisticated tools from analysis, geometry, algebra, topology, and numerical methods.

This book provides an introduction to the theory of PDE, covering both classical and modern topics such as:

• The basic concepts and examples of PDE

• The representation formulas for solutions using integrals and transforms

• The theory for linear PDE such as Laplace's equation, heat equation, wave equation, etc.

• The theory for nonlinear PDE such as Hamilton-Jacobi equations, conservation laws, nonlinear wave equations, etc.

• The variational methods and calculus of variations for PDE

• The Sobolev spaces and functional analysis for PDE

• The regularity and existence theory for elliptic PDE

• The maximum principle and comparison principle for PDE

• The weak solutions and distribution theory for PDE

• The viscosity solutions and optimal control theory for PDE

The book also includes more than 80 new exercises, several new sections, a new chapter on nonlinear wave equations, and a significantly expanded bibliography.

## Who is the author of this book?

The author of this book is Lawrence C. Evans, who is a professor of mathematics at the University of California, Berkeley. He is a leading expert in the field of PDE and has made many contributions to the theory of nonlinear PDE, especially in the areas of viscosity solutions, optimal transportation, mean curvature flow, geometric measure theory, etc. He has also written several other books on PDE and related topics, such as Weak Convergence Methods for Nonlinear Partial Differential Equations, Differential Equations: Methods and Applications, Measure Theory and Fine Properties of Functions, etc. He has received many honors and awards for his research, such as the AMS Steele Prize, the SIAM von Neumann Prize, the Bôcher Memorial Prize, the Bergman Prize, etc. He is also a fellow of the American Academy of Arts and Sciences, the American Mathematical Society, and the Society for Industrial and Applied Mathematics.

## Why is this book important and useful?

This book is important and useful for several reasons:

### The advantages of this book over other texts on PDE

There are many other texts on PDE available, but this book stands out for its:

• Wide scope and depth: The book covers a large range of topics in PDE, from the basic to the advanced, from the classical to the modern, from the linear to the nonlinear, from the analytical to the numerical. It also provides a lot of details and explanations for the proofs and techniques used in PDE.

• Clear exposition and style: The book is written in a clear, concise, and rigorous manner, with a lot of examples, figures, remarks, and intuition. The author also uses a friendly and engaging tone, making the book enjoyable to read and easy to follow.

• Balance between theory and applications: The book emphasizes both the theoretical aspects and the practical applications of PDE. It shows how PDE can model various phenomena in science and engineering, and how they can be solved using various methods. It also explains the underlying mathematical concepts and principles behind PDE, and how they can be generalized and extended to other situations.

### The intended audience and prerequisites for this book

This book is intended for graduate students and researchers in mathematics, physics, engineering, and other related fields who want to learn more about PDE. It can also be used as a textbook for a graduate course in PDE or as a reference for self-study.

The prerequisites for this book are:

• A solid background in undergraduate mathematics, especially in real analysis, complex analysis, linear algebra, ordinary differential equations, etc.

• A familiarity with some basic topics in PDE, such as separation of variables, Fourier series, Fourier transform, Green's functions, etc.

• A willingness to learn new concepts and techniques in PDE, such as Sobolev spaces, weak solutions, viscosity solutions, etc.

### The features and organization of this book

This book has several features that make it user-friendly and helpful for learning PDE:

• Each chapter begins with an introduction that summarizes the main goals and results of the chapter.

• Each section ends with a list of exercises that test the understanding and application of the material covered in the section.

• Each chapter ends with a list of references that provide further reading and sources for the topics covered in the chapter.

• The book has an extensive index that allows easy access to the terms and concepts used in the book.

• The book has a website that provides additional resources such as errata, solutions to selected exercises, supplementary notes, etc.

The book is organized into four parts:

• Part I: Representation Formulas for Solutions. This part covers some basic methods for finding explicit or implicit formulas for solutions of PDE using integrals and transforms. It includes topics such as fundamental solutions, Green's functions, Poisson's formula, Duhamel's principle, Fourier series, Fourier transform, Laplace transform, etc.

Part II: Theory for Linear Partial Differential Equations. This part covers some general theory for linear PDE such as existence, uniqueness, regularity, stability, etc. It includes topics such as well-posed problems, energy methods 71b2f0854b