Sequences and Series in Calculus.

Format:

Book

Author/Creator:

Fehribach, Joseph D.

Series:

De Gruyter Textbook Series

Language:

English

Subjects (All):

Sequences (Mathematics).

Physical Description:

1 online resource (134 pages)

Edition:

1st ed.

Place of Publication:

Berlin/Boston : Walter de Gruyter GmbH, 2023.

Summary:

The book Sequences and Series in Calculus is designed as the first college/university calculus course for students who take and do well on the AP AB exam in high school and who are interested in a more proof-oriented treatment of calculus. The text begins with an ε-ℕ treatment of sequence convergence, then builds on this to discuss convergence of series—first series of real numbers, then series of functions. The difference between uniform and pointwise convergence is discussed in some detail. This is followed by a discussion of calculus on power series and Taylor series. Finally improper integrals, integration by parts and partial fractions integration all are introduced. This book is designed both to teach calculus, and to give the readers and students a taste of analysis to help them determine if they wish to study this material even more deeply. It might be used by colleges and universities who teach special versions of calculus courses for their most mathematically advanced entering first-year students, as might its older sibling text Multivariable and Vector Calculus which appeared in 2020 and is intended for students who take and do well on the AP BC exam.

Contents:

Intro

Foreword

Notes to the reader

Contents

1 Sequences in ℝ

2 The real numbers, ℝ

3 Infinite series in ℝ

4 Sequences and series of functions

5 Improper Riemann integrals

Bibliography

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783110768398

3110768399

OCLC:

1390920191