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241 pages

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en

This book is the exercise companion to A youtube Calculus Workbook (part II). Its structures in modules mirrors that of the workbook.

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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

- 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

- 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

- M3 Worksheet: Rule of De l’Hospital
- M3 Homework set: Rule of De l’Hospital
- M3 Homework set: Solutions

- 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

- 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
- M6A Homework set: Solutions
- M6B Worksheet: partial fractions (repeated linear factors; non-repeated irreducible quadratic factors)
- M6B Homework set: partial fractions (repeated linear factors; non-repeated 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

- Mock Test 2
- Mock Test 2 Solutions
- 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

- Mock Test 3
- Mock Test 3 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

- Mock Test 4
- Mock Test 4 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

- Sample Final Exam
- Sample Final Solutions
- Endnotes

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