This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.The Babylonians divided the circle into 360Ad, probably because this was the approximate number of days in the year. Half the ... However, as for logarithms, there is a natural measure, based on the arc length of a circle of radius 1, the radian (see ... 4.2), and then, with the help of tables, try to find the angle, or vice versa.

Title | : | Analysis by Its History |

Author | : | Ernst Hairer, Gerhard Wanner |

Publisher | : | Springer Science & Business Media - 2008-05-30 |

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