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Global Analysis

Functional Analysis Examples c-1

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Language:  English
In this book you find the basic mathematics that is needed by engineers and university students .
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In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.

Topics as Topological, metric, Hilbert and Banach spaces and Spectral Theory are illustrated.

This book requires knowledge of Calculus 1 and Calculus 2.

  1. Introduction
  2. Metric Spaces
  3. Topology 1
  4. Continuous mappings
  5. Topology 2
  6. Sequences
  7. Semi-continuity
  8. Connected sets, differentiation a.o.
  9. Addition and multiplication by scalars in normed vector spaces
  10. Normed vector spaces and integral operators
  11. Differentiable mappings
  12. Complete metric spaces
  13. Local Existence and Uniqueness Theorem for Autonomous Ordinary Differential Equations
  14. Euler-Lagrange's equations
  15. Index
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