Intermediate calculus : infinite series / Tunc Geveci.

Format:

Book

Author/Creator:

Geveci, Tunc., author.

Language:

English

Subjects (All):

Calculus.

Series, Infinite.

Genre:

Libros electronicos.

Physical Description:

1 online resource (iv, 146 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

New York, [New York] (222 East 46th Street, New York, NY 10017) : Momentum Press, 2016.

Summary:

With a "less is more" approach to building upon the basic foundations of calculus, this sequence of 5 books introduces the reader to the topics commonly found in a 2nd semester/2nd year level of college-level calculus. They cover in greater detail the methods of integration and the uses of both the integral and differential equations in common problems encountered in most STEM curricula.

Contents:

1. Approximation of arbitrary functions using Taylor polynomials

Taylor polynomials based at 0

Taylor polynomials based at an arbitrary point

2. Error in approximation using Taylor polynomials

The error in the approximation by a Taylor polynomial

The limit as the order of Taylor polynomial increases

3. Introduction to the infinite series

4. Tests for absolute convergence

The monotone convergence principle and absolute

Convergence

The ratio test

The root test

The proofs of the ratio test and the root test

5. An introduction to power series

The definitions

Convergence properties of a power series

Differentiation of functions defined by power series

6. Using termwise integration, multiplication and division to determine Taylor series

Termwise integration of power series

Arithmetic operations on Taylor series

The binomial series

7. Testing for absolute convergence with the integral and comparison tests

The integral test

Error estimates related to the integral test

Comparison tests

8. Using conditional convergence to determine alternating series

Alternating series

9. An introduction to the Fourier series

Fourier series of 2[pi]-periodic functions

Fourier series when the period is different from 2[pi]

Index.

Notes:

Co-published with Cognella Academic Publishing.

Includes index.

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

ISBN:

1-60650-867-9

OCLC:

939718503