Integral Transformation and Their Application Third Edition

Abstract

A teacher can never truly teach unless he is still learning himself. A lamp can never light another lamp unless it continues to burn its own flame. The teacher who has come to the end of his subject, who has no living traffic with his knowledge but merely repeats his lessons to his students, can only load their minds; he cannot quicken them.” Rabindranath Tagore, Nobel Prize for Literature (1913) The previous two editions of the book were well received and used as a senior undergraduate or first-year graduate-level text and reference in the United States and abroad for the several years. We received various comments and suggestions from many students, faculty, and researchers around the world. All these comments and criticisms have been very helpful, beneficial, and encouraging. The third edition is the result of these suggestions and comments. The selection, arrangement, and presentation of the material in this edition have carefully been made based on our past and present teaching, research, and professional experience. In particular, this book has evolved from regularly teaching courses in integral transforms, boundary value problems, differential equations, applied mathematics, and advanced engineering mathematics over many years to students of mathematics and engineering in the United States and abroad. It is essentially designed to cover advanced mathematical methods for science and engineering students with heavy emphasis on many different and varied applications. It differs from many textbooks with similar titles due to the major emphasis placed on numerous topics, and systematic development of the underlying theory before making applications and inclusion of many new and modern topics such as the double Laplace transforms, the Radon transforms, Gabor transforms, wavelet transforms. Moreover, an attempt has been made to provide a modern approach to the Fourier, Laplace, Hankel, Mellin, and Z transforms with new worked-out examples, and problems in exercises which are not available in other similar textbooks. The above transforms are used to solve boundary and initial value problems for difference, functional, ordinary, and partial differential equations which