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The Probability Integral Its Origin, Its Importance, and Its Calculation /

This book tells the story of the probability integral, the approaches to analyzing it throughout history, and the many areas of science where it arises. The so-called probability integral, the integral over the real line of a Gaussian function, occurs ubiquitously in mathematics, physics, engineerin...

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Détails bibliographiques
Auteur principal: Nahin, Paul J. (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:anglais
Publié: Cham : Springer Nature Switzerland : Imprint: Springer, 2023.
Édition:1st ed. 2023.
Sujets:
Mathematical physics.
Engineering mathematics.
Measure theory.
Probabilities.
Statistics .
History.
Mathematics.
Mathematical Methods in Physics.
Engineering Mathematics.
Measure and Integration.
Probability Theory.
History of Statistics.
History of Mathematical Sciences.
Accès en ligne:https://doi.org/10.1007/978-3-031-38416-5
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Table des matières:
  • Chapter 1. De Moivre and the Discovery of the Probability Integral
  • Chapter 2. Laplace’s First Derivation
  • Chapter 3. How Euler Could Have Done It Before Laplace (but did he?)
  • Chapter 4. Laplace’s Second Derivation
  • Chapter 5. Generalizing the Probability Integral
  • Chapter 6. Poisson’s Derivation
  • Chapter 7. Rice’s Radar Integral
  • Chapter 8. Liouville’s Theorem that Has No Finite Form
  • Chapter 9. How the Error Function Appeared in the Electrical Response of the Trans-Atlantic Telegraph Cable
  • Chapter 10. Doing the Probability Integral with Differentiation
  • chapter 11. The Probability Integral as a Volume
  • Chapter 12. How Cauchy Could Have Done It (but didn’t)
  • Chapter 13. Fourier Has the Penultimate Technical Word
  • Chapter 14. Finbarr Holland Has the Last Technical Word
  • Chapter 15. A Final Comment on Mathematical Proofs.

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