| Description |
1 online resource (xiii, 212 pages) : illustrations |
| Contents |
Mathematics and physics -- Fourier's mathematics -- The heat equation -- Solving the heat equation -- William Thomson and the infinitely long telegraph cable equation -- Epilogue |
| Summary |
"This book is a testament to the intimate, mutual embrace of mathematics and physics. It achieves that by telling the story of an historical event of tremendous impact upon society, both spiritually and technically -- the mid-19th century construction of the trans-Atlantic telegraph cable, which reduced the time to send a message across the ocean from weeks to minutes. The story of the cable actually begins decades earlier, at the start of the century, with the French mathematical physicist Joseph Fourier's development of the mathematics that the Scottish physicist William Thomson (later Lord Kelvin) would use to analyze the electrical physics of the cable. The story of Fourier opens the book, that of Thomson completes it, and in-between the reader will learn how to derive Fourier's second-order partial differential equation for the flow of heat energy in matter, how Fourier solved the heat equation, how Thomson used Fourier's solutions to calculate the age of the Earth (imagined to be the result of the of an initially molten sphere of blinding brilliance) and, finally, how Thomson showed that the heat equation also describes the Atlantic cable. An epilogue describing the post-Thomson developments completes the book. All readers who have completed first courses at the level of AP-calculus and AP-physics will be able to read this book. This is a perhaps surprising feature of the book, as the mathematics discussed is normally not encountered until the second year (or even later) of college-level work. This book shows that, in fact, the technical material is fully graspable by a college freshman. Unlike a pure technical book, readers will also find a lot of fascinating history in this book (including the bizarre story of how the English novelist Charles Dickens used the Atlantic cable to send a coded message -- during his 1867 American reading tour -- to avoid a career-damaging scandal concerning his mistress)"-- Provided by publisher |
| Analysis |
1866 cable |
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AP-calculus |
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AP-physics |
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Atlantic cable equation |
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Charles Dicken's mistress |
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Dirichlet's discontinuous integral |
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Duhamel's integral |
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Elena Prestini |
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Fourier series |
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Fourier transforms |
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Fourier's law of conduction |
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Fourier's theorem on polynomial real roots |
|
François Budan |
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History of science and technology |
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Jacques Sturm |
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Joseph-Louis Lagrange |
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Lord Kelvin |
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Peter Dirichlet, Claude Louis Navier |
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The Evolution of Applied Harmonic Analysis |
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Who is Fourier? |
|
analytical theory of heat |
|
circular ring |
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cooling sphere |
|
electrical physics |
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electronic computation |
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flow of heat energy |
|
greenhouse effect |
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heat equation in a long radiating wire |
|
heat equation in a sphere |
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heat equation in an infinite mass |
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insulated sphere |
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molten sphere |
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second order partial differential equation |
|
semi-infinite mass with a finite thickness |
|
semi-infinite mass with infinite thickness |
| Bibliography |
Includes bibliographical references and index |
| Notes |
In English |
|
Print version record |
| Subject |
Fourier, Jean-Baptiste-Joseph, 1768-1830.
|
|
Kelvin, William Thomson, Baron, 1824-1907.
|
|
Fourier, Jean-Baptiste-Joseph, 1768-1830 |
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Kelvin, William Thomson, Baron, 1824-1907 |
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Heat equation.
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Mathematical physics -- History -- 19th century
|
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Transatlantic cables -- History
|
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Telegraph cables -- History
|
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SCIENCE -- Mechanics -- Thermodynamics.
|
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Heat equation
|
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Mathematical physics
|
|
Telegraph cables
|
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Transatlantic cables
|
| Genre/Form |
Electronic books
|
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History
|
| Form |
Electronic book
|
| ISBN |
9780691199948 |
|
0691199949 |
|
