Read Book Integral Transform Techniques for Greens Function

Total Page:16

File Type:pdf, Size:1020Kb

Read Book Integral Transform Techniques for Greens Function INTEGRAL TRANSFORM TECHNIQUES FOR GREENS FUNCTION 2ND EDITION PDF, EPUB, EBOOK Kazumi Watanabe | 9783319345871 | | | | | Integral Transform Techniques for Greens Function 2nd edition PDF Book An integral transform "maps" an equation from its original "domain" into another domain. Cold Books. Finite Laplace Transforms. Vikram Jain Books. Millions of books are added to our site everyday and when we find one that matches your search, we'll send you an e-mail. Sanctum Books. Applications of Laplace Transforms. This physics kernel is the kernel of integral transform. Jacobi and Gegenbauer Transforms. For other uses, see Transformation mathematics. A7 Mittag Leffler Function. Tables of Integral Transforms. Chapter 1 Fundamentals. Fractional Malliavin Stochastic Variations. Added to Your Shopping Cart. Legendre Transforms. Mean value theorem Rolle's theorem. The equation cast in terms of complex frequency is readily solved in the complex frequency domain roots of the polynomial equations in the complex frequency domain correspond to eigenvalues in the time domain , leading to a "solution" formulated in the frequency domain. Are you a frequent reader or book collector? Hilbert and Stieltjes Transforms. E-Book Rental Days. From Wikipedia, the free encyclopedia. Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. However, for each quantum system, there is a different kernel. There are many classes of problems that are difficult to solve—or at least quite unwieldy algebraically—in their original representations. The general theory of such integral equations is known as Fredholm theory. Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem. Chapter 4 Dynamic Analysis and Forces. Fourier Transforms and Their Applications. International Edition. The sines and cosines in the Fourier series are an example of an orthonormal basis. Glossary of calculus. New paperback. Show Details Description:. Add to cart Buy Now Item Price. The input of this transform is a function f , and the output is another function Tf. Mathematical notation aside, the motivation behind integral transforms is easy to understand. Another usage example is the kernel in path integral :. The Radon Transform and Its Applications. Chapter 2 Kinematics of Robots: Position Analysis. Employing the inverse transform , i. A5 Laguerre and Associated Laguerre Functions. Appendix B Image Acquisition Systems. Integral Transform Techniques for Greens Function 2nd edition Writer NO YES. There are many classes of problems that are difficult to solve—or at least quite unwieldy algebraically—in their original representations. Laguerre Transforms. October 22, Biblio is open and shipping orders. The solution is then mapped back to the original domain with the inverse of the integral transform. Using the Fourier series, just about any practical function of time the voltage across the terminals of an electronic device for example can be represented as a sum of sines and cosines , each suitably scaled multiplied by a constant factor , shifted advanced or retarded in time and "squeezed" or "stretched" increasing or decreasing the frequency. Added to Your Shopping Cart. Chapter 3 Differential Motions and Velocities. Answers and Hints to Selected Exercises. Chapter 8 Sensors. Sanctum Books. Undetected location. Mapping involving integration between function spaces. Manipulating and solving the equation in the target domain can be much easier than manipulation and solution in the original domain. International Edition. Hankel Transforms and Their Applications. It also covers microprocessor applications, control systems, vision systems, sensors, and actuators, making the book useful to mechanical engineers, electronic and electrical engineers, computer engineers and engineering technologists. Chapter 4 Dynamic Analysis and Forces. View Instructor Companion Site. Students Textbooks. Chapter 2 Kinematics of Robots: Position Analysis. Fractional Calculus and Its Applications. The transformed function can generally be mapped back to the original function space using the inverse transform. Later the Fourier transform was developed to remove the requirement of finite intervals. Download as PDF Printable version. Complex frequency is similar to actual, physical frequency but rather more general. Seller rating : This seller has earned a 4 of 5 Stars rating from Biblio customers. Hermite Transforms. Depending on the situation, the kernel is then variously referred to as the Fredholm operator , the nuclear operator or the Fredholm kernel. Wavelets and Wavelet Transforms. Benchmark Trading. Finite Fourier Sine and Cosine Transforms. Add to cart Buy Now Item Price. Here integral transforms are defined for functions on the real numbers, but they can be defined more generally for functions on a group. This physics kernel is the kernel of integral transform. In this example, polynomials in the complex frequency domain typically occurring in the denominator correspond to power series in the time domain, while axial shifts in the complex frequency domain correspond to damping by decaying exponentials in the time domain. Specialized Fractional Malliavin Stochastic Variations. This is a technique that maps differential or integro-differential equations in the "time" domain into polynomial equations in what is termed the "complex frequency" domain. Designed to meet the needs of different readers, this book covers a fair amount of mechanics and kinematics, including manipulator kinematics, differential motions, robot dynamics, and trajectory planning. Categories : Integral transforms. An integral transform "maps" an equation from its original "domain" into another domain. This is a dummy description. Integral Transforms. New To This Edition New and expanded coverage of modeling. Although the properties of integral transforms vary widely, they have some properties in common. Would you like to change to the site? Integral Transform Techniques for Greens Function 2nd edition Reviews Mellin Transforms and Their Applications. The sines and cosines in the Fourier series are an example of an orthonormal basis. The solution is then mapped back to the original domain with the inverse of the integral transform. In mathematics , an integral transform maps a function from its original function space into another function space via integration , where some of the properties of the original function might be more easily characterized and manipulated than in the original function space. Permissions Request permission to reuse content from this site. Try adding this search to your want list. E-Book Rental Days. A2 Bessel and Airy Functions. Using the Fourier series, just about any practical function of time the voltage across the terminals of an electronic device for example can be represented as a sum of sines and cosines , each suitably scaled multiplied by a constant factor , shifted advanced or retarded in time and "squeezed" or "stretched" increasing or decreasing the frequency. Other integral transforms find special applicability within other scientific and mathematical disciplines. In this theory, the kernel is understood to be a compact operator acting on a Banach space of functions. A7 Mittag Leffler Function. A - Z Books. Add to want list. Chapter 10 Fuzzy Logic Control. Cold Books. The Radon Transform and Its Applications. A5 Laguerre and Associated Laguerre Functions. A3 Legendre and Associated Legendre Functions. Learn More. Later the Fourier transform was developed to remove the requirement of finite intervals. Fractional Calculus and Its Applications. Chapter 1 Fundamentals. Glossary of calculus List of calculus topics. Students Textbooks. This is a technique that maps differential or integro-differential equations in the "time" domain into polynomial equations in what is termed the "complex frequency" domain. Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem. The transformed function can generally be mapped back to the original function space using the inverse transform. There are many classes of problems that are difficult to solve—or at least quite unwieldy algebraically—in their original representations. Hilbert and Stieltjes Transforms. International Edition. Bateman transform Convolution kernel Circular convolution Circulant matrix Differential equations Kernel method List of transforms List of operators List of Fourier-related transforms Nachbin's theorem Nonlocal operator Reproducing kernel Symbolic integration. Integral Transform Techniques for Greens Function 2nd edition Read Online International Edition. The transformed function can generally be mapped back to the original function space using the inverse transform. Students Textbooks. Help Learn to edit Community portal Recent changes Upload file. Each is specified by a choice of the function K of two variables , the kernel function , integral kernel or nucleus of the transform. Mapping involving integration between function spaces. Fourier sine transform. Added to Your Shopping Cart. Jacobi and Gegenbauer Transforms. This is a technique that maps differential or integro-differential equations in the "time" domain into polynomial equations in what is termed the "complex frequency" domain. Answers and Hints to Selected
Recommended publications
  • Some Schemata for Applications of the Integral Transforms of Mathematical Physics
    mathematics Review Some Schemata for Applications of the Integral Transforms of Mathematical Physics Yuri Luchko Department of Mathematics, Physics, and Chemistry, Beuth University of Applied Sciences Berlin, Luxemburger Str. 10, 13353 Berlin, Germany; [email protected] Received: 18 January 2019; Accepted: 5 March 2019; Published: 12 March 2019 Abstract: In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed. Keywords: integral transforms; Laplace integral transform; transmutation operator; generating operator; integral equations; differential equations; operational calculus of Mikusinski type; Mellin integral transform MSC: 45-02; 33C60; 44A10; 44A15; 44A20; 44A45; 45A05; 45E10; 45J05 1. Introduction In this survey article, we discuss some schemata for applications of the integral transforms of mathematical physics to differential, integral, and integro-differential equations, and in the theory of special functions. The literature devoted to this subject is huge and includes many books and reams of papers.
    [Show full text]
  • Methods of Integral Transforms - V
    COMPUTATIONAL METHODS AND ALGORITHMS – Vol. I - Methods of Integral Transforms - V. I. Agoshkov, P. B. Dubovski METHODS OF INTEGRAL TRANSFORMS V. I. Agoshkov and P. B. Dubovski Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia Keywords: Integral transform, Fourier transform, Laplace transform, Mellin transform, Hankel transform, Meyer transform, Kontorovich-Lebedev transform, Mehler-Foque transform, Hilbert transform, Laguerre transform, Legendre transform, convolution transform, Bochner transform, chain transform, wavelet, wavelet transform, problems of the oscillation theory, heat conductivity problems, problems of the theory of neutron slowing-down, problems of hydrodynamics, problems of the elasticity theory, Boussinesq problem, coagulation equation, physical kinetics. Contents 1. Introduction 2. Basic integral transforms 2.1. The Fourier Transform 2.1.1. Basic Properties of the Fourier Transform 2.1.2. The Multiple Fourier Transforms 2.2. The Laplace Transform 2.2.1. The Laplace Integral 2.2.2. The Inversion Formula for the Laplace Transform 2.2.3. Limit Theorems 2.3. The Mellin Transform 2.4. The Hankel Transform 2.5. The Meyer Transform 2.6. The Kontorovich-Lebedev Transform 2.7. The Mehler-Foque Transform 2.8. The Hilbert Transform 2.9. The Laguerre and Legendre Transforms 2.10. The Bochner Transform, the Convolution Transform, the Wavelet and Chain Transforms 3. The application of integral transforms to problems of the oscillation theory 3.1. Electric Oscillations 3.2. TransverseUNESCO Oscillations of a String – EOLSS 3.3. Transverse Oscillations of an Infinite Round Membrane 4. The application of integral transforms to heat conductivity problems 4.1. The SolutionSAMPLE of the Heat Conductivity CHAPTERS Problem by the use of the Laplace Transform 4.2.
    [Show full text]
  • Adaptive Learning Methods and Their Use in Flaw Classification Sriram Chavali Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1996 Adaptive learning methods and their use in flaw classification Sriram Chavali Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Structures and Materials Commons Recommended Citation Chavali, Sriram, "Adaptive learning methods and their use in flaw classification" (1996). Retrospective Theses and Dissertations. 111. https://lib.dr.iastate.edu/rtd/111 This Thesis is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. r r Adaptive learning methods and their use in flaw classification r by r Sriram Chavali r A thesis submitted to the graduate faculty in partial fulfillment of the requirements for the degree of r MASTER OF SCIENCE r Department: Aerospace Engineering and Engineering Mechanics Major: Aerospace Engineering r1 r Major Professor: Dr. Lester W. Schmerr r r r r r r Iowa State University Ames, Iowa r 1996 r Copyright© Sriram Chavali, 1996. All rights reserved. r( r 11 r Graduate College r Iowa State University rI I This is to certify that the Master's thesis of Sriram Chavali has met the thesis requirements of Iowa State University r r r r r r rt r r r rm I l rl r r ll1 r {l1m'l r 1 TABLE OF CONTENTS {1m 1, I )11m ACKNOWLEDGMENTS Vlll I i ABSTRACT ....
    [Show full text]
  • Partial Derivative Approach to the Integral Transform for the Function Space in the Banach Algebra
    entropy Article Partial Derivative Approach to the Integral Transform for the Function Space in the Banach Algebra Kim Young Sik Department of Mathematics, Hanyang University, Seoul 04763, Korea; [email protected] Received: 27 July 2020; Accepted: 8 September 2020; Published: 18 September 2020 Abstract: We investigate some relationships among the integral transform, the function space integral and the first variation of the partial derivative approach in the Banach algebra defined on the function space. We prove that the function space integral and the integral transform of the partial derivative in some Banach algebra can be expanded as the limit of a sequence of function space integrals. Keywords: function space; integral transform MSC: 28 C 20 1. Introduction The first variation defined by the partial derivative approach was defined in [1]. Relationships among the Function space integral and transformations and translations were developed in [2–4]. Integral transforms for the function space were expanded upon in [5–9]. A change of scale formula and a scale factor for the Wiener integral were expanded in [10–12] and in [13] and in [14]. Relationships among the function space integral and the integral transform and the first variation were expanded in [13,15,16] and in [17,18] In this paper, we expand those relationships among the function space integral, the integral transform and the first variation into the Banach algebra [19]. 2. Preliminaries Let C0[0, T] be the class of real-valued continuous functions x on [0, T] with x(0) = 0, which is a function space. Let M denote the class of all Wiener measurable subsets of C0[0, T] and let m denote the Wiener measure.
    [Show full text]
  • Basic Magnetic Resonance Imaging
    Basic Magnetic Resonance Imaging Mike Tyszka, Ph.D. Magnetic Resonance Theory Course 2004 Caltech Brain Imaging Center California Institute of Technology Spatial Encoding Spatial Localization of Signal Va r y B sp a t i a l l y ω=γB Linear Field Gradients Linear Magnetic Field Gradients One-Dimensional Tw o -Dimensional Gradient direction Bz(x,z) Bz z Distance (x) x Deviation from B0 typically very small (~0.1%) Frequency Encoding Total signal from spins in plane perpendicular to gradient direction Signal Gradient direction Frequency (ω) Distance (ω/γG) The FID in a Field Gradient • FID contains total signal from all spins at all frequencies/locations. • Each frequency component represents the total signal from a plane perpendicular to the gradient direction. • Frequency analysis of FID reveals “projection” of object. MRI from Projections • Can projections be turned into an image? Back Projection • Sweep gradient direction through 180° • Acquire projections of object for each direction Sinogram Back Projection or Inverse Radon Transform Frequency Analysis for MRI MR Signal as a Complex Quantity • Both the magnitude and phase of the MR signal are measured. y’ • Two signal channels are commonly referred to as “real” and “imaginary”. A M φ y x’ Mx The Fourier Transform (FT) The Fourier Transform is an Integral Transform which, for MRI, relates a time varying waveform to the corresponding frequency spectrum. FORWARD TRANSFORM (time -> frequency) REVERSE TRANSFORM (frequency -> time) The Fast Fourier Transform (FFT) • Numerical algorithm for efficient computation of the discrete Fourier Transform. • Requires discrete complex valued samples. • Both forward and reverse transforms can be calculated.
    [Show full text]
  • The Wavelet Tutorial Second Edition Part I by Robi Polikar
    THE WAVELET TUTORIAL SECOND EDITION PART I BY ROBI POLIKAR FUNDAMENTAL CONCEPTS & AN OVERVIEW OF THE WAVELET THEORY Welcome to this introductory tutorial on wavelet transforms. The wavelet transform is a relatively new concept (about 10 years old), but yet there are quite a few articles and books written on them. However, most of these books and articles are written by math people, for the other math people; still most of the math people don't know what the other math people are 1 talking about (a math professor of mine made this confession). In other words, majority of the literature available on wavelet transforms are of little help, if any, to those who are new to this subject (this is my personal opinion). When I first started working on wavelet transforms I have struggled for many hours and days to figure out what was going on in this mysterious world of wavelet transforms, due to the lack of introductory level text(s) in this subject. Therefore, I have decided to write this tutorial for the ones who are new to the topic. I consider myself quite new to the subject too, and I have to confess that I have not figured out all the theoretical details yet. However, as far as the engineering applications are concerned, I think all the theoretical details are not necessarily necessary (!). In this tutorial I will try to give basic principles underlying the wavelet theory. The proofs of the theorems and related equations will not be given in this tutorial due to the simple assumption that the intended readers of this tutorial do not need them at this time.
    [Show full text]
  • Study of the Mellin Integral Transform with Applications in Statistics and Probability
    Available online a t www.scholarsresearchlibrary.com Scholars Research Library Archives of Applied Science Research, 2012, 4 (3):1294-1310 (http://scholarsresearchlibrary.com/archive.html) ISSN 0975-508X CODEN (USA) AASRC9 Study of the mellin integral transform with applications in statistics And probability S. M. Khairnar 1, R. M. Pise 2 and J. N. Salunkhe 3 1Department of Mathematics, Maharashtra Academy of Engineering, Alandi, Pune, India 2Department of Mathematics, (A.S.& H.), R.G.I.T. Versova, Andheri (W), Mumbai, India 3Department of Mathematics, North Maharastra University, Jalgaon, Maharashtra, India ______________________________________________________________________________ ABSTRACT The Fourier integral transform is well known for finding the probability densities for sums and differences of random variables. We use the Mellin integral transforms to derive different properties in statistics and probability densities of single continuous random variable. We also discuss the relationship between the Laplace and Mellin integral transforms and use of these integral transforms in deriving densities for algebraic combination of random variables. Results are illustrated with examples. Keywords: Laplace, Mellin and Fourier Transforms, Probability densities, Random Variables and Applications in Statistics. AMS Mathematical Classification: 44F35, 44A15, 44A35, 44A12, 43A70. ______________________________________________________________________________ INTRODUCTION The aim of this paper , we define a random variable (RV) as a value in some domain , say ℜ , representing the outcome of a process based on a probability laws .By the information above the probability distribution ,we integrate the probability density function (p d f)in the case of the Gaussian , the p d f is 1 X −π − ( )2 1 σ − ∞ < < ∞ f (x)= E 2 , x σ 2π when µ is mean and σ 2 is the variance.
    [Show full text]
  • Introduction to the Fourier Transform
    Chapter 4 Introduction to the Fourier transform In this chapter we introduce the Fourier transform and review some of its basic properties. The Fourier transform is the \swiss army knife" of mathematical analysis; it is a powerful general purpose tool with many useful special features. In particular the theory of the Fourier transform is largely independent of the dimension: the theory of the Fourier trans- form for functions of one variable is formally the same as the theory for functions of 2, 3 or n variables. This is in marked contrast to the Radon, or X-ray transforms. For simplicity we begin with a discussion of the basic concepts for functions of a single variable, though in some de¯nitions, where there is no additional di±culty, we treat the general case from the outset. 4.1 The complex exponential function. See: 2.2, A.4.3 . The building block for the Fourier transform is the complex exponential function, eix: The basic facts about the exponential function can be found in section A.4.3. Recall that the polar coordinates (r; θ) correspond to the point with rectangular coordinates (r cos θ; r sin θ): As a complex number this is r(cos θ + i sin θ) = reiθ: Multiplication of complex numbers is very easy using the polar representation. If z = reiθ and w = ½eiÁ then zw = reiθ½eiÁ = r½ei(θ+Á): A positive number r has a real logarithm, s = log r; so that a complex number can also be expressed in the form z = es+iθ: The logarithm of z is therefore de¯ned to be the complex number Im z log z = s + iθ = log z + i tan¡1 : j j Re z µ ¶ 83 84 CHAPTER 4.
    [Show full text]
  • 1 Linear System Modeling Using Laplace Transformation
    A Brief Introduction To Laplace Transformation Dr. Daniel S. Stutts Associate Professor of Mechanical Engineering Missouri University of Science and Technology Revised: April 13, 2014 1 Linear System Modeling Using Laplace Transformation Laplace transformation provides a powerful means to solve linear ordinary differential equations in the time domain, by converting these differential equations into algebraic equations. These may then be solved and the results inverse transformed back into the time domain. Tables of Laplace transforms are available to facilitate this operation. Laplace transformation belongs to a general area of mathematics called operational calculus which focuses on the analysis of linear systems. 1.1 Laplace Transformation Laplace transformation belongs to a class of analysis methods called integral transformation which are studied in the field of operational calculus. These methods include the Fourier transform, the Mellin transform, etc. In each method, the idea is to transform a difficult problem into an easy problem. For example, taking the Laplace transform of both sides of a linear, ODE results in an algebraic problem. Solving algebraic equations is usually easier than solving differential equations. The one-sided Laplace transform which we are used to is defined by equation (1), and is valid over the interval [0; 1). This means that the domain of integration includes its left end point. This is why most authors use the term 0− to represent the bottom limit of the Laplace integral. Z 1 L ff(t)g = f(t)e−stdt (1) 0− The key thing to note is that Equation (1) is not a function of time, but rather a function of the Laplace variable s = σ + j!.
    [Show full text]
  • Arxiv:1904.11370V1 [Math.GM] 19 Apr 2019
    NEW INTEGRAL TRANSFORM: SHEHU TRANSFORM A GENERALIZATION OF SUMUDU AND LAPLACE TRANSFORM FOR SOLVING DIFFERENTIAL EQUATIONS SHEHU MAITAMA∗, WEIDONG ZHAO Abstract. In this paper, we introduce a Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms for solving differential equations in the time do- main. The proposed integral transform is successfully derived from the clas- sical Fourier integral transform and is applied to both ordinary and partial differential equations to show its simplicity, efficiency, and the high accuracy. 1. Introduction Historically, the origin of the integral transforms can be traced back to the work of P. S. Laplace in 1780s and Joseph Fourier in 1822. In recent years, differential and integral equations have been solved using many integral transforms ([1]-[11]). The Laplace transform, and Fourier integral transforms are the most commonly used in the literature. The Fourier integral transform [12] was named after the French mathematician Joseph Fourier. Mathematically, Fourier integral transform is defined as: 1 Z 1 z[f(t)] = f(!) = p exp (−i!t) f(t)dt: (1.1) 2π −∞ The Fourier transform have many applications in physics and engineering processes [13]. The Laplace integral transform is similar with the Fourier transform and is defined as: Z 1 $[f(t)] = F (s) = exp (−st) f(t)dt: (1.2) −∞ The Laplace transform is highly efficient for solving some class of ordinary and partial differential equations [14]. By replacing the variable i! with the variable s in Equ.(1.1), the well-known Fourier transform will become a Laplace transform and the vice-versa.
    [Show full text]
  • Chapter 2 Integral Transform
    Chapter 2 Integral Transform 2.1 Introduction Consider pairs of functions related by an expression of the form: ⌢ b F (α) = K(α, x) f (x)dx (2.1-1) ∫a ⌢ The function F (α) is called the integral transform of f(x) by the kernel K(α, x). The operation may also be considered as mapping a function f(x) in x-space into another function ⌢ F (α) in α-space. Figure 2.1-1 depicts the idea behind the application of integral transform. Certain problems can be solved, if at all, in the original coordinates (space). These problems might be solved relatively easily in the transform coordinates. Then, the inverse transform returns the solution from the transform coordinates to the original system. Problem in Relative easy solution Solution in transform space transform space Integral Inverse transform transform Original Difficult solution Solution of problem original problem Figure 2.1-1 Application of integral transform. Two of the most useful of the infinite number of possible transforms are the Laplace transform, ⌢ ∞ F (s) = e−sx f (x)dx (2.1-2) ∫0 and the Fourier transform, ⌢ ∞ F (k) = e−ikx f (x)dx (2.1-3) ∫−∞ Integral transform can be used to reduce the number of independent variables in a partial differential equation by one. Thus, the one-dimensional heat equation or wave equation can ⌢ be transformed into an ordinary differential equation in the transformed function F (α). An ordinary differential equation becomes an algebraic equation in the transformed domain. It is usually easier to solve the resultant equation in the transform space than it is to solve the original equation.
    [Show full text]
  • Use of the Generalized Integral Transform Method for Solving Equation of Mass Transfer in Food Drying
    Proceedings of COBEM 2009 20th International Congress of Mechanical Engineering Copyright © 2009 by ABCM November 15-20, 2009, Gramado, RS, Brazil USE OF THE GENERALIZED INTEGRAL TRANSFORM METHOD FOR SOLVING EQUATION OF MASS TRANSFER IN FOOD DRYING Cristiane Kelly F. da Silva, [email protected] Universidade Federal da Paraíba – UFPB, Laboratório de Energia Solar, Castelo Branco, 58051-970, João Pessoa, Paraíba, Brasil Andréa Samara Santos de Oliveira [email protected] Instituto Federal de Educação, Ciência e Tecnologia do Ceará, Campus Juazeiro do Norte, Av. Plácido Aderaldo Castelo, 1646, Planalto, 63040-000, Juazeiro do Norte, Ceará, Brasil Zaqueu Ernesto da Silva, [email protected] Universidade Federal da Paraíba – UFPB, Laboratório de Energia Solar, Castelo Branco, 58051-970, João Pessoa, Paraíba, Brasil Antônio Carlos Cabral dos Santos, [email protected] Universidade Federal da Paraíba – UFPB, Laboratório de Energia Solar, Castelo Branco, 58051-970, João Pessoa, Paraíba, Brasil Edilma Pereira, [email protected] Universidade Federal da Paraíba – UFPB, Laboratório de Energia Solar, Castelo Branco, 58051-970, João Pessoa, Paraíba, Brasil Abstract. Dried fruit and vegetables have gained commercial importance and their growth on a commercial scale has become an important sector of the agricultural industry. Plots of drying curves are used in the determination of the drying process behavior inside the samples and of the optimal drying conditions, taking into account the quality of the dried product and also the economical aspects. This research was developed with the objective of studying and modeling the phenomenon of the mass transfer in the agricultural products drying process, using the diffusional model (Fick’s Second Law of Diffusion) adapted to infinite flat plate geometry.
    [Show full text]