Analysis Tools with Applications
by Bruce K. Driver
Publisher: Springer 2003
Number of pages: 790
These are lecture notes from Real analysis and PDE. Contents: Basic Topological, Metric and Banach Space Notions; The Riemann Integral and Ordinary Differential Equations; Lebesbgue Integration Theory; Hilbert Spaces and Spectral Theory of Compact Operators; Synthesis of Integral and Differential Calculus; Miracle Properties of Banach Spaces; Complex Variable Theory; The Fourier Transform; Generalized Functions; PDE Examples; First Order Scalar Equations Elliptic ODE; Constant Coefficient Equations; Sobolev Theory; Variable Coefficient Equations; Heat Kernel Properties; Heat Kernels on Vector Bundles; PDE Extras.
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by Joseph Fels Ritt - The American Mathematical Society
We shall be concerned, in this monograph, with systems of differential equations, ordinary or partial, which are algebraic in the unknowns and their derivatives. The algebraic side of the theory of such systems seems is developed in this book.
by H.T.H. Piaggio - G. Bell
The object of this book is to give an account of the central parts of the subject in as simple a form as possible, suitable for those with no previous knowledge of it, and to point out the different directions in which it may be developed.
by Jiří Lebl - Lulu.com
One semester introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, and the Laplace transform.
by A. N. Varchenko, P. I. Etingof - American Mathematical Society
This book concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot remains an algebraic curve of degree four in the course of evolution.