Introduction to Partial Differential Equations

__This textbook is designed for a one year course covering the fundamentals of partial differential equations, aimed towards advanced undergraduates and beginning graduate students. It features examples and exercises connected to real world problems.

Many interesting examples and exercises that are connected to real world problems balanced with well explained theory Provides an excellent reading course for undergraduate partial differential equations Treats both linear and nonlinear partial differential equations Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material

Autorentext

Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests are centered on the development of symmetry-based methods for differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research journals as well as 4 other books, including the definitive Springer graduate text, Applications of Lie Groups to Differential Equations, and another undergraduate text, Applied Linear Algebra.

Inhalt
What are Partial Differential Equations?.- Linear and Nonlinear Waves.- Fourier Series.- Separation of Variables.- Finite Differences.- Generalized Functions and Green's Functions.- Complex Analysis and Conformal Mapping.- Fourier Transforms.- Linear and Nonlinear Evolution Equations.- A General Framework for Linear Partial Differential Equations.- Finite Elements and Weak Solutions.- Dynamics of Planar Media.- Partial Differential Equations in Space.