Exercises for A youtube Calculus Workbook Part II
a flipped classroom model
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About the book
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Description
This book is the exercise companion to A youtube Calculus Workbook (part II). Its structures in modules mirrors that of the workbook. The book includes, for 31 topics, a worksheet of exercises without solutions, which are typically meant to be either worked out in class with the help of the teacher or assigned, a homework set consisting of exercises similar to those of the worksheet, and the complete solutions of the homework sets. It also contains four mock tests with solutions, and a sample final exam with solutions.
Additionally, a brief discussion of the use of the Workbook and the exercise book in a flipped classroom model is included.
Preface
This book of exercises is a companion to A youtube Calculus Workbook (Part II), which is itself a companion to a playlist of 109 youtube video lectures covering material consistent with a second semester long college level Calculus course.
Part I was similarly a companion to a playlist of 94 youtube instructional videos consistent with a semester long first Calculus course at the college level. This book incorporated exercises and sample tests. In contrast, the second part is split into the workbook which is a set of extensive notes on the material covered in the videos, to simplify study from the playlist, and the present book of exercises.
The latter includes, for 31 topics, a worksheet of exercises without solutions, which are typically meant to be either worked out in class with the help of the teacher or assigned, a homework set consisting of exercises similar to those of the worksheet, and the complete solutions of the homework sets. It is organized to mirror the structure of the workbook, which itself references the parts of this exercises book that can be worked on at various points in your study.
Four Mock Tests with full solutions, as well as a Sample Final with full solutions are included to test yourself on a regular basis. This is meant for self study, or use in a flipped classroom setting as outlined below.
I hope that only few errors are left, but some are bound to remain. I welcome feedback and comments at calculusvideos@gmail.com.
Content
Preface
To the instructor: A brief description of a flipped classroom model
 M1: Natural Logarithm and Exponential
 M1A Worksheet: Natural Logarithm
 M1A Homework set: Natural Logarithm
 M1A Homework set: Solutions
 M1B Worksheet: inverse functions
 M1B Homework set: Inverse functions
 M1B Homework set: Solutions
 M1C Worksheet: natural exponential
 M1C Homework set: natural exponential
 M1C Homework set: Solutions
 M2: More transcendental functions
 M2A Worksheet: general exponential and logarithm
 M2A Homework set: general exponential and logarithm
 M2A Homework set: Solutions
 M2B Worksheet: inverse trig functions
 M2B Homework set: inverse trig functions
 M2B Homework set: Solutions
 M2C Worksheet: hyperbolic functions
 M2C Homework set: hyperbolic functions
 M2C Homework set: Solutions
 Rule of De l’Hospital
 M3 Worksheet: Rule of De l’Hospital
 M3 Homework set: Rule of De l’Hospital
 M3 Homework set: Solutions
 M4: Integration review and Integration by parts
 M4A Worksheet: Review of integration
 M4A Homework set: Review of Integration
 M4A Homework set: Solutions
 M4B Worksheet: Integration by parts
 M4B Homework set: Integration by parts
 M4B Homework set: Solutions
 M5: Trigonometric integrals and trigonometric substitutions
 M5A Worksheet: Trig integrals
 M5A Homework set: Trig integrals
 M5A Homework solutions
 M5B Worksheet: Trig substitution
 M5B homework set: trig substitution
 M5B homework set solutions
 M6: Partial Fractions
 M6A Worksheet: partial fractions; nonrepeated linear factors
 M6A Homework set: partial fractions; nonrepeated linear factors
 M6A Homework set: Solutions
 M6B Worksheet: partial fractions (repeated linear factors; nonrepeated irreducible quadratic factors)
 M6B Homework set: partial fractions (repeated linear factors; nonrepeated irreducible quadratic factors)
 M6B Homework set: Solutions
 M6C Worksheet: partial fractions (repeated irreducible quadratic factors)
 M6C Homework set: partial fractions (repeated irreducible quadratic factors)
 M6C Homework set: Solutions
 M7: Improper Integrals
 M7A Worksheet: improper integrals, type I
 M7A Homework set: Improper Integrals, type I
 M7A Homework set: Solutions
 M7B Worksheet: Improper integral type II and comparison
 M7B Homework set: Improper integral type II and comparison
 M8: Parametric Curves
 M8A Worksheet: parametric curves
 M8A Homework set: parametric curves
 M8A Homework set: Solutions
 M8B Worksheet: length and surface areas
 M8B Homework set: length and surface areas
 M8B Homework set: Solutions
 Polar curves
 M9A Worksheet: polar coordinates
 M9A Homework set: polar coordinates
 M9A Homework set: Solutions
 M9B Worksheet: polar curves
 M9B Homework set: polar curves
 M9B Homework set: Solutions
 M10: Sequences and Series
 M10A Worksheet: Sequences
 M10A Homework set: Sequences
 M10A Homework set: Solutions
 M10B Worksheet: Sequences defined inductively
 M10B Homework set: Sequences defined inductively
 M10B Homework set: Solutions
 M10C Worksheet: Series
 M10C Homework set: Series
 M10C Homework set: Solutions
 M11: Integral Test and Comparison Test
 M11A Worksheet: Integral Test
 M11A Homework set: Integral Test
 M11A Homework set: Solutions
 M11B Worksheet: Comparison for series
 M11B Homework set: Solutions
 M12: Alternating Series Test
 M12 Worksheet: Alternating Series
 M12 Homework set: Alternating Series
 M12 Homework set: Solutions
 M13: Ratio and Root Tests
 M13 Worksheet: Ratio and Root Tests
 M13 Homework set: Ratio and Root Test
 M13 Homework set: Solutions
 M14: Strategies to test series for convergence
 M14 Worksheet: review of numerical series
 M14 Homework set: Review of numerical series
 M14 Homework set: solutions
 M15: Power Series and Taylor Series
 M15A Worksheet: Intervals of convergence
 M15A Homework set: Intervals of convergence
 M15A Homework set: Solutions
 M15B Worksheet: power series representation
 M15B Homework set: power series representation
 M15B Homework set: Solutions
 M15C Worksheet: Taylor series
 M15C Homework set: Taylor Series
 M15C Homework set: Solutions
 M16: Applications of power series
 M16 Worksheet: applications of power series
 M16 Homework set: Applications of power Series
 M16 Homework set: Solutions
Mock Test 1
Mock Test 1 Solutions
Mock Test 2
Mock Test 2 Solutions
Mock Test 3
Mock Test 3 Solutions
Mock Test 4
Mock Test 4 Solutions
Sample Final Exam
Sample Final Solutions
Endnotes
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