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Introductory calculus i : understanding the derivative.

Author: Tunc Geveci.
Publisher: New York : Momentum Press
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Tunc Geveci.
ISBN: 1606508555 9781606508558
OCLC Number: 938357227
Description: 1 online resource
Contents: 1. The foundation of the derivative --
The derivative of a function at a point --
The derivative as a function --
The Leibniz notation. 2. Using the derivative for powers and linear combinations --
The derivatives of rational powers of x --
The derivatives of linear combinations --
Higher-order derivatives --
The proof of the power rule for arbitrary rational powers. 3. Using the derivatives of sine and cosine --
The derivatives of sine and cosine at 0 --
The derivative functions corresponding to sine and cosine. 4. Using the derivative in velocity and acceleration. 5. Local linear approximations --
The differential --
The traditional notation for the differential --
The accuracy of local linear approximations. 6. Understanding the product and quotient rules --
The quotient rule. 7. Applying the chain rule --
A plausibility argument for the chain rule --
The chain rule in the Leibniz notation --
The chain rule for more than two functions --
The proof of the chain rule. 8. The problems of related rates. 9. The intermediate value theorem --
Newton's method. 10. Using implicit differentiation.

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