Screen LibraryOperational calculus /
Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable fun...
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| Main Authors: | |
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| Corporate Authors: | |
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| Published: |
Pergamon,
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| Publisher Address: | Oxford : |
| Publication Dates: | 1987. |
| Literature type: | eBook |
| Language: | English |
| Edition: | Second edition. |
| Series: |
International series of monographs in pure and applied mathematics ;
volume 110 |
| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/book/9780080264790 |
| Summary: |
Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-ho. |
| Item Description: | Previous edition: published in 1v. 1959. |
| Carrier Form: | 1 online resource (263 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 254-257) and index. |
| ISBN: |
9781483161457 1483161455 |
| Index Number: | QA432 |
| CLC: | O177.6 |
| Contents: |
Front Cover; Operational Calculus; Copyright Page; Table of Contents; FOREWORD TO THE FIRST ENGLISH EDITION; FOREWORD TO THE SECOND ENGLISH EDITION; SUPPLEMENTS TO VOLUME I; (A) Supplement to Part I, Chapter VI; (B) Supplement to Part III, Chapter VIII; PART IV: AN OUTLINE OF THE GENERAL THEORY OF LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS; CHAPTER I. Homogeneous equations; 1. Introductory remarks; 2. Characteristic equations; 3. On exponential functions; 4. Logarithms; 5. Multiple roots of the characteristic equation; 6. The general solution. 7. Theorem on uniqueness of solution 8. The logarithmic equation; 9. Linear differential expressions; 10. Operations on linear differential expressions; 11. Characteristic polynomials of linear differential expressions; 12. Pure equations; 13. Mixed equations; 14. Adapting the solution to given initial, boundary and other conditions; CHAPTER II. Non-homogeneous equations; 15. The general solution of a non-homogeneous equation; 16. The case where the right side is a polynomial; 17. The case where the right side is an exponential function. 18. The case where the right side is a product of a polynomial and an exponential function 19. The case where the right side is a linear combination of two functions; 20. The case where the right side is a trigonometric function; 21. Adapting the solution to additional conditions; CHAPTER III. Applications to partial differential equations; 22. Reducing partial operational equations to operational equations; 23. Remarks on additional conditions; 24. An incorrect solution; 25. Explaining the apparent contradiction. 26. The Cauchy conditions and the question of their being equivalent to the general conditions 27. Solving restrictive equations; 28. The question of the equivalence of a partial equation and an operational equation; 29. Further examples of solving partial equations; 30. General remarks on solving partial equations by the operational method; 31. Mixed problems; PART V: INTEGRAL OPERATIONAL CALCULUS; CHAPTER I. The integral of an operational function and its applications; 1. Operational functions of class (K); 2. The definition of the integral; 3. Properties of the integral. 4. Operational functions of two variables 5. Cutting down a function; 6. The integral form of a certain particular solution of the logarithmic differential equation; 7. Application to the equation of a vibrating string; 8. Application of infinite series and definite integrals; CHAPTER II. Integral transformations; 9. The Laplace transform; 10. The Laplace transform as a basis for the operational calculus; 11. A comparison of the direct method and the method of Laplace transform; 12. Other related methods; PART VI: ADVANCED TOPICS IN THE OPERATIONAL CALCULUS. |