A youtube Calculus Workbook (Part I)

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.

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 e-book 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:

https://www.youtube.com/user/calculusvideos.

1. M1: Limits
   1. Definition of the limit of a function
   2. Limit laws
   3. Evaluating limits
   4. Squeeze Theorem
   5. Applications
   6. M1 Sample Quiz
   7. Solutions to M1 sample Quiz
2. M2: One-sided limits; infinite limits and limits at infinity
   1. one-sided limits: definition
   2. one-sided limits: examples
   3. M2 Sample Quiz 1: one-sided limits
   4. Solutions to the M2 sample Quiz
   5. Definition of infinite limits
   6. Finding vertical asymptotes
   7. Limits at infinity and horizontal asymptotes
   8. Finding horizontal asymptotes
   9. Slant asymptotes
   10. 1M2 sample Quiz 2: infinite limits, limits at infinity, asymptotes
   11. 1Solutions to the M2 sample Quiz
3. M3: Continuity and Derivatives
   1. Continuity: definition
   2. Finding discontinuities
   3. The Intermediate Value Theorem
   4. M3 Sample Quiz 1: continuity
   5. M3 Sample Quiz 1 Solutions
   6. Definition of the derivative
   7. Derivative as a function
   8. Derivative: Examples and applications
   9. M3 Sample Quiz 2: derivative
   10. 1M3 Sample Quiz 2 Solutions
4. Review for the first 3 modules
   1. MOCK TEST
   2. Solutions to Mock Test
5. M4: Differentiation Rules
   1. Power Rule for differentiation
   2. Constant multiple and Sum Rules for derivatives
   3. Product Rule for differentiation
   4. Quotient Rule for derivatives
   5. Differentiation Rules, examples and applications
   6. M4 Sample Quiz
   7. M4 Sample Quiz Solutions
6. M5: Derivatives of Trigonometric functions; Chain Rule
   1. Derivatives of trig functions
   2. Derivatives of trig functions: Examples
   3. M5 Sample Quiz 1: derivatives of trig functions
   4. M5 Sample Quiz 1 Solutions
   5. Chain Rule
   6. Examples using the Chain Rule
   7. M5 Sample Quiz 2: Chain Rule
   8. M5 Sample Quiz 2 Solutions
7. M6: Implicit Differentiation; Related Rates Problems
   1. Implicit Differentiation
   2. Implicit Differentiation: Examples
   3. M6 Sample Quiz 1: Implicit Differentiation
   4. M6 Sample Quiz 1 Solutions
   5. Related Rates: first problems
   6. Related Rates: filling up a tank
   7. Related Rates: Radar gun
   8. Related Rates: moving shadow
   9. M6 Sample Quiz 2: Related Rates
   10. 1M6 Sample Quiz 2 Solutions
8. Review on modules M4 to M
   1. MOCK TEST
   2. MOCK TEST 2 Solutions
9. M7: Extreme Values of a function
   1. Extrema
   2. local extrema and critical values
   3. Closed Interval Method
   4. M7 Sample Quiz
   5. M7 Sample Quiz Solutions
10. M8: the Mean Value Theorem and first derivative Test
    1. Rolle’s Theorem
    2. The Mean Value Theorem
    3. Applications of the Mean Value Theorem
    4. M8 Sample Quiz 1: Mean Value Theorem
    5. M8 Sample Quiz 1 Solutions
    6. Intervals of increase and decrease
    7. First Derivative Test: further examples
    8. M8 Sample Quiz 2: Intervals of increase and decrease
    9. M8 Sample Quiz 2 Solutions
11. M9: Curve Sketching
    1. Concavity and inflection points
    2. Second derivative Test
    3. Curve Sketching: Examples
    4. M9 Sample Quiz: Curve Sketching
    5. M9 Sample Quiz Solutions
12. M10: Optimization
    1. Optimization: First examples and general method
    2. Example: an open box
    3. Example: the best poster
    4. Example: across the marshes
    5. Example: the best soda can
    6. M10 Sample Quiz: optimization
    7. M10 sample Quiz Solutions
13. Review on modules 7 through 1
    1. MOCK TEST
    2. MOCK TEST 3 Solutions
14. M11: Definite Integral
    1. Preliminaries: Sums
    2. The area problem
    3. Formal definition of the definite integral
    4. First examples of definite integrals
    5. Properties of integrals
    6. M11 Sample Quiz
    7. M11 Sample Quiz Solutions
15. M12: Indefinite Integral
    1. Antiderivatives
    2. Antiderivatives: Examples
    3. M12 Sample Quiz: indefinite integrals
    4. M12 Sample Quiz Solutions
16. M13: Calculating Integrals
    1. Fundamental Theorem of Calculus
    2. Proof of the Fundamental Theorem of Calculus
    3. M13 Sample Quiz 1: FTC applied
    4. M13 Sample Quiz 1 Solutions
    5. Substitution for indefinite integrals
    6. Substitution for definite integrals
    7. Integrals and symmetry
    8. M13 Sample Quiz 2: substitution
    9. M13 Sample Quiz 2 Solutions
17. M14: areas and other applications
    1. Area between two curves
    2. M14 Sample Quiz 1: areas
    3. M14 Sample Quiz 1 Solutions
    4. Arc Length
    5. Work
    6. M14 Sample Quiz 2: applications
    7. M14 Sample Quiz 2 Solutions
18. M15: Volumes
    1. Volume by cross-section
    2. Volume by cross-section: solids of revolution
    3. Volume by cylindrical Shells
    4. M15 Sample Quiz: volumes
    5. M15 Sample Quiz Solutions
19. Review on Modules 11 through 1
    1. MOCK TEST
    2. MOCK TEST 4 Solutions
20. Index
21. Endnote