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An accessible introduction to the heat equation and its role in the development of one of the greatest engineering feats of the 19th century: the trans-Atlantic telegraph cable.

Nahin, Paul J.

Hot Molecules, Cold Electrons

From the Mathematics of Heat to the Development of the Trans-Atlantic Telegraph Cable


    40,95 € / $47.00 / £40.00*

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    Publication Date:
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    To be published:
    March 2020
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    Aims and Scope

    An entertaining mathematical exploration of the heat equation and its role in the triumphant development of the trans-Atlantic telegraph cable

    Heat, like gravity, shapes nearly every aspect of our world and universe, from how milk dissolves in coffee to how molten planets cool. The heat equation, a cornerstone of modern physics, demystifies such processes, painting a mathematical picture of the way heat diffuses through matter. Presenting the mathematics and history behind the heat equation, Hot Molecules, Cold Electrons tells the remarkable story of how a foundational idea brought about one of the greatest technological advancements of the modern era.

    Paul Nahin vividly recounts the heat equation’s tremendous influence on society, showing how French mathematical physicist Joseph Fourier discovered, derived, and solved the equation in the early nineteenth century. Nahin then follows Scottish physicist William Thomson, whose further analysis of Fourier’s explorations led to the groundbreaking trans-Atlantic telegraph cable. This feat of engineering reduced the time a message could be sent across the ocean from weeks to minutes. Readers also learn that Thomson used Fourier’s solutions to calculate the age of the earth, and, in a bit of colorful lore, that writer Charles Dickens relied on the trans-Atlantic cable to save himself from a career-damaging scandal. The book’s mathematical and scientific explorations can be easily understood by anyone with a basic knowledge of high school calculus and physics, and MATLAB code is included to aid readers who would like to solve the heat equation themselves.

    A testament to the intricate links between mathematics and physics, Hot Molecules, Cold Electrons offers a fascinating glimpse into a formative equation’s relationship with one of the most important developments in human communication.


    208 pages
    37 b/w illus.
    History of science and technology; Lord Kelvin; analytical theory of heat; Fourier series; Fourier transforms; Dirichlet’s discontinuous integral; heat equation in an infinite mass; heat equation in a sphere; heat equation in a long radiating wire; semi-infinite mass with a finite thickness; cooling sphere; semi-infinite mass with infinite thickness; circular ring; insulated sphere; electrical physics; Atlantic cable equation; 1866 cable; Duhamel’s integral; electronic computation; second order partial differential equation; flow of heat energy; molten sphere; AP-calculus; AP-physics; Charles Dicken’s mistress; Who is Fourier?; The Evolution of Applied Harmonic Analysis; Elena Prestini; greenhouse effect; Fourier’s law of conduction; Joseph-Louis Lagrange; Peter Dirichlet, Claude Louis Navier; Fourier’s theorem on polynomial real roots; François Budan; Jacques Sturm
    General/trade;Professional and scholarly;College/higher education;

    More ...

    Paul J. Nahin is the author of many popular math books, including How to Fall Slower Than Gravity, Dr. Euler’s Fabulous Formula, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire and received the 2017 Chandler Davis Prize for Excellence in Expository Writing in Mathematics. He lives in Exeter, New Hampshire.


    "This well-written book offers a basic introduction to harmonic analysis and the history of the heat equation, one of the major achievements of the nineteenth century. Filled with numerous interesting historical capsules, Hot Molecules, Cold Electrons is a beautiful work."—Rafael Benguria, Pontifical Catholic University of Chile

    "Introducing readers to some of the most important scientific questions and technological challenges of the nineteenth century, this delightful book shows how they were solved using the heat equation. Reliving this exciting period through letters, stories, and insights, Hot Molecules, Cold Electrons is a triumphant success."—Christopher Tully, author of Elementary Particle Physics in a Nutshell

    "This enjoyable book tells the story of Fourier series and transforms, their role in solving the heat equation, and subsequent applications. Providing a multitude of takeaways, Paul Nahin masterfully moves back and forth between the mathematical advances involved in the development and usage of Fourier analysis and the historical events and characters associated with the field."—Oscar Fernandez, author of Calculus Simplified

    "Hot Molecules, Cold Electrons vividly demonstrates the power of mathematical tools for studying the heat equation in connection to the trans-Atlantic cable. This excellent book will be useful to anyone with an interest in mathematics, physics, or engineering."—Yasuyuki Kawahigashi, University of Tokyo

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