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Operational Calculus Based on the Two-Sided LaPlace Integral
Balth Van Der Pol and H. Bremmer
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AMS Chelsea Publishing
1950; 415 pp; hardcover
Reprint/Revision History:
third printing with corrections 1989
ISBN-10: 0-8284-0327-9
ISBN-13: 978-0-8284-0327-6
List Price: US$47
Member Price: US$42.30
Order Code: CHEL/327
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From the Preface: "Primarily this book is intended for application of the operational calculus to mathematics, physics and technical problems. We have therefore given not only the basic principles, ideas and theorems as clearly as possible (and rather extensively), but also many worked-out problems from purely mathematical and physical as well as from technical fields ... [S]ome of the deeper theorems have been omitted, and for these the reader is referred to the mathematical literature ... Nonetheless, it is believed that the purely mathematical treatment is more advanced than is usual in books devoted primarily to practical applications ... It is therefore hoped that the book may be of value to those pure mathematicians who are interested in a rapid and simple derivation of complicated and unexpected relations between various mathematical functions, as well as to the engineer in search, for example, of a very simple treatment of transient phenomena in electrical networks, such as filters. In both cases the operational calculus appears to its best advantage."

Table of Contents

  • General introduction
  • The Fourier integral as basis of the operational calculus
  • Elementary operational images
  • Elementary rules
  • The delta or impulse function
  • Questions concerning the convergence of the definition integral
  • Asymptotic relations and operational transposition of series
  • Linear differential equations with constant coefficients
  • Simultaneous linear differential equations with constant coefficients; Electric-circuit theory
  • Linear differential equations with variable coefficients
  • Operational rules of more complicated character
  • Step functions and other discontinuous functions
  • Difference equations
  • Integral equations
  • Partial differential equations in the operational calculus of one variable
  • Simultaneous operational calculus
  • `Grammar'
  • `Dictionary'
  • List of authors quoted
  • General index
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