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Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Sections 801, 802, 803 Lecture 3

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Overview of Today’s Class Derivatives (cont) Indefinite integrals Definite integrals

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Quiz 6x 2 +5 If what is the derivative of x(t) with respect to t? If f(x)=2x 3 +5x what is the derivative of f(x) with respect to x?

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Derivatives or Function x(t) is a machine: you plug in the value of argument t and it spits out the value of function x(t). Derivative d/dt is another machine: you plug in the function x(t) and it spits out another function V(t) = dx/dt

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Derivatives A derivative of a function at a point is a slope of a tangent of this function at this point.

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Indefinite integral (anti-derivative) A function F is an “anti-derivative” or an indefinite integral of the function f if

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Indefinite integral (anti-derivative)

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Definite integral F is indefinite integral

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Definite integral

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Integrals Indefinite integral: n – any number except -1 Definite integral:

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Gottfried Leibniz These are Leibniz’ notations: Integral sign as an elongated S from “Summa” and d as a differential (infinitely small increment). 1646-1716

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Leibniz-Newton calculus priority dispute

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Have a great day! Reading: Chapter 2 Do not forget about hw quiz on Monday

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