## Second Year Calculus: From Celestial Mechanics to Special RelativitySecond Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics. |

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### Contents

II | 1 |

III | 5 |

IV | 9 |

V | 16 |

VI | 18 |

VII | 26 |

VIII | 29 |

IX | 34 |

XLI | 197 |

XLII | 201 |

XLIII | 205 |

XLIV | 207 |

XLV | 211 |

XLVI | 213 |

XLVII | 216 |

XLVIII | 221 |

X | 39 |

XI | 46 |

XII | 50 |

XIII | 53 |

XIV | 65 |

XV | 66 |

XVI | 75 |

XVII | 77 |

XVIII | 79 |

XIX | 86 |

XX | 89 |

XXI | 96 |

XXII | 99 |

XXIII | 105 |

XXIV | 107 |

XXV | 111 |

XXVI | 113 |

XXVII | 119 |

XXVIII | 120 |

XXIX | 131 |

XXX | 134 |

XXXI | 139 |

XXXII | 146 |

XXXIII | 157 |

XXXIV | 158 |

XXXV | 163 |

XXXVI | 169 |

XXXVII | 171 |

XXXVIII | 178 |

XXXIX | 181 |

XL | 187 |

### Other editions - View all

Second Year Calculus: From Celestial Mechanics to Special Relativity David M. Bressoud Limited preview - 2012 |

Second Year Calculus: From Celestial Mechanics to Special Relativity DAVID BRESSOUD No preview available - 2001 |

### Common terms and phrases

algebra approaches assume axis boundary bounded calculus called closed column compute consider constant continuous coordinates corresponds crosses curve defined definition denote described determinant differential differential forms dimensions direction distance dx dy dx dy dz dz dx ellipse equal Equation evaluate example Exercise exist expressed fact Figure Find flow fluid force function given implies integral inverse Lemma length line segment linear transformation magnetic mapping mass mathematics matrix means moving multiplying negative Newton's Note observe orbit oriented origin parallel partial derivatives path perpendicular physical plane positive potential problem Proof Prove pullback region respect result rule satisfies scalar field Show side space special relativity surface theorem theory triangle unit variables vector algebra volume zero