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Elements of Partial Differential Equations
Partial Differential Equations (PDE) is a very large field of mathematics. Most of the problems originated in the characterization of fields occurring in classical and modern physics such as potential and wave equations associated with gravitation, electromagnetism, and quantum mechanics.
Some books in this subject are quite theoretical, and deal quite extensively with existence proofs such as the necessary and sufficient conditions required for a solution (Example: Courant Hilbert Methods of Mathematical Physics Volume 2, Petrovsky's Lecture on PDE or Sobolev's PDE of Mathematical Physics ), others are much more applied, and oriented towards explaining and illustrating various techniques, that can be used to solve various PDE (Example: Morse Fesbach's Methods of Theoretical Physics, Sommerfeld's PDE or Farlow's PDE for Scientists and Engineers).
The author Ian Sneddon was an outstanding applied mathematician, whose
most outstanding book is Fourier Transform.
The present book is a more modest book, as the title indicates it is anintroduction. The book tends to be towards applied side of PDE, though it
develops the subject using theorems and proofs (and examples). The content of the book is fairly standard, it overlaps with most other PDE books (equations of mathematical physics).
It does not discuss extensively special functions (this topics can be found in many other books), though the reader is invited to get acquainted with these functions through solving problems at the end each chapter (Answers to odd number problems can be found at he end of the book.)
Nor does it discuss the use of generalized functions to solve PDE (he bookwas written in 1957)
There are some topics present, which are usually not included in other books on PDE. I found the discussion on Pfaffian differential equation
and its application to Caratheodory's formulation for the 2nd law of thermodynamics enlightening (those who are familiar with differential forms (see Frankel's Geometry of Physics) may find the exposition somewhat old fashioned, but I think the underlying concept is still the same).
The parts of the book I read, I found quite clear, but still requiring some patience in spite of the fact that I already knew about PDE from other books (in a rather haphazard manner)(there may not be a royal road to PDE)
In summary, this is a sound introduction to PDE. It requires some patience to read, if you are only interested in solving PDE, you will probably find Farlow's better suited for your need.

Global, integrability..
The chapter on first order partial differential equations is an excellent primer on examples of global integrability in dynamical systems theory (including but not restricted to Hamilton-Jacobi theory, driven-dissipative systems are implicitly included), although the word integrability is never mentioned. The rest of the text is ok but fairly standard. I also like and have used the book by Duff (Toronto) but do not find it listed. ... Read more

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