这本独立的教科书提供了偏微分方程（PDE）的基本介绍，主要关注线性方程，但也通过Hamilton–Jacobi方程、具有可测量系数的椭圆方程和DeGiorgi类，提供了非线性方程的观点。通过实例、问题和解决方案来补充说明，以增强理解并探索相关方向。
本修订版第二版的大部分内容经过了精简和改写，纳入了多年的课堂反馈，纠正了印刷错误，提高了清晰度。这本书可以作为数学、物理、工程和自然科学的高等本科生和研究生的教材，也可以作为应用数学家和数学物理学家的优秀参考。
新增加的最后三章，关于一阶非线性偏微分方程（第8章）、带可测系数的拟线性椭圆方程（第9章）和DeGiorgi类（第10章），指出了当前研究的前沿问题和方向。
第一版评论
作者的意图是介绍PDE的基本介绍…与其他关于PDE的初级教材相比。关于拉普拉斯方程、热和波动方程等三个基本方程，我们将提供更多的资料。演讲内容清晰，组织有序。课文中有大量的练习和证据提示。
——数学评论
这是一篇关于线性偏微分方程的完整的基础介绍。
Partial Differential Equations: Second Edition by Emmanuele DiBenedetto
This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton–Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions.
Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve 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.
The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations.
Reviews of the first edition
The author’s intent is to present an elementary introduction to PDEs… In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace’s equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs.
–-Mathematical Reviews
This is a well-written, self-contained, elementary introduction to linear, partial differential equations.
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