Ebook: Generalized Functions: Theory and Applications

This third edition of "Generalized Functions" expands the treatment of fundamental concepts and theoretical background material and delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optimal control problems in economics, and more. In applying the powerful tools of generalized functions to better serve the needs of physicists, engineers, and applied mathematicians, this work is quite distinct from other books on the subject.

Key new topics and important features:

* Examination of the Poisson Summation Formula and the concepts of differential forms and the delta distribution on wave fronts

* Enhanced presentation of the Schroedinger, Klein–Gordon, Helmholtz, heat and wave equations

* Exposition driven by additional examples and exercises

* Comprehensive bibliography and index

* Prerequisites: advanced calculus, ordinary and partial differential equations

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From the Reviewers:

"Kanwal’s book is a worthy member of this company [Gelfand and Shilov, Semanian, Friedman, Jones, and Barros-Neto]. Its strength lies in the application to classical physics….[it presents] a wealth of applications that cannot be found in any other single source…Kanwal has written a valuable book accessible to first-year graduate students in physics and engineering."

--Ivar Stakgold, Mathematics, University of Delaware

"The advantage of this text is in carefully gathered examples explaining how to use corresponding properties…. Even the standard material connecting with partial and ordinary differential equations is rewritten in modern terminology."

--Zentralblatt

---

This third edition of "Generalized Functions" expands the treatment of fundamental concepts and theoretical background material and delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optimal control problems in economics, and more. In applying the powerful tools of generalized functions to better serve the needs of physicists, engineers, and applied mathematicians, this work is quite distinct from other books on the subject.

Key new topics and important features:

* Examination of the Poisson Summation Formula and the concepts of differential forms and the delta distribution on wave fronts

* Enhanced presentation of the Schroedinger, Klein–Gordon, Helmholtz, heat and wave equations

* Exposition driven by additional examples and exercises

* Comprehensive bibliography and index

* Prerequisites: advanced calculus, ordinary and partial differential equations

-----

From the Reviewers:

"Kanwal’s book is a worthy member of this company [Gelfand and Shilov, Semanian, Friedman, Jones, and Barros-Neto]. Its strength lies in the application to classical physics….[it presents] a wealth of applications that cannot be found in any other single source…Kanwal has written a valuable book accessible to first-year graduate students in physics and engineering."

--Ivar Stakgold, Mathematics, University of Delaware

"The advantage of this text is in carefully gathered examples explaining how to use corresponding properties…. Even the standard material connecting with partial and ordinary differential equations is rewritten in modern terminology."

--Zentralblatt

---

This third edition of "Generalized Functions" expands the treatment of fundamental concepts and theoretical background material and delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optimal control problems in economics, and more. In applying the powerful tools of generalized functions to better serve the needs of physicists, engineers, and applied mathematicians, this work is quite distinct from other books on the subject.

Key new topics and important features:

* Examination of the Poisson Summation Formula and the concepts of differential forms and the delta distribution on wave fronts

* Enhanced presentation of the Schroedinger, Klein–Gordon, Helmholtz, heat and wave equations

* Exposition driven by additional examples and exercises

* Comprehensive bibliography and index

* Prerequisites: advanced calculus, ordinary and partial differential equations

-----

From the Reviewers:

"Kanwal’s book is a worthy member of this company [Gelfand and Shilov, Semanian, Friedman, Jones, and Barros-Neto]. Its strength lies in the application to classical physics….[it presents] a wealth of applications that cannot be found in any other single source…Kanwal has written a valuable book accessible to first-year graduate students in physics and engineering."

--Ivar Stakgold, Mathematics, University of Delaware

"The advantage of this text is in carefully gathered examples explaining how to use corresponding properties…. Even the standard material connecting with partial and ordinary differential equations is rewritten in modern terminology."

--Zentralblatt

Content:
Front Matter....Pages i-xvii
The Dirac Delta Function and Delta Sequences....Pages 1-16
The Schwartz-Sobolev Theory of Distributions....Pages 17-48
Additional Properties of Distributions....Pages 49-70
Distributions Defined by Divergent Integrals....Pages 71-98
Distributional Derivatives of Functions with Jump Discontinuities....Pages 99-138
Tempered Distributions and the Fourier Transform....Pages 139-177
Direct Products and Convolutions of Distributions....Pages 178-216
The Laplace Transform....Pages 217-227
Applications to Ordinary Differential Equations....Pages 228-264
Applications to Partial Differential Equations....Pages 265-311
Applications to Boundary Value Problems....Pages 312-358
Applications to Wave Propagation....Pages 359-395
Interplay Between Generalized Functions and the Theory of Moments....Pages 396-419
Linear Systems....Pages 420-433
Miscellaneous Topics....Pages 434-464
Back Matter....Pages 465-476

---

This third edition of "Generalized Functions" expands the treatment of fundamental concepts and theoretical background material and delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optimal control problems in economics, and more. In applying the powerful tools of generalized functions to better serve the needs of physicists, engineers, and applied mathematicians, this work is quite distinct from other books on the subject.

Key new topics and important features:

* Examination of the Poisson Summation Formula and the concepts of differential forms and the delta distribution on wave fronts

* Enhanced presentation of the Schroedinger, Klein–Gordon, Helmholtz, heat and wave equations

* Exposition driven by additional examples and exercises

* Comprehensive bibliography and index

* Prerequisites: advanced calculus, ordinary and partial differential equations

-----

From the Reviewers:

"Kanwal’s book is a worthy member of this company [Gelfand and Shilov, Semanian, Friedman, Jones, and Barros-Neto]. Its strength lies in the application to classical physics….[it presents] a wealth of applications that cannot be found in any other single source…Kanwal has written a valuable book accessible to first-year graduate students in physics and engineering."

--Ivar Stakgold, Mathematics, University of Delaware

"The advantage of this text is in carefully gathered examples explaining how to use corresponding properties…. Even the standard material connecting with partial and ordinary differential equations is rewritten in modern terminology."

--Zentralblatt

Content:
Front Matter....Pages i-xvii
The Dirac Delta Function and Delta Sequences....Pages 1-16
The Schwartz-Sobolev Theory of Distributions....Pages 17-48
Additional Properties of Distributions....Pages 49-70
Distributions Defined by Divergent Integrals....Pages 71-98
Distributional Derivatives of Functions with Jump Discontinuities....Pages 99-138
Tempered Distributions and the Fourier Transform....Pages 139-177
Direct Products and Convolutions of Distributions....Pages 178-216
The Laplace Transform....Pages 217-227
Applications to Ordinary Differential Equations....Pages 228-264
Applications to Partial Differential Equations....Pages 265-311
Applications to Boundary Value Problems....Pages 312-358
Applications to Wave Propagation....Pages 359-395
Interplay Between Generalized Functions and the Theory of Moments....Pages 396-419
Linear Systems....Pages 420-433
Miscellaneous Topics....Pages 434-464
Back Matter....Pages 465-476
....