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.

This book of exercises is a companion to A youtube Calculus Workbook (Part II), which is itself a companion to a play-list 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 play-list 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.

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

Mock Test 1

Mock Test 1 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; non-repeated linear factors

M6A Homework set: partial fractions; non-repeated linear factors

Dr. Frédéric Mynard is a mathematician, currently Full 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 35 research articles, and is an active member of the mathematical community, particularly as a conference organizer.