Introduction To The Operational Calculus - 1st Edition - ISBN: 9780123957610, 9780323162456

Introduction To The Operational Calculus

1st Edition

Authors: Lothar Berg
eBook ISBN: 9780323162456
Imprint: North Holland
Published Date: 1st January 1967
Page Count: 304
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Description

Introduction to the Operational Calculus is a translation of "Einfuhrung in die Operatorenrechnung, Second Edition."

This book deals with Heaviside's interpretation, on the Laplace integral, and on Jan Mikusinki's fundamental work "Operational Calculus." Throughout the book, basic algebraic concepts appear as aids to understanding some relevant points of the subject. An important field for research in analysis is asymptotic properties. This text also discusses examples to show the potentialities in applying operational calculus that run beyond ordinary differential equations with constant coefficients. In using operational calculus to solve more complicated problems than those of ordinary differential equations with constant coefficients, the concept of convergence assumes a significant role in the field of operators. This book also extends the Laplace transformation and applies it to non-transformable functions. This text also present three methods in which operational calculus can be modified and become useful in solving specific ranges of problems. These methods pertain to the finite Laplace transformation, to partial differential equations, and to the Volterra integral equations and ordinary differential equations with variable coefficients.

This book can prove valuable for mathematicians, students, and professor of calculus and advanced mathematics.

Table of Contents


Introduction


1. General Survey


2. The Heaviside Method


3. A Rigorous Approach


4. Derivation of an Integral Transformation


5. Numerical Evaluations


6. Improved Approximations


Chapter I. Algebraic Foundations


1. Rings and Domains of Integrity


2. Fields


3. Polynomial Rings


4. Rational Functions


5. Isomorphisms and Extensions


6. Ideals and Residue Class Rings


Chapter II. Functions of a Discrete Variable


7. The Function Ring


8. Quotient Fields


9. Linear Difference Equations


10. Passage to the Limit


11. The Operator q as Complex Variable


12. Applications


Chapter III. Functions of a Continuous Variable


13. The Duhamel Product


14. Function Powers of t


15. Comparison Between Function and Value Products


16. Titchmarsh's Theorem


17. The Field of Operators


18. Rational Operators in p


Chapter IV. Applications


19. Differential Equations with Constant Coefficients


20. Examples


21. Systems of Differential Equations


22. Degenerate Systems


23. Control Engineering


24. Integral Equations


Chapter V. Convergent Sequences of Operators


25. The Concept of Convergence


26. Infinite Series


27. Discontinuous Functions


28. The Displacement Operator


29. Step Functions


30. The Delta Operator


Chapter VI. The Laplace Transformation


31. The Operator p as Complex Variable


32. Properties


33. Examples


34. Inverse Transformations


35. The Complex Inversion Formula


36. Fou

Details

No. of pages:
304
Language:
English
Copyright:
© North Holland 1967
Published:
Imprint:
North Holland
eBook ISBN:
9780323162456

About the Author

Lothar Berg

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