UID:
almafu_9958110719702883
Umfang:
1 online resource (285 p.)
ISBN:
1-281-76770-0
,
9786611767709
,
0-08-087383-9
Serie:
Pure and applied mathematics, a series of monographs and textbooks ; 67
Inhalt:
The Heat Equation
Anmerkung:
Description based upon print version of record.
,
Front Cover; The Heat Equation; Copyright Page; Contents; Preface; Symbols and Notation; Chapter I. Introduction; 1. Introduction; 2. The Physical Model; 3. The Heat Equation; 4. Generalities; 5. Basic Solutions of the Heat Equation; 6. Methods of Generating Solutions; 7. Definitions and Notations; Chapter II. Boundary-Value Problems; I. Introduction; 2. Uniqueness; 3. The Maximum Principle; 4. A Criterion for Temperature Functions; 5. Solution of Problem 1 in a Special Case; 6. Uniqueness for the Infinite Rod; Chapter III. Further Developments; 1. Introduction; 2. The Source Solution
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3. The Addition Formula for k(x, t)4. The Homogeneity of k(x, t ); 5. An Integral Representation of k(x, t ); 6. A Further Addition Formula for k(x, t); 7. Laplace Transform of k(x, ts); 8. Laplace Transform of h(x, t); 9. Operational Calculus; 10. Three Classes of Functions; 11. Examples of Class II; 12. Relation among the Classes; 13. Series Expansions of Functions in Class I; 14. Series Expansions of Functions in Class II; 15. Series Expansions of Functions in Class III; 16. A Temperature Function Which Is Not Entire in the Space Variable; Chapter IV. Integral Transforms
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1. Poisson Transforms2. Convergence; 3. Poisson Transform in H; 4. Analyticity; 5. Inversion of the Poisson-Lebesgue Transform; 6. Inversion of the Poisson-Stieltjes Transform; 7. The h-Transform; 8. h-Transform in H; 9. Analyticity; 10. Inversion of the h-Lebesgue Transform; 11. The k-Transform; 12. A Basic Integral Representation; 13. Analytic Character of Every Temperature Function; Chapter V. Theta-Functions; 1. Introduction; 2. Analyticity; 3.?-Functions in H; 4. Alternate Expansions; 5. Two Positive Kernels; 6. A ?-Transform; 7. A f-Transform; 8. Fourier's Ring
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9. A Solution of the First Boundary-Value Problem10. Uniqueness; Chapter VI. Green's Function; 1. Green's Function for a Rectangle; 2. An Integral Representation; 3. Problem I Again; 4. A Property of G(x, t ; ?, n); 5. Green's Function for an Arbitrary Rectangle; 6. Series of Temperature Functions; 7. The Reflection Principle; 8. Isolated Singularities; Chapter VII. Bounded Temperature Functions; 1. The Infinite Rod; 2. TheSemi-Infinite Rod; 3. Semi-Infinite Rod, Continued; 4. Semi-Infinite Rod, General Case; 5. The Finite Rod; Chapter VIII. Positive Temperature Functions
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1. The Infinite Rod2. Uniqueness, Positive Temperatures on an Infinite Rod; 3. Stieltjes Integral Representation, Infinite Rod; 4. Uniqueness, Semi-Infinite Rod; 5. Representation, Semi-Infinite Rod; 6. The Finite Rod; 7. Examples; 8. Further Classes of Temperature Functions; Chapter IX. The Huygens Property; 1. Introduction; 2. Blackman's Example; 3. Conditionally Convergent Poisson Integrals; 5. Heat Polynomials and Associated Functions; Chapter X. Series Expansions of Temperature Functions; 1. Introduction; 2. Asymptotic Estimates; 3. A Generating Function; 4. Region of Convergence
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5. Strip of Convergence
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English
Weitere Ausg.:
ISBN 0-12-748540-6
Sprache:
Englisch
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