I liked "Transforms in Signals and Systems" by Peter Kraniauskas a lot. A few years back I went through a lot of these books, but this is the one that helped me the most.

I liked "Transforms in Signals and Systems" by Peter Kraniauskas a lot. A few years back I went through a lot of these books, but this is the one that helped me the most.

I recommend:

1. Brian Davies. Integral_Transforms_and_their_Applications

2.Lokenath Debnath and Dambaru Bhatta. Integral transforms and their applications

3. Dimitris N. , Chorafas Integral_Transforms_and_Their Applicatioms

4. Clement John_Tranter. Integral_Transforms In Mathematical Physics

5. N. N. Lebedev, I. P. Skalʹskai︠a︡, Ia.S. Ufliand. Worked Problems in Applied Mathematics

P. Malits

This is a good question. In addition to the helpful answers already given, there is a bit more to add.

A downloadable pdf file for a comprehensive book on integral transforms is

L. Debnath, D. Bhatta, Integral Transforms and Their Applications (see the attached image).

Another good book is

Book Integral Transforms and Their Applications

These suggestions were entered about the same time as the excellent list of suggestions by @ Pinchas Malits.

https://www.taylorfrancis.com/books/9781420010916

1. Excellent book to learn integral transform method for solution of boundary value problems:

M. Necati Özıșık

Boundary Value Problems of Heat Conduction (Dover Books on Engineering)

Intended for first-year graduate courses in heat transfer, this volume includes topics relevant to chemical and nuclear engineering and aerospace engineering. The systematic and comprehensive treatment employs modern mathematical methods of solving problems in heat conduction and diffusion. Starting with precise coverage of heat flux as a vector, derivation of the conduction equations, integral-transform technique, and coordinate transformations, the text advances to problem characteristics peculiar to Cartesian, cylindrical, and spherical coordinates; application of Duhamel's method; solution of heat-conduction problems; and the integral method of solution of nonlinear conduction problems. Additional topics include useful transformations in the solution of nonlinear boundary value problems of heat conduction; numerical techniques such as the finite differences and the Monte Carlo method; and anisotropic solids in relation to resistivity and conductivity tensors. Illustrative examples and problems amplify the text, which is supplemented by helpful appendixes.

📷

2.

Lokenath Debnath, Dambaru Bhatta

Integral Transforms and Their Applications, Third Edition 3rd Edition

Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications.

New to the Third Edition

· New material on the historical development of classical and modern integral transforms

· New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle

· Revised material on Laplace transforms and double Laplace transforms and their applications

· New examples of applications in mechanical vibrations, electrical networks, quantum mechanics, integral and functional equations, fluid mechanics, mathematical statistics, special functions, and more

· New figures that facilitate a clear understanding of physical explanations

· Updated exercises with solutions, tables of integral transforms, and bibliography

Through numerous examples and end-of-chapter exercises, this book develops readers’ analytical and computational skills in the theory and applications of transform methods. It provides accessible working knowledge of the analytical methods and proofs required in pure and applied mathematics, physics, and engineering, preparing readers for subsequent advanced courses and research in these areas.

📷

3. Lecture notes on Integral transform methods can be found in

http://www.et.byu.edu/~vps/ME505/ME505.htm

I read the first few chapters of Integral Transform for Engineers by L. Andrews and B. Shivamoggi. Although it is not a classically-structured math book (meaning, Theorem, Proof, Definition, Proposition, Example, etc.), it provides a friendly learning format through examples and problems. I definitely, recommend it.

As an extra advantage, below you can find a digital version of the book for free. I hope it can be useful.

http://simplifiedsm.cloudapp.net/Google%20Drive/Maths/Transforms%20and%20Differential%20Equations/(SPIE%20Press%20Monograph%20Vol.%20PM66)%20Larry%20C.%20Andrews,%20Bhimsen%20K.%20Shivamoggi-Integral%20Transforms%20for%20Engineers-SPIE%20Publications%20(1999).pdf

Lokenath Debnath and Dambaru Bhatta. Integral transforms and their applications 3rd Ed.

See also

https://math.stackexchange.com/questions/1096414/good-recommendations-for-solving-pdes-by-integral-transforms

agree with @ Hugh Lachlan Kennedy

regards

I recommend:

1.C.J. Tranter, Integral Transforms in Matematikal Physics [Djv- 1.5M]

http://publ.lib.ru/ARCHIVES/T/TRANTER_K._Dj/_Tranter_K.Dj..html

2.http://www.unn.ru/books/met_files/zhislin.pdf

3. vital.lib.tsu.ru/vital/access/services/Download/vtls:000052505/SOURCE1

4. https://rucont.ru/file.ashx?guid=fa3344df-9843-4311-83c0-82e50df2f779

5.ВЕРЛАНЬ А.Ф.,СИЗИКОВ В.С.

ИНТЕГРАЛЬНЫЕ УРАВНЕНИЯ

I recommend:

1.C.J. Tranter, Integral Transforms in Matematikal Physics [Djv- 1.5M]

http://publ.lib.ru/ARCHIVES/T/TRANTER_K._Dj/_Tranter_K.Dj..html

2.http://www.unn.ru/books/met_files/zhislin.pdf

3. vital.lib.tsu.ru/vital/access/services/Download/vtls:000052505/SOURCE1

4. https://rucont.ru/file.ashx?guid=fa3344df-9843-4311-83c0-82e50df2f779

5.ВЕРЛАНЬ А.Ф.,СИЗИКОВ В.С.

ИНТЕГРАЛЬНЫЕ УРАВНЕНИЯ

I recommend; Lokenath Debnath and Dambaru Bhatta. Integral transforms and their applications.

If you are interested in the applications of Integral Transformations to physical problems in the areas of Atomic physics, Nuclear physics, Hydrodynamics, Heat conduction in solids or Elasticity, I recommend the book "Fourier Trasnforms", I.N. Sneddon, McGraw-Hill Book Company, First Edition, 1951.

Thank you,

The references will be very useful in particular, " L. Debnath, D. Bhatta, Integral Transforms and Their Applications".

Si consigues ler en Portugués, puedo enviarte textos que yoy tengo para un libro que estoy a finalizar.

[email protected]

To solve the problems of mathematical physics and mechanics you must know General functions theory and Fourier transformation in the space of generalized functions. The best books for their study are the books of Vladimirov V.S. General functions in mathematical physics (Moscow, 1978 ) and Equations of mathematical physics (Moscow, 1976 ) . There are the later publishing of these books.

An Introduction to Integral Transforms

Baidyanath Patra

Hardback £115.00eBook £103.50eBook Rental from £57.50

February 12, 2018 by CRC Press Reference - 412 Pages - 7 B/W Illustrations

I will recommend you use Mathematical Physics by B.D Gupta, K .A Stroud Advanced Engineering Mathematics for Integral transforms

I would recommend:

1. I. N. Sneddon, Fourier Transforms, McGraw-Hill, 1951.

2. I. N. Sneddon, The Use of Integral Transforms, McGraw-Hill, 1974.

4. Dean Duffy, Transform Methods for Solving Partial Differential Equations.

5. Dean Duffy, Mixed Boundary Value Problems.

6. Dean Duffy, Green's Functions with Applications.

If you are looking for a book on general transform theory, I recently bought "An Introduction To Transform Theory" by D.V. Widder. The book covers Dirichlet Series, Zeta Functions, the Laplace Transform, the Stieltjes Transform, Tauberian Theorems, and even covers the basics of Fractional Integrals and Fractional Derivatives. I hope this helps.

"Integral Transforms for Engineers" by Bhimsen K. Shivamoggi and Larry C. Andrews has a decent amount of Fourier and Laplace transformations and practice problems with numerous applications. They include short chapters on Mellin and Hankel transforms with just a page or so devoted to Z and Sturm-Liouvilles as well. You can purchase a PDF here: https://spie.org/publications/book/339204?SSO=1

All the books, there are many, on Signals and Systems cover the most important transforms. The most known is the book of Oppenheim and Wilski (Prentice-Hall), The book of Roberts (McGraw-Hill) is very good.

Thanks Ms. Stanfield and Mr. Duarte.

I think to the book "Integral Transforms and Their Applications" of Lokenath Debnath, Dambaru Bhatta, Taylor & Francis Group, 2007

Integral Transforms and Their Applications"

Authors: Lokenath Debnath, Dambaru Bhatta,

As soon as Dirac delta "functions" are involved you will need to consider all functions as so-called generalized functions. In this case I recommend A.H. Zemanian's "Generalized Integral Transforms".

Article Generalized Integral Transformations

He is one of the pioneers in generalized functions theory. This book is mathematically rigorous and describes integral transforms in the light of generalized functions theory. All functions can be derived infinitely often in this theory. This fact alone solves many practical problems.

Try an old fashion mini computer

As it might be seen from all answers, there are many books dealing with this subjects. The underlying idea is that, in the study of Partial Differential Equations (where by the way, the transform methods are another way of introducing separation of the variables), you obtain non-rational transforms and you need a more involved analysis. It depends on the deepness of the theoretical analysis you seek for. I would recommend first of all the magnificent treatise of Gustav Doetsch "Handbuch der Laplace Transformation" (3 volumes published by Birkhauser basel in 1958-59) also the extended lists of transforms contained in the books of V. A. Ditkin and in those more recent of Polyanin and his co-authors. The books on signal processing are more comprehensive but less rigorous in my opinion. I repeat, it depends on what are you seeking for...

It is clear from all answers that there are many books concerning the

integral transforms. You must check what manner of their exposition is suitable for you and bring lite and deep understanding of the matter. But according my personal experience as Professor Rasvan I highly recommend the book of Gustav Doetsch " Introduction to the Theory and Application of the Laplace transformation" Springer Verlag 1974. It must be noted that in this book which is rare, are explained the one side and two side Laplace transform, the distribution transform, the complex inverse formula and etc.. In this book you can find several applications and useful appendix concerning the distribution theory as well as excellent table of Laplace transform.

I would recommend this one "Dimitris N. Chorafas , Integral Transforms and Their Applications"

Integral Transforms and Their Applications"

Authors: Lokenath Debnath, Dambaru Bhatta,

In additional (but first I recommend to study the book of Gustav Doetsch ), there is a new engineer oriented book which almost all integral transforms, written by Baidyanath Patra "An Introduction to Integral Transforms".

I would suggest a good book on "Signals and Systems", mainly for the bilateral Laplace and transforms. Mathematicians did not realize that the initial conditions of the one sided Laplace transform (Doetsch) are usually wrong.

Remark that thee are two references to Gustav Doetsch: the "Introduction to... " which is a single volume, translated also in English, and "Handbuch of..." which is 3-volume only in German. Nobody had enough courage and time to translate it in English or Russian. I do not quite understand why the initial conditions of the Laplace transform are "wrong". The feature of the one-sided (genuine) Laplace transform is exactly to take into account the initial conditions. The two-sided transform is like the Fourier transform, best suited for steady state. If one thinks to the initial conditions to be considered is PDEs then the problem is not for the Laplace transform but of the sense of the solution (classical, distributional). An interesting reference might be to look at Laplace Stieltjes transform (the book of D.V. Widder). The sense of the integral is important for both initial conditions and for inversion

Dear Vladimir

The initial conditions depend on the system at hand, not on the tool we use to study it. For this reason, it depends on the past of the system, not on the future.

See the paper "Initial conditions, generalized functions, and the Laplace transform: troubles at the origin". This only analysis the integer order case. When you go into fractional, the situation is worst. See my paper in attach.

I think book(Handbook Of Integral Equations - Polyanin) is useful.

Peyman,

I guess the best reference about integral transformation techniques is the book by late Prof. Ian Sneddon named "The Use of Integral Transform". His entire publications are great examples of application of integral transforms in contact and fracture mechanics problems.

Good luck.

Integral Transforms and Their Applications of Lokenath Debnath and Dambaru Bhatta, is good....

The prerequisite for studying integral transform is the theory of complex variable. Playing with the contour integrations on the complex domain might be a good start to learn integral transforms.