Fehribach J. Sequences and Series in Calculus 2023

Textbook in PDF format

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 design 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