UID:
almahu_9949697544502882
Format:
1 online resource (305 p.)
ISBN:
0-323-16245-2
Series Statement:
North-Holland series on applied mathematics and mechanics ; v. 2
Uniform Title:
Einführung in die Operatorenrechnung.
Content:
Introduction To The Operational Calculus
Note:
Translation of Einfuhrung in die Operatorenrechnung.
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Front Cover; Introduction to the Operational Calculus; Copyright Page; FOREWORD TO THE FIRST EDITION; FOREWORD TO THE SECOND EDITION; FOREWORD TO THE ENGLISH EDITION; 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
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CHAPTER II. FUNCTIONS OF A DISCRETE VARIABLE7. 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
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23. Control engineering24. 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 operatorp as complex variable; 32. Properties; 33. Examples; 34. Inverse transformations; 35. The complex inversion formula; 36. Fourier's integral theorem; CHAPTER VII. APPLICATIONS; 37. The method of residues; 38. Series expansions; 39. Differential equations with polynomial coefficients
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40. Partial differential equations41. Difference equations in the image domain; 42. Integral equations; CHAPTER VIII. ASYMPTOTIC PROPERTIES; 43. Definitions; 44. Abelian theorems; 45. Further types of singularity; 46. Tauberian theorems; 47. Problems of stability; 48. Euler's summation formula; CHAPTER IX. GENERALIZATIONS; 49. Asymptotic series; 50. Asymptotic integrals; 51. The general operational calculus; 52. Partial differential equations; 53. Differential-difference equations; 54. The finite part of an integral; CHAPTER X. FURTHER OPERATIONAL METHODS
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55. The finite Laplace transformation56. Boundary value problems; 57. Functions of two variables; 58. Partial differential equations; 59. Groups; 60. Differential equations with variable coefficients; APPENDIX; ANSWERS TO EXERCISES; REFERENCES; A. Text-books and monographs; B. Original papers; Formulae; Subject index
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English
Additional Edition:
ISBN 0-12-395761-3
Language:
English
