Sequences and Series in Calculus / / Joseph D. Fehribach.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1
• VerfasserIn: Fehribach, Joseph D.,
• MitwirkendeR: Fehribach, Joseph D.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2023]; ©2023
• Year of Publication: 2023
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (XII, 121 p.)
• Other title: Frontmatter --; 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110768398; 9783111175782; 9783111319292; 9783111318912; 9783111319209; 9783111318608
• DOI: 10.1515/9783110768398
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Joseph D. Fehribach.

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.