New Jersey City University, Bookboon, 2013. — 299 p. — ISBN: 978-87-403-0538-8This 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 first Calculus course, or equivalently an AP Calculus AB 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 15 thematic learning modules. At the end of each learning module, one or more quiz with full solutions is provided. Every 3 or 4 modules, a mock test on the previous material, with full solutions, is also provided. This will help you test your knowledge as you go along. 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 playlist of Calculus instructional videos. The format, level of details and rigor, and progression of topics are consistent with a semester long college level first Calculus course, or equivalently an AP Calculus AB 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 playlist and the book are divided into 15 thematic learning modules. At the end of each learning module, one or more quiz with full solutions is provided. Every 3 or 4 modules, a mock test on the previous material, with full solutions, is also provided. This will help you test your knowledge as you go along.
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.
Content
Limits
One-sided limits; infinite limits and limits at infinity
Continuity and Derivatives
Review for the first 3 modules
Differentiation Rules
Derivatives of Trigonometric functions; Chain Rule
Implicit Differentiation; Related Rates Problems
Review on modules M4 to M
Extreme Values of a function
the Mean Value Theorem and first derivative Test
Curve Sketching
Optimization
Review on modules 7 through 1
Definite Integral
Indefinite Integral
Calculating Integrals
areas and other applications
Volumes
Review on Modules 11 through 1
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
