Operational Calculus
2nd Edition
Published on 14. July 2014
322 pages
978-1-4832-7893-3 (ISBN)
Description
Pure and Applied Mathematics, Volume 109: Operational Calculus, Second Edition. Volume I presents the foundations of operational calculus and its applications to physics and engineering. This book introduces the operators algebraically as a kind of fractions. Organized into three parts, this volume begins with an overview of the concept as well as the characteristics of a convolution of continuous functions. This text then examines the transitivity, associativity, and distributivity of convolution with regard to addition. Other parts consider the methods of solving other difference equations, particularly in the field of electrical engineering, in which the variable runs over integer values only. This book discusses as well the solution of differential equations under given initial conditions. The final part deals with the characteristic properties of a derivative and provides the definition of algebraic derivative to any operators. This book is a valuable resource for physicists, electrical engineers, mathematicians, and research workers.
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Jan Mikusinski
Operational Calculus: v. 1
Book
06/1981
2nd Edition
Pergamon
€22.91
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Content
ForewordForeword to the Second English EditionPart I - Operational Algebra Chapter I. The Concept and Properties of a Convolution of Continuous Functions § 1. Definition of Convolution § 2. Class ?? § 3. Commutativity of Convolution § 4. Associativity of Convolution § 5. Addition and Convolution as Fundamental Operations in the Operational Calculus § 6. Function and Value of a Function § 7. Symbolics § 8. Integral Operator Chapter II. Theorem of Titchmarsh § 9. Formulation of the Theorem and General Remarks § 10. Theorem of Phragmén § 11. Theorem on Moments § 12. Proof of Titschmarsh's Theorem in the Case f = g § 13. General Proof Chapter III. Operators § 14. An Operation Inverse to Convolution § 15. Operators § 16. Operations on Operators § 17. Numerical Operators § 18. Remarks on Terminology § 19. Product of a Number and a Function § 20. Numbers 0 and 1 § 21. Differential Operator § 22. Powers of Operator 8 § 23. Polynomials of Operator 8 § 24. Connections of the Operator 8 with the Exponential Function § 25. Connections of the Operator 8 with Trigonometric Functions § 26. Rational Operators § 27. Some Properties of Operators. Moments Chapter IV. Ordinary Differential Equations with Constant Coefficients § 28. General Method and Examples Chapter V. Theory of Electric Circuit § 29. Remarks on the Application of the Operational Calculus to Physical and Technical Problems § 30. The Electric Circuit § 31. The Short-Circuit Current § 32. Impedance § 33. Sine Wave Currents § 34. Kirchhoff's Laws § 35. Wheatstone Bridge § 36. Anderson Bridge § 37. General Remarks on Forming Equations for Network Currents § 38. Impedance and the Short-Circuit Current of Compound Two-Terminal Networks § 39. The Case of a Sinusoidal Electromotive Force § 40. The Electromotive Impulse and its Application to the Measurement of Impedance § 41. Inductive Couplings § 42. Four-Terminal Networks § 43. Connecting Four-Terminal Networks § 44. Connection of Three Four-Terminal Networks § 45. Four-Terminal Networks with Short-Circuited Terminals § 46. Four-Terminal Networks with Free Terminals § 47. Four-Terminal Network with Terminals Short-Circuited by a Two-Terminal Network § 48. Chain of Four-Terminal Networks § 49. Transformers § 50. Cathode-Ray Tube as a Four-Terminal Network § 51. Four Terminal Network with Determinant 1 § 52. Inverted Four-Terminal Networks and Symmetrical Four-Terminal Networks Chapter VI. General Eolutione of Differential Equations and Boundary Problems § 53. General Solution. Transfer Functions § 54. Boundary Problems § 55. Solution of Differential Equations Under Given Initial Conditions At the Point to ¿ 0 Chapter VII. Discontinuous Functions § 56. Functions of Class ?? § 57. Operations on Functions of Class ?? § 58. Euler's Gamma Integral § 59. Non-Integer Powers of the Operators ?? and ?? - a § 60. Functions Having a Derivative of Class ?? § 61. Differential Equations with a Discontinuous Right Side § 62. Jump Function and Translation Operator § 63. Derivatives of Certain Discontinuous Functions § 64. Approximation of the Translation Operator by Functions § 65. Various Interpretations of the Translation Operator § 66. Functions Defined on the Whole Axis t Chapter VIII. Applications to the Statics of Beams § 67.
