An edition of A youtube Calculus Workbook (Part I)
(2013)
A youtube Calculus Workbook (Part I)
by Frédéric Mynard
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Last edited by Alice Kirk
August 23, 2015 | History
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.
You can download the book via the link below.
Publish Date
2013
Publisher
Bookboon.com
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Book Details
Table of Contents
Contenido
1. M1: Limits
1.1. Definition of the limit of a function
1.2. Limit laws
1.3. Evaluating limits
1.4. Squeeze Theorem
1.5. Applications
1.6. M1 Sample Quiz
1.7. Solutions to M1 sample Quiz
2. M2: One-sided limits; infinite limits and limits at infinity
2.1. one-sided limits: definition
2.2. one-sided limits: examples
2.3. M2 Sample Quiz 1: one-sided limits
2.4. Solutions to the M2 sample Quiz
2.5. Definition of infinite limits
2.6. Finding vertical asymptotes
2.7. Limits at infinity and horizontal asymptotes
2.8. Finding horizontal asymptotes
2.9. Slant asymptotes
2.10. 1M2 sample Quiz 2: infinite limits, limits at infinity, asymptotes
2.11. 1Solutions to the M2 sample Quiz
3. M3: Continuity and Derivatives
3.1. Continuity: definition
3.2. Finding discontinuities
3.3. The Intermediate Value Theorem
3.4. M3 Sample Quiz 1: continuity
3.5. M3 Sample Quiz 1 Solutions
3.6. Definition of the derivative
3.7. Derivative as a function
3.8. Derivative: Examples and applications
3.9. M3 Sample Quiz 2: derivative
3.10. 1M3 Sample Quiz 2 Solutions
4. Review for the first 3 modules
4.1. MOCK TEST
4.2. Solutions to Mock Test
5. M4: Differentiation Rules
5.1. Power Rule for differentiation
5.2. Constant multiple and Sum Rules for derivatives
5.3. Product Rule for differentiation
5.4. Quotient Rule for derivatives
5.5. Differentiation Rules, examples and applications
5.6. M4 Sample Quiz
5.7. M4 Sample Quiz Solutions
6. M5: Derivatives of Trigonometric functions; Chain Rule
6.1. Derivatives of trig functions
6.2. Derivatives of trig functions: Examples
6.3. M5 Sample Quiz 1: derivatives of trig functions
6.4. M5 Sample Quiz 1 Solutions
6.5. Chain Rule
6.6. Examples using the Chain Rule
6.7. M5 Sample Quiz 2: Chain Rule
6.8. M5 Sample Quiz 2 Solutions
7. M6: Implicit Differentiation; Related Rates Problems
7.1. Implicit Differentiation
7.2. Implicit Differentiation: Examples
7.3. M6 Sample Quiz 1: Implicit Differentiation
7.4. M6 Sample Quiz 1 Solutions
7.5. Related Rates: first problems
7.6. Related Rates: filling up a tank
7.7. Related Rates: Radar gun
7.8. Related Rates: moving shadow
7.9. M6 Sample Quiz 2: Related Rates
7.10. 1M6 Sample Quiz 2 Solutions
8. Review on modules M4 to M
8.1. MOCK TEST
8.2. MOCK TEST 2 Solutions
9. M7: Extreme Values of a function
9.1. Extrema
9.2. local extrema and critical values
9.3. Closed Interval Method
9.4. M7 Sample Quiz
9.5. M7 Sample Quiz Solutions
10. M8: the Mean Value Theorem and first derivative Test
10.1. Rolle’s Theorem
10.2. The Mean Value Theorem
10.3. Applications of the Mean Value Theorem
10.4. M8 Sample Quiz 1: Mean Value Theorem
10.5. M8 Sample Quiz 1 Solutions
10.6. Intervals of increase and decrease
10.7. First Derivative Test: further examples
10.8. M8 Sample Quiz 2: Intervals of increase and decrease
10.9. M8 Sample Quiz 2 Solutions
11. M9: Curve Sketching
11.1. Concavity and inflection points
11.2. Second derivative Test
11.3. Curve Sketching: Examples
11.4. M9 Sample Quiz: Curve Sketching
11.5. M9 Sample Quiz Solutions
12. M10: Optimization
12.1. Optimization: First examples and general method
12.2. Example: an open box
12.3. Example: the best poster
12.4. Example: across the marshes
12.5. Example: the best soda can
12.6. M10 Sample Quiz: optimization
12.7. M10 sample Quiz Solutions
13. Review on modules 7 through 1
13.1. MOCK TEST
13.2. MOCK TEST 3 Solutions
14. M11: Definite Integral
14.1. Preliminaries: Sums
14.2. The area problem
14.3. Formal definition of the definite integral
14.4. First examples of definite integrals
14.5. Properties of integrals
14.6. M11 Sample Quiz
14.7. M11 Sample Quiz Solutions
15. M12: Indefinite Integral
15.1. Antiderivatives
15.2. Antiderivatives: Examples
15.3. M12 Sample Quiz: indefinite integrals
15.4. M12 Sample Quiz Solutions
16. M13: Calculating Integrals
16.1. Fundamental Theorem of Calculus
16.2. Proof of the Fundamental Theorem of Calculus
16.3. M13 Sample Quiz 1: FTC applied
16.4. M13 Sample Quiz 1 Solutions
16.5. Substitution for indefinite integrals
16.6. Substitution for definite integrals
16.7. Integrals and symmetry
16.8. M13 Sample Quiz 2: substitution
16.9. M13 Sample Quiz 2 Solutions
17. M14: areas and other applications
17.1. Area between two curves
17.2. M14 Sample Quiz 1: areas
17.3. M14 Sample Quiz 1 Solutions
17.4. Arc Length
17.5. Work
17.6. M14 Sample Quiz 2: applications
17.7. M14 Sample Quiz 2 Solutions
18. M15: Volumes
18.1. Volume by cross-section
18.2. Volume by cross-section: solids of revolution
18.3. Volume by cylindrical Shells
18.4. M15 Sample Quiz: volumes
18.5. M15 Sample Quiz Solutions
19. Review on Modules 11 through 1
19.1. MOCK TEST
19.2. MOCK TEST 4 Solutions
20. Index
21. Endnote
ID Numbers
Links outside Open Library
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| August 23, 2015 | Edited by Alice Kirk | Edited without comment. |
| August 23, 2015 | Created by Alice Kirk | Added new book. |