Partial Differential Equations I: Basic Theory

This book is a comprehensive introduction to partial differential equations, covering basic examples and developing tools for their solution. It is targeted at graduate students and professional mathematicians interested in PDEs, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition expands the material and includes new theorems and applications.

Format: Hardback
Length: 714 pages
Publication date: 11 December 2023
Publisher: Springer International Publishing AG

This comprehensive three-volume set delves into the realm of partial differential equations (PDEs), presenting foundational examples from diverse fields such as continuum mechanics, electromagnetism, complex analysis, and more. It develops a diverse array of analytical tools, including Fourier analysis, distribution theory, and Sobolev spaces, enabling the solution of these complex equations. These tools are then applied to tackle fundamental problems in linear PDEs, encompassing the Laplace equation, heat equation, wave equation, as well as broader elliptic, parabolic, and hyperbolic equations.

The primary audience for this book includes advanced graduate students in mathematics, as well as professional mathematicians with a keen interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.

The third edition of this text takes the material to new heights by incorporating numerous groundbreaking theorems and applications throughout. It further strengthens the connections between concepts across chapters, enriching the overall understanding of the subject matter.

In addition to the core content, the third edition includes expanded coverage of topics such as rigid body motion, probabilistic results related to random walks, operator theory in quantum mechanics, overdetermined systems, and the Euler equation for incompressible fluids. The appendices have also been thoroughly revised, presenting additional results ranging from weak convergence of measures to the curvature of Kahler manifolds.

Michael E. Taylor, a renowned Professor of Mathematics at the University of North Carolina, Chapel Hill, NC, has authored this authoritative text. His extensive expertise and clear writing style make it an invaluable resource for students and scholars alike.

Review of the first edition:

"These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted." (Peter Lax, SIAM review, June 1998)

Weight: 1376g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031338588
Edition number: 3rd ed. 2023