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Introductory calculus : maxima, minima, and special functions

Author: Tunc Geveci
Publisher: New York, [New York] (222 East 46th Street, New York, NY 10017) : Momentum Press, 2015.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Geveci, Tunc
Introductory Calculus I: Maxima, Minima, and Special Functions
New York : Momentum Press,c2015
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Tunc Geveci
ISBN: 9781606508541 1606508547
OCLC Number: 939718450
Notes: Co-published with Cognella Academic Publishing.
Includes index.
Index.
Description: 1 online resource (1 PDF (216 pages) :) illustrations.
Contents: 1. Increasing and decreasing functions and extrema --
Some terminology --
The derivative test for monotonicity and extrema --
The proof of Fermat's theorem --
2. Understanding the mean value theorem --
Rolle's theorem and the mean value theorem --
3. Determining concavity and extrema --
The second derivative and extrema --
The proof of the second derivative test for local extrema --
4. Drawing the graph of a function --
5. Using maxima and minima in real applications --
Optimization --
Applications to economics --
6. The importance of inverse functions --
Inverse trigonometric functions --
7. Using the derivative of an inverse function --
The general expression --
The derivatives of inverse trigonometric functions --
The proof of theorem 1 (optional) --
8. Applying the natural exponential function and the natural logarithm --
The natural logarithm --
9. Exponential functions with arbitrary bases --
Logarithmic functions with arbitrary bases --
Arbitrary powers of x --
10. Orders of magnitude in exponential functions --
Logarithmic growth --
The natural exponential function as a limit of polynomials --
11. Using exponential functions in growth and decay rates --
The solution of the differential equation y = ky --
Compound interest --
12. Introduction to hyperbolic and inverse --
Hyperbolic functions --
Inverse hyperbolic functions --
13. Using L'Hopital's rule for indeterminate forms --
The indeterminate form 0/0 --
The indeterminate form [infinity] / [infinity] --
The indeterminate form 0 / [infinity] --
The indeterminate forms 1[infinity], [infinity]0 and 00 --
The indeterminate form [infinity] --
[infinity] --
Responsibility: Tunc Geveci.
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