# Analysis Tools with Applications

Analysis Tools with Applications
by

Publisher: Springer
Number of pages: 790

Description:
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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