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200 14$aThe Probability Integral $eIts Origin, Its Importance, and Its Calculation /$fby Paul J. Nahin
205   $a1st ed. 2023.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023.
215   $a1 online resource (205 pages)
311 08$aPrint version: Nahin, Paul J. The Probability Integral Cham : Springer,c2023 9783031384158 
327   $aChapter 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.
330   $aThis 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. Stubbornly resistant to the undergraduate toolkit for handling integrals, calculating its value and investigating its properties occupied such mathematical luminaries as De Moivre, Laplace, Poisson, and Liouville. This book introduces the probability integral, puts it into a historical context, and describes the different approaches throughout history to evaluate and analyze it. The author also takes entertaining diversions into areas of math, science, and engineering where the probability integral arises: as well as being indispensable to probability theory and statistics, it also shows up naturally in thermodynamics and signal processing. Designed to be accessibleto anyone at the undergraduate level and above, this book will appeal to anyone interested in integration techniques, as well as historians of math, science, and statistics.
606   $aMathematical physics
606   $aEngineering mathematics
606   $aMeasure theory
606   $aProbabilities
606   $aStatistics
606   $aHistory
606   $aMathematics
606   $aMathematical Methods in Physics
606   $aEngineering Mathematics
606   $aMeasure and Integration
606   $aProbability Theory
606   $aHistory of Statistics
606   $aHistory of Mathematical Sciences
615  0$aMathematical physics.
615  0$aEngineering mathematics.
615  0$aMeasure theory.
615  0$aProbabilities.
615  0$aStatistics.
615  0$aHistory.
615  0$aMathematics.
615 14$aMathematical Methods in Physics.
615 24$aEngineering Mathematics.
615 24$aMeasure and Integration.
615 24$aProbability Theory.
615 24$aHistory of Statistics.
615 24$aHistory of Mathematical Sciences.
676   $a530.15
676   $a519.2
700   $aNahin$b Paul J$048655
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910746094103321
996   $aThe Probability Integral$93562720
997   $aUNINA