In the name of Allah the Merciful

Sequences and Series in Calculus

Joseph D. Fehribach, 3110768356, 3110768461, 9783110768350, 9783110768466, 9783110768398, 978-3110768350, 978-3110768466, 978-3110768398

15 $

English | 2023 | Original PDF

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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.

A detailed presentation  of sequences and series in calculus, ideal for either courses or for  self-study, includes many exercises and diagrams of interest to students  and lecturers alike.