## The Equations: Icons of KnowledgeThe mysteries of the physical world speak to us through equations--compact statements about the way nature works, expressed in nature's language, mathematics. In this book by the renowned Dutch physicist Sander Bais, the equations that govern our world unfold in all their formal grace--and their deeper meaning as core symbols of our civilization. Trying to explain science without equations is like trying to explain art without illustrations. Consequently Bais has produced a book that, unlike any other aimed at nonscientists, delves into the details--historical, biographical, practical, philosophical, and mathematical--of seventeen equations that form the very basis of what we know of the universe today. A mathematical These are the seventeen equations that represent radical turning points in our understanding--from mechanics to electrodynamics, hydrodynamics to relativity, quantum mechanics to string theory--their meanings revealed through the careful and critical observation of patterns and motions in nature. Mercifully short on dry theoretical elaborations, the book presents these equations as they are--with the information about their variables, history, and applications that allows us to chart their critical function, and their crucial place, in the complex web of modern science. Reading |

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### Contents

Contents Introduction 11 The tautological toolkit | 11 |

Rise and fall The logistic equation | 18 |

Mechanics and gravity Newtons dynamical equations and universal law of gravity | 22 |

The electromagnetic force The Lorentz force | 28 |

A local conservation law The continuity equation | 32 |

Electrodynamics The Maxwell equations | 34 |

Electromagnetic waves The wave equations | 40 |

Solitary waves The KortewegDe Vries equation | 42 |

Hydrodynamics The NavierStokes equations | 54 |

Special relativity Relativistic kinematics | 58 |

General relativity The Einstein equations | 64 |

Quantum mechanics The Schrödinger equation | 70 |

The relativistic electron The Dirac equation | 76 |

8O The strong force Quantum chromodynamics | 80 |

Electroweak interactions The GlashowWeinbergSalam model | 84 |

String theory The superstring action | 88 |

Thermodynamics The three laws of thermodynamics | 44 |

Kinetic theory The Boltzmann equation | 50 |

Back to the future A final perspective | 93 |