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4434Partial Differential Equations
http://www.merlot.org/merlot/viewMaterial.htm?id=440439
This is a free, online wikibook, so the content is continually being updated and refined. According to the authors, "This book is intended as a Partial Differential Equations (PDEs) reference for individuals who already posses a firm understanding of ordinary differential equations and at least have a basic idea of what a partial derivative is. This book is meant to be easily readable to engineers and scientists while still being (almost) interesting enough for mathematics students. Be advised that in depth proofs of such matters as series convergence, uniqueness, and existence will not be given; this fact will appall some and elate others. This book is meant more toward solving or at the very least extracting information out of problems involving partial differential equations. The first few chapters are built to be especially simple to understand so that, say, the interested engineering undergraduate can benefit; however later on important and more mathematic topics such as vector spaces will be introduced and used.״Partial differential equations and operators - Fundamental solutions and semigroups Part I
http://www.merlot.org/merlot/viewMaterial.htm?id=837026
This is a free textbook offered by BookBoon.'In this book, which is basically self-contained, we concentrate on partial differential equations in mathematical physics and on operator semigroups with their generators. A central theme is a thorough treatment of distribution theory. This is done via convolution products, Fourier transforms, and fundamental solutions of partial differential operators with constant coefficients. Linear initial value problems are treated via operator semigroups. A relationship between so-called Feller-Dynkin semigroups and Markov processes is described. Finally, Feynman-Kac semigroups are introduced.'