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College and Engineering Physics Calculus 1 TOC Derivatives Integrals

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College and Engineering Physics Calculus 2 TOC Definition of a Derivative We call the limit of the ratio of a change in two quantities as the denominator goes to zero a derivative. Derivatives are the slope of a curve. For example, the instantaneous velocity is the derivative of the position with respect to time.

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College and Engineering Physics Calculus 3 TOC Slopes of curves are the derivative of the function that makes the curve. The derivative of the line is shown below for various points.

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College and Engineering Physics Calculus 4 TOC The derivative of a sum is the sum of the derivatives. If two derivatives are multiplied, it is possible to cancel

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College and Engineering Physics Calculus 5 TOC There are two groups of derivatives that we will most often use in this class. Polynomials Trigonometric Functions

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College and Engineering Physics Calculus 6 TOC Definition of Integration Integration is the inverse of derivation. To find an integral we find the thing that, when a derivative is taken, we get the thing in the integral. The integral of a derivative is the thing in the integral. There are two types of integrals, definite and indefinite. Integrals may be thought of as infinite sums and they tell us the area under a curve.

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College and Engineering Physics Calculus 7 TOC Area under a curve is the integral. The integral of the line between various points is shown in the figure below. negative area positive area

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College and Engineering Physics Calculus 8 TOC There are two groups of integrals that we will most often use in this class. (Other integrals are found in appendix D.) Polynomials Trigonometric Functions

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College and Engineering Physics Calculus 9 TOC The integral of a sum is the sum of the integrals. The process of substitution Definite integrals

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College and Engineering Physics Calculus 10 TOC This is the last slide. Click the back button on your browser to return to the Ebook.

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Differentiability and Rates of Change. To be differentiable, a function must be continuous and smooth. Derivatives will fail to exist at: cornercusp vertical.

Differentiability and Rates of Change. To be differentiable, a function must be continuous and smooth. Derivatives will fail to exist at: cornercusp vertical.

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