Introductory calculus : : understanding the derivative / / Tunc Geveci.

• VerfasserIn: Geveci, Tunc.,
• Place / Publishing House: New York, [New York] (222 East 46th Street, New York, NY 10017) : : Momentum Press,, 2015.
• Year of Publication: 2015
• Language: English
• Physical Description: 1 online resource (136 pages) :; illustrations.
• Notes: Co-published with Cognella Academic Publishing.; Includes index.

Table of 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
• Index.