Prinzipien der Fourier-Analyse (Lehrbücher in Mathematik) von Howell
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Prinzipien der Fourier-Analys
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eBay-Artikelnr.:136087456957
Artikelmerkmale
- Artikelzustand
- Gut
- Hinweise des Verkäufers
- “Used book in good condition. Shows typical wear. Quick shipping. Satisfaction guaranteed!”
- Book Title
- Principles of Fourier Analysis (Textbooks in Mathematics)
- Topic
- Applied
- Narrative Type
- Applied
- Genre
- N/A
- Intended Audience
- N/A
- ISBN
- 9781498734097
Über dieses Produkt
Product Identifiers
Publisher
CRC Press LLC
ISBN-10
149873409X
ISBN-13
9781498734097
eBay Product ID (ePID)
19038392035
Product Key Features
Number of Pages
804 Pages
Language
English
Publication Name
Principles of Fourier Analysis
Publication Year
2016
Subject
Functional Analysis, General, Applied, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Series
Textbooks in Mathematics Ser.
Format
Hardcover
Dimensions
Item Height
1.9 in
Item Weight
55.3 Oz
Item Length
10.3 in
Item Width
7.4 in
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
LCCN
2016-031351
Dewey Edition
21
Illustrated
Yes
Dewey Decimal
515/.2433
Table Of Content
PRELIMINARIES The Starting Point Basic Terminology, Notation, and Conventions Basic Analysis I: Continuity and Smoothness Basic Analysis II: Integration and Infinite Series Symmetry and Periodicity Elementary Complex Analysis Functions of Several Variables FOURIER SERIES Heuristic Derivation of the Fourier Series Formulas The Trigonometric Fourier Series Fourier Series over Finite Intervals (Sine and Cosine Series) Inner Products, Norms, and Orthogonality The Complex Exponential Fourier Series Convergence and Fourier's Conjecture Convergence and Fourier's Conjecture: The Proofs Derivatives and Integrals of Fourier Series Applications CLASSICAL FOURIER TRANSFORMS Heuristic Derivation of the Classical Fourier Transform Integrals on Infinite Intervals The Fourier Integral Transforms Classical Fourier Transforms and Classically Transformable Functions Some Elementary Identities: Translation, Scaling, and Conjugation Differentiation and Fourier Transforms Gaussians and Other Very Rapidly Decreasing Functions Convolution and Transforms of Products Correlation, Square-Integrable Functions, and the Fundamental Identity of Fourier Analysis Identity Sequences Generalizing the Classical Theory: A Naive Approach Fourier Analysis in the Analysis of Systems Gaussians as Test Functions, and Proofs of Some Important Theorems GENERALIZED FUNCTIONS AND FOURIER TRANSFORMS A Starting Point for the Generalized Theory Gaussian Test Functions Generalized Functions Sequences and Series of Generalized Functions Basic Transforms of Generalized Fourier Analysis Generalized Products, Convolutions, and Definite Integrals Periodic Functions and Regular Arrays General Solutions to Simple Equations and the Pole Functions THE DISCRETE THEORY Periodic, Regular Arrays Sampling and the Discrete Fourier Transform APPENDICES
Edition Description
Revised edition,New Edition
Synopsis
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas. Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented. Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.
LC Classification Number
QA403.5.H69 2017
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