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The Mechanical Universe by Tom M. Apostol, Richard P. Olenick, Steven C. Frautschi

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CHAPTER 3THE LANGUAGE OF NATURE: DERIVATIVES AND INTEGRALS

    It is most useful that the true origins of memorable Inventions be known, especially of those which were conceived not by accident but by an effort of meditation. … One of the noblest inventions of our time has been a new kind of mathematical analysis, known as the differential calculus.

    Gottfried Wilhelm Leibniz. Historia et origo calculi differentialis (1714)

3.1 THE DEVELOPMENT OF DIFFERENTIAL CALCULUS

After the advent of algebra in the sixteenth century, a flood of mathematical discoveries swept through Europe. The most important were differential calculus and integral calculus, bold new methods for attacking a host of problems that had challenged the world’s best minds for ...

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