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.

Author: Joseph D. Fehribach
Binding Type: Paperback
Publisher: de Gruyter
Published: 07/24/2023
Series: de Gruyter Textbook
Pages: 133
Weight: 0.5lbs
Size: 9.61h x 6.69w x 0.29d
ISBN: 9783110768350

About the Author

Joseph Fehribach

received his PhD from Duke Univ (1985) and has worked in applied math since in NY, AL, MN, CO and NL. He has taught math at WPI for over 30 years. He and his wife Jan have three children: Jamie, Jess and Andrew.