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Fourier Analysis and Partial Differential Equations 1st Edition by Rafael Jose Iorio Jr ISBN 052162116X 9780511623745

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Fourier Analysis and Partial Differential Equations 1st Edition Rafael José Iorio Jr Digital Instant Download

Author(s): Rafael José Iorio Jr, Valéria de Magalhães Iorio
ISBN(s): 052162116X
Edition: 1
File Details: PDF, 50.83 MB
Year: 2001
Language: english
SKU: EB-4674046 Category: Tags: ,

Fourier Analysis and Partial Differential Equations 1st Edition by Rafael Jose Iorio  Jr – Ebook PDF Instant Download/Delivery: 052162116X, 9780511623745
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ISBN 10: 052162116X 
ISBN 13: 9780511623745
Author: Rafael Jose Iorio  Jr

This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems that do not occur in the periodic case.

Fourier Analysis and Partial Differential Equations 1st Table of contents:

1. Introduction to Fourier Analysis

  • Historical Background

  • Basic Concepts of Fourier Series

  • Convergence and Applications

2. Fourier Series

  • Definition and Properties

  • Pointwise and Uniform Convergence

  • Applications to Boundary Value Problems

3. Fourier Transforms

  • Definition and Basic Properties

  • Inversion Theorem

  • Plancherel and Parseval Theorems

4. Distributions and Generalized Functions

  • Introduction to Distributions

  • Dirac Delta Function

  • Applications in PDEs

5. Introduction to Partial Differential Equations (PDEs)

  • Classification of PDEs

  • Well-Posed Problems

  • Initial and Boundary Conditions

6. The Heat Equation

  • Derivation and Physical Interpretation

  • Solution Techniques Using Fourier Series

  • Maximum Principles

7. The Wave Equation

  • Formulation and Properties

  • Solutions via Fourier Methods

  • Energy Methods

8. The Laplace Equation

  • Harmonic Functions

  • Boundary Value Problems

  • Green’s Functions

9. Sobolev Spaces and Functional Analysis Tools

  • Introduction to Sobolev Spaces

  • Embedding Theorems

  • Applications to PDEs

10. Advanced Topics in PDEs and Fourier Analysis

  • Nonlinear PDEs

  • Spectral Theory

  • Modern Applications

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Tags: Rafael Jose Iorio Jr, Fourier Analysis, Partial Differential