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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Generalized Functions Theory and Technique - Theory and Technique (Paperback, 2nd ed. 1998)
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Generalized Functions Theory and Technique - Theory and Technique (Paperback, 2nd ed. 1998)
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This second edition of Generalized Functions has been strengthened
in many ways. The already extensive set of examples has been
expanded. Since the publication of the first edition, there has
been tremendous growth in the subject and I have attempted to
incorporate some of these new concepts. Accordingly, almost all the
chapters have been revised. The bibliography has been enlarged
considerably. Some of the material has been reorganized. For
example, Chapters 12 and 13 of the first edition have been
consolidated into Chapter 12 of this edition by a judicious process
of elimination and addition of the subject matter. The new Chapter
13 explains the interplay between the theories of moments,
asymptotics, and singular perturbations. Similarly, some sections
of Chapter 15 have been revised and included in earlier chapters to
improve the logical flow of ideas. However, two sections are
retained. The section dealing with the application of the
probability theory has been revised, and I am thankful to Professor
Z.L. Crvenkovic for her help. The new material included in this
chapter pertains to the modern topics of periodic distributions and
microlocal theory. I have demonstrated through various examples
that familiarity with the generalized functions is very helpful for
students in physical sciences and technology. For instance, the
reader will realize from Chapter 6 how the generalized functions
have revolutionized the Fourier analysis which is being used
extensively in many fields of scientific activity.
General
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