A youtube Calculus Workbook (Part I)
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About the book
Reviews
Paul A. Ziegler, PhD ★★★★★
This textbook is definitely a fivestar addition to the literature of mathematics. The topics and especially the excellent way they are presented do, indeed, cover the first semester (and perhaps a little more) of a university calculus course. Moreover, this book is an excellent resource for a firsttime student in the subject or for the person who would like a refresher in the basic of calculus. This outstanding effort is even ideal for students not studying one of the mathematical sciences.
hbchen@lanl.gov ★★★★★
Excellent, very useful.
Alex Stokolos ★★★★★
It's a great book, wellstructured, easily implementing, could safe in class time for explanations. Gave to my students as a supplementary material, they like it.
Paul Ziegler, Ph.D. ★★★★★
The author of this text presents the methods of AP Calculus AB in a readable and thorough manner. This book is ideal for selfstudy, use as a student study guide, or as a guide for instructors. There are several topics covered here that are not taught in the traditional American curriculum; most notably, the existence and uniqueness of the solution of a polynomial equation by use of the Intermediate Value Theorem. A refreshing addition to current books on the market.
Goran Lesaja ★★★★★
This Calculus project is very much student oriented. It is made having in mind a modern generation of students that grew up in the information age society and are online constantly. The explosion of content that is accessible online does not make it always easier to learn a large body of knowledge such as Calculus which is very much interconnected and requires consistency. On the contrary, jumping around and sorting through thousands of links can be exhausting and contra productive. These books and accompanied videos are an excellent example of using technology effectively to present classical material in new ways that modern, informationage students are more inclined to use and benefit from its consistency, rigor and efforts to develop critical thinking. These are universal goals of studying that are needed no less than before if not more in creating the future generation of workforce that will be creative, dynamic and flexible and will continue to learn throughout their careers. In conclusion, this is easily the best Calculus resource I have seen in recent years and I strongly recommend it. I think that the projects of this type are much needed for other common undergraduate mathematics classes and more generally for science and engineering classes.
Description
This 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 exampleseven though fully stepbystep 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 ebook 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.
To the reader who would like to complement it with a more formal, yet free, textbook I would recommend a visit to Paul Hawkins’ Calculus I pages at http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx, where a free ebook and a more extensive supply of practice problems are available.
For future reference, the play list of all the videos, as well as a Calculus II playlist, are available at:
Content
 M1: Limits
 Definition of the limit of a function
 Limit laws
 Evaluating limits
 Squeeze Theorem
 Applications
 M1 Sample Quiz
 Solutions to M1 sample Quiz
 M2: Onesided limits; infinite limits and limits at infinity
 onesided limits: definition
 onesided limits: examples
 M2 Sample Quiz 1: onesided limits
 Solutions to the M2 sample Quiz
 Definition of infinite limits
 Finding vertical asymptotes
 Limits at infinity and horizontal asymptotes
 Finding horizontal asymptotes
 Slant asymptotes
 1M2 sample Quiz 2: infinite limits, limits at infinity, asymptotes
 1Solutions to the M2 sample Quiz
 M3: Continuity and Derivatives
 Continuity: definition
 Finding discontinuities
 The Intermediate Value Theorem
 M3 Sample Quiz 1: continuity
 M3 Sample Quiz 1 Solutions
 Definition of the derivative
 Derivative as a function
 Derivative: Examples and applications
 M3 Sample Quiz 2: derivative
 1M3 Sample Quiz 2 Solutions
 Review for the first 3 modules
 MOCK TEST
 Solutions to Mock Test
 M4: Differentiation Rules
 Power Rule for differentiation
 Constant multiple and Sum Rules for derivatives
 Product Rule for differentiation
 Quotient Rule for derivatives
 Differentiation Rules, examples and applications
 M4 Sample Quiz
 M4 Sample Quiz Solutions
 M5: Derivatives of Trigonometric functions; Chain Rule
 Derivatives of trig functions
 Derivatives of trig functions: Examples
 M5 Sample Quiz 1: derivatives of trig functions
 M5 Sample Quiz 1 Solutions
 Chain Rule
 Examples using the Chain Rule
 M5 Sample Quiz 2: Chain Rule
 M5 Sample Quiz 2 Solutions
 M6: Implicit Differentiation; Related Rates Problems
 Implicit Differentiation
 Implicit Differentiation: Examples
 M6 Sample Quiz 1: Implicit Differentiation
 M6 Sample Quiz 1 Solutions
 Related Rates: first problems
 Related Rates: filling up a tank
 Related Rates: Radar gun
 Related Rates: moving shadow
 M6 Sample Quiz 2: Related Rates
 1M6 Sample Quiz 2 Solutions
 Review on modules M4 to M
 MOCK TEST
 MOCK TEST 2 Solutions
 M7: Extreme Values of a function
 Extrema
 local extrema and critical values
 Closed Interval Method
 M7 Sample Quiz
 M7 Sample Quiz Solutions
 M8: the Mean Value Theorem and first derivative Test
 Rolle’s Theorem
 The Mean Value Theorem
 Applications of the Mean Value Theorem
 M8 Sample Quiz 1: Mean Value Theorem
 M8 Sample Quiz 1 Solutions
 Intervals of increase and decrease
 First Derivative Test: further examples
 M8 Sample Quiz 2: Intervals of increase and decrease
 M8 Sample Quiz 2 Solutions
 M9: Curve Sketching
 Concavity and inflection points
 Second derivative Test
 Curve Sketching: Examples
 M9 Sample Quiz: Curve Sketching
 M9 Sample Quiz Solutions
 M10: Optimization
 Optimization: First examples and general method
 Example: an open box
 Example: the best poster
 Example: across the marshes
 Example: the best soda can
 M10 Sample Quiz: optimization
 M10 sample Quiz Solutions
 Review on modules 7 through 1
 MOCK TEST
 MOCK TEST 3 Solutions
 M11: Definite Integral
 Preliminaries: Sums
 The area problem
 Formal definition of the definite integral
 First examples of definite integrals
 Properties of integrals
 M11 Sample Quiz
 M11 Sample Quiz Solutions
 M12: Indefinite Integral
 Antiderivatives
 Antiderivatives: Examples
 M12 Sample Quiz: indefinite integrals
 M12 Sample Quiz Solutions
 M13: Calculating Integrals
 Fundamental Theorem of Calculus
 Proof of the Fundamental Theorem of Calculus
 M13 Sample Quiz 1: FTC applied
 M13 Sample Quiz 1 Solutions
 Substitution for indefinite integrals
 Substitution for definite integrals
 Integrals and symmetry
 M13 Sample Quiz 2: substitution
 M13 Sample Quiz 2 Solutions
 M14: areas and other applications
 Area between two curves
 M14 Sample Quiz 1: areas
 M14 Sample Quiz 1 Solutions
 Arc Length
 Work
 M14 Sample Quiz 2: applications
 M14 Sample Quiz 2 Solutions
 M15: Volumes
 Volume by crosssection
 Volume by crosssection: solids of revolution
 Volume by cylindrical Shells
 M15 Sample Quiz: volumes
 M15 Sample Quiz Solutions
 Review on Modules 11 through 1
 MOCK TEST
 MOCK TEST 4 Solutions
 Index
 Endnote
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, available on youtube (www.youtube.com/user/calculusvideos).
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.
Author profile: http://is.gd/fmynard