New Jersey City University, Bookboon, 2014. — 268 p. — ISBN: 978-87-403-0619-4This book is a guide through a playlist of Calculus instructional videos. The format, level of details and rigor, and progression of topics are consistent with a semester long college level second Calculus course, or equivalently, together with the first workbook, an AP Calculus BC course. The book further provides simple summary of videos, written definitions and statements, worked out examples--even though fully step-by-step solutions are to be found in the videos-- and an index. The playlist and the book are divided into 16 thematic learning modules. Exercises, some with and some without solutions, and sample tests with solutions are provided in a separate companion manual. The book can be used for self study, or as a textbook for a Calculus course following the “flipped classroom” model.
Preface
With the explosion of resources available on the internet, virtually anything can be learned on your own, using free online resources. Or can it, really? If you are looking for instructional videos to learn Calculus, you will probably have to sort through thousands of hits, navigate through videos of inconsistent quality and format, jump from one instructor to another, all this without written guidance.
This free e-book is a guide through a play-list of Calculus instructional videos. The play-list and the book are divided into 16 thematic learning modules. The format, level of details and rigor, and progression of topics are consistent with a semester long college level Calculus II course, the first volume covering the equivalent of a Calculus I course. The continuity of style should help you learn the material more consistently than jumping around the many options available on the internet. The book further provides simple summary of videos, written definitions and statements, worked out examples – even though fully step by step solutions are to be found in the videos – and an index.
The present book is a guide to instructional videos, and as such can be used for self study, or as a textbook for a Calculus course following the flipped classroom model.
An essential companion to this book is the exercise manual Exercises for A youtube Calculus Workbook Part II: a flipped classroom model, which also outlines and discusses the structure for a flipped classroom course based on this material.
Content
Natural Logarithm and Exponential
More transcendental functions
Rule of De l’Hospital
Trigonometric integrals and trigonometric substitutions
Partial Fractions
Improper Integrals
Parametric Curves
Polar Curves
Sequences and Series
Integral Test and Comparison Test
Alternating Series Test
Ratio and Root Tests
Applications of power series
Notations
About the Author
Dr. Frédéric Mynard is a mathematician, currently Associate Professor at New Jersey City University. He is an experienced teacher and has taught a wide variety of math courses, from junior high school to graduate level courses. In particular, he has extensive experience teaching Calculus, both in class and online. For the purpose of online classes, he has developed a comprehensive set of Calculus educational videos.
Frédéric is also an active researcher, specializing in general topology, categorical methods in topology, and their applications in Analysis. He has published over 30 research articles, and is an active member of the mathematical community, particularly as a conference organizer.
