Introductory calculus : understanding the derivative / Tunc Geveci.

Co-published with Cognella Academic Publishing.

Includes index.

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

Title from PDF title page (viewed on December 9, 2015).

Annotation With a "less is more" approach to introducing the reader to the fundamental concepts and uses of Calculus, this sequence of four books covers the usual topics of the first semester of calculus, including limits, continuity, the derivative, the integral and important special functions such exponential functions, logarithms, and inverse trigonometric functions.

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