Partial Differential Equations: Methods and Applications (2nd Edition)

Designed to prepare readers to better understand the current literature in research journals, this book explains the basics of classical PDEs and a wide variety of more modern methods—especially the use of functional analysis—which has characterized much of the recent development of PDEs. It gives equal treatment to elliptic, hyperbolic, and parabolic theory, and features an abundance of applications to equations that are important in physics and engineering—both on the basic and more advanced level. Provides worked, figures and illustrations, and extensive references to other literature. First-Order Equations. Principles for Higher-Order Equations. The Wave Equation. The Laplace Equation. The Heat Equation. Linear Functional Analysis. Differential Calculus Methods. Linear Elliptic Theory. Two Additional Methods. Systems of Conservation Laws. Linear and Nonlinear Diffusion. Linear and Nonlinear Waves. Nonlinear Elliptic Equations. Appendix on Physics. For anyone using PDEs in physics and engineering applications.

• Partial Differential Equations (Graduate Studies in Mathematics)
• The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Dover Civil and Mechanical Engineering)
• Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)
• Real Analysis: Modern Techniques and Their Applications
• Partial Differential Equations: An Introduction
• Numerical Methods for Conservation Laws
• Schaum's Outline of Advanced Calculus, Third Edition (Schaum's Outlines)
• Scientific Computing
• Real Analysis for Graduate Students, Second Edition
• Elementary Differential Geometry, Revised 2nd Edition