Probability Integral

Its Origin, Its Importance, and Its Calculation

Inbunden, Engelska, 2023

Av Paul J. Nahin

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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, engineering and probability theory.

Produktinformation

Utgivningsdatum2023-09-09
Mått155 x 235 x 23 mm
Vikt486 g
FormatInbunden
SpråkEngelska
Antal sidor189
FörlagSpringer International Publishing AG
ISBN9783031384158

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Paul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire. He is the author of 21 books on mathematics, physics, and the history of science, published by Springer, and the university presses of Princeton and Johns Hopkins. He received the 2017 Chandler Davis Prize for Excellence in Expository Writing in Mathematics (for his paper “The Mysterious Mr. Graham,” The Mathematical Intelligencer, Spring 2016). He gave the invited 2011 Sampson Lectures in Mathematics at Bates College, Lewiston, Maine.

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.