## Mathematical Methods in Science'Mathematics, taught and learned appropriately, improves the mind and implants good habits of thought.' This tenet underlies all of Professor Pólya's works on teaching and problem-solving. This book captures some of Pólya's excitement and vision. In it he provides enlightenment for all those who have ever wondered how the laws of nature were worked out mathematically. The distinctive feature of the present book is the stress on the history of certain elementary chapters of science; these can be a source of enjoyment and deeper understanding of mathematics even for beginners who have little, or perhaps no, knowledge of physics. |

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### Contents

INTRODUCTION | 1 |

SUCCESSIVE APPROXIMATION | 32 |

From the History of Statics | 47 |

section J VECTORS | 58 |

From the History of Dynamics | 82 |

NEWTON | 105 |

THE PENDULUM | 125 |

Physical Reasoning in Mathematics | 159 |

POWER SERIES | 192 |

PHYSICAL ANALOGY | 224 |

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### Common terms and phrases

air speed angle angular velocity approximation Archimedes Aristotle body calculus cannon ball catenary centripetal acceleration chain circle compute conjecture consequently constant course cross section cube curve determine differential equation dimensions displacement distance dy/dx Earth Earth's gravitational equal equilibrium Figure fluid force acting force exerted formula free fall friction ft/sec Galileo geometry George Polya gravitational field gravitational pull horizontal illustrated by Fig inclined plane increase initial condition Kepler's Kepler's Third Law Leibniz length lever Mars mass mathematics measured meridian method Moon move Newton observation obtain obvious orbit oscillation Parallelogram Law parallelogram of forces particle pendulum physical position power series precisely problem proportional question radius ratio resultant rotation solution solve square Stevinus string Substituting suppose surface swing tangent theory triangle uniform circular motion unit vector vertical weight x-axis