An edition of A youtube Calculus Workbook (Part II)
(2013)
A youtube Calculus Workbook (Part II)
by Frédéric Mynard
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Last edited by Alice Kirk
June 25, 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 second Calculus course, or equivalently, together with the first workbook, an AP Calculus BC 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
Content
Preface
1. M1: Natural Logarithm and Exponential
1.1. Natural Logarithm: definition and logarithm laws
1.2. Calculus of Logarithms
1.3. Logarithmic Differentiation
1.4. One-to-one functions and inverse functions
1.5. Finding inverse functions
1.6. Calculus of inverse functions
1.7. Natural Exponential: definition and properties
1.8. Derivatives and integrals with exponentials
1.9. Exponential and logarithmic equations and inequalities
2. M2: More transcendental functions
2.1. General exponential functions
2.2. General logarithm functions
2.3. Inverse trig functions: arcsine
2.4. Inverse trig functions: other inverse trig functions
2.5. Inverse trig functions: derivative and integrals
2.6. Hyperbolic functions
2.7. Inverse hyperbolic functions
3. M3: Rule of De l’Hospital
3.1. Rule of De L’Hospital: statement and proof
3.2. Rule of de l’Hospital: examples (quotients)
3.3. Rule of De L’Hospital: indeterminate products
3.4. Rule of De L’Hospital: indeterminate powers
4. M4: Integration review and Integration by parts
4.1. Review of Integration: basics and completing the square
4.2. Review of Integration: trig formulas and manipulating fractions
4.3. Integration by parts: indefinite integrals
4.4. Integration by parts: definite integrals
4.5. Integration by parts: one more example
5. M5: Trigonometric integrals and trigonometric substitutions
5.1. Powers of sine and cosine
5.2. Products of sine and cosine
5.3. (co)secant, (co)tangent and their powers
5.4. Trig substitutions
6. M6: Partial Fractions
6.1. Partial fractions: generalities; long division
6.2. only non-repeated linear factors
6.3. with repeated linear factors
6.4. with irreducible quadratic factors
6.5. with repeated irreducible quadratic factors
7. M7: Improper Integrals
7.1. Improper integrals of type I
7.2. Improper integrals of type II
7.3. Comparison for improper integrals
8. M8: Parametric Curves
8.1. Introduction to parametric curves
8.2. Tangent lines to parametric curves
8.3. Symmetry; concavity
8.4. plane areas
8.5. arc length
8.6. Surface area of surface of revolutions
9. M9: Polar Curves
9.1. Polar coordinates
9.2. Polar regions and polar curves
9.3. tangent lines to polar curves
9.4. arc length for polar curves
9.5. area enclosed by a sector of a polar curve
10. M10: Sequences and Series
10.1. Sequences
10.2. limit of sequences
10.3. abstract properties of sequences
10.4. limit of sequences defined inductively
10.5. fixed points and limits of sequences defined inductively
10.6. Series
10.7. Series: a criterion for divergence
10.8. Geometric Series
10.9. Telescoping sums
11. M11: Integral Test and Comparison Test
11.1. Integral Test
11.2. p-series
11.3. Estimating the sum
11.4. Direct Comparison Test
11.5. Limit Comparison Test
11.6. Estimating sums revisited
12. M12: Alternating Series Test
12.1. Alternating Series Test
12.2. Absolute and conditional convergence
12.3. Estimating sums with the Alternating Series Test
13. M13: Ratio and Root Tests
13.1. Ratio Test (Statement and proof)
13.2. Ratio Test: examples
13.3. Root Test
13.4. Strategies to test series for convergence (M14)
14. M15: Power Series and Taylor Series
14.1. Power series
14.2. Intervals of convergence
14.3. Representation of functions as power series
14.4. term-by-term differentiation and integration of power series
14.5. more power series representations
14.6. Power series and sums of numerical series
14.7. Taylor and MacLaurin series
14.8. Examples of Taylor Series
14.9. Convergence of Taylor Series
14.10. More examples of Taylor Series
15. M16: Applications of power series
15.1. Power series and sums of numerical series
15.2. Estimating integrals
15.3. Calculating limits
15.4. More power series: products
15.5. More power series: Binomial series
16. Notations
17. Index
18. Endnotes
ID Numbers
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| June 25, 2015 | Edited by Alice Kirk | Edited without comment. |
| June 25, 2015 | Created by Alice Kirk | Added new book. |