Introductory calculus : understanding the derivative / Tunc Geveci.

Format:

Book

Author/Creator:

Geveci, Tunc., author.

Language:

English

Subjects (All):

Calculus.

Derivatives (Mathematics).

Genre:

Libros electronicos.

Physical Description:

1 online resource (136 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

New York, [New York] (222 East 46th Street, New York, NY 10017) : Momentum Press, 2015.

Language Note:

English

Summary:

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.

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.

Notes:

Co-published with Cognella Academic Publishing.

Includes index.

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

ISBN:

1-60650-855-5

OCLC:

922702274