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 Paul Dawkins - Lamar University
Contents: Basic Concepts; First Order Differential Equations; Second Order DE; Laplace Transforms; Systems of Differential Equations; Series Solutions; Higher Order DE; Boundary Value Problems and Fourier Series; Partial Differential Equations.
by Edward Nelson - Princeton University Press
Lecture notes for a course on differential equations covering differential calculus, Picard's method, local structure of vector fields, sums and Lie products, self-adjoint operators on Hilbert space, commutative multiplicity theory, and more.
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 M. Kuranishi - Tata Institute of Fundamental Research
Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.