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Principles of Fourier analysis / 3G E-Learning.

By: Material type: TextTextLanguage: English Series: 3GE Collection on mathematicsPublication details: New York, NY : 3G E-learning LLC, c2018Description: 244 pages : illustrations ; 26 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9781680959130 (hardback)
Subject(s): LOC classification:
  • QA403.5 T41 2018
Online resources:
Contents:
Fourier series -- Fourier transform -- Laplace transform -- Convolution and transforms of products -- Correlation and regression -- Signal sampling -- Legendre’s equation and simple properties of P (x).
Summary: "Fourier analysis is the branch of mathematics named in the honor of French mathematician Jean Baptiste Joseph fourier1 (1768-1830), whose treatise on heat flow first introduced most of these concepts. Today, Fourier analysis is, among other things, perhaps the single most important mathematical tool used in what we call signal processing. Frequency domain analysis and Fourier transform are the foundation of signal and system analysis. These philosophies are also one of the conceptual pillars within electrical engineering. Among all of the mathematical tools utilized in electrical engineering, frequency domain analysis is arguably the most far-reaching. In fact, these ideas are so important that they are widely used in many fields – not just in electrical engineering, but in practically all branches of engineering and science, and several areas of mathematics. It represents the fundamental procedure by which complex physical “signals” may be decomposed into simpler ones and, conversely, by which complicated signals may be created out of simpler building blocks. Mathematically, Fourier analysis has spawned some of the most fundamental developments in our understanding of infinite series and function approximation – developments which are, unfortunately, much beyond the scope of these notes. Equally important, Fourier analysis is the tool with which many of the everyday phenomena – the perceived differences in sound between violins and drums, sonic booms, and the mixing of colors – can be better understood. As we shall come to see, Fourier analysis does this by establishing a simultaneous dual view of phenomena – what we shall come to call the frequency domain and the time domain representations. This book provides key insights, techniques and elegant results of Fourier analysis, and for their applications. It addresses the circle of ideas that includes Fourier series, Fourier and Laplace transforms, and eigenfunction expansions for differential operators, striking a balance between pure and applied mathematics. The reason why Fourier analysis is so important is that many of the differential equations that govern physical systems are linear, which implies that the sum of two solutions is again a solution. Therefore, since Fourier analysis tells us that any function can be written in terms of sinusoidal functions, we can limit our attention to these functions when solving the differential equations. And then we can build up any other function from these special ones. This is a very helpful strategy, because it is invariably easier to deal with sinusoidal functions than general ones. This novel edition is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis."--Back cover
List(s) this item appears in: Print Books 2022
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Item type Current library Collection Call number Materials specified Status Notes Date due Barcode
Books Books Ladislao N. Diwa Memorial Library Reserve Section Non-fiction RUS QA403.5 T41 2018 (Browse shelf(Opens below)) Room use only 78176 00079122

Includes bibliographical references and index.

Fourier series -- Fourier transform -- Laplace transform -- Convolution and transforms of products -- Correlation and regression -- Signal sampling -- Legendre’s equation and simple properties of P (x).

"Fourier analysis is the branch of mathematics named in the honor of French mathematician Jean Baptiste Joseph fourier1 (1768-1830), whose treatise on heat flow first introduced most of these concepts. Today, Fourier analysis is, among other things, perhaps the single most important mathematical tool used in what we call signal processing. Frequency domain analysis and Fourier transform are the foundation of signal and system analysis. These philosophies are also one of the conceptual pillars within electrical engineering. Among all of the mathematical tools utilized in electrical engineering, frequency domain analysis is arguably the most far-reaching. In fact, these ideas are so important that they are widely used in many fields – not just in electrical engineering, but in practically all branches of engineering and science, and several areas of mathematics. It represents the fundamental procedure by which complex physical “signals” may be decomposed into simpler ones and, conversely, by which complicated signals may be created out of simpler building blocks. Mathematically, Fourier analysis has spawned some of the most fundamental developments in our understanding of infinite series and function approximation – developments which are, unfortunately, much beyond the scope of these notes. Equally important, Fourier analysis is the tool with which many of the everyday phenomena – the perceived differences in sound between violins and drums, sonic booms, and the mixing of colors – can be better understood. As we shall come to see, Fourier analysis does this by establishing a simultaneous dual view of phenomena – what we shall come to call the frequency domain and the time domain representations.
This book provides key insights, techniques and elegant results of Fourier analysis, and for their applications. It addresses the circle of ideas that includes Fourier series, Fourier and Laplace transforms, and eigenfunction expansions for differential operators, striking a balance between pure and applied mathematics.
The reason why Fourier analysis is so important is that many of the differential equations that govern physical systems are linear, which implies that the sum of two solutions is again a solution. Therefore, since Fourier analysis tells us that any function can be written in terms of sinusoidal functions, we can limit our attention to these functions when solving the differential equations. And then we can build up any other function from these special ones. This is a very helpful strategy, because it is invariably easier to deal with sinusoidal functions than general ones. This novel edition is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis."--Back cover

Fund 164 CD Books International, Inc. Purchased 11/18/2020 78176 pnr PHP 4,509.00 2020-10-371A 2020-1-0324

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