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
October 13, 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 for free via the link below.
Publish Date
2013
Publisher
Bookboon.com
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Book Details
Table of Contents
Sisältö
Preface
M1: Natural Logarithm and Exponential
Natural Logarithm: definition and logarithm laws
Calculus of Logarithms
Logarithmic Differentiation
One-to-one functions and inverse functions
Finding inverse functions
Calculus of inverse functions
Natural Exponential: definition and properties
Derivatives and integrals with exponentials
Exponential and logarithmic equations and inequalities
M2: More transcendental functions
General exponential functions
General logarithm functions
Inverse trig functions: arcsine
Inverse trig functions: other inverse trig functions
Inverse trig functions: derivative and integrals
Hyperbolic functions
Inverse hyperbolic functions
M3: Rule of De l’Hospital
Rule of De L’Hospital: statement and proof
Rule of de l’Hospital: examples (quotients)
Rule of De L’Hospital: indeterminate products
Rule of De L’Hospital: indeterminate powers
M4: Integration review and Integration by parts
Review of Integration: basics and completing the square
Review of Integration: trig formulas and manipulating fractions
Integration by parts: indefinite integrals
Integration by parts: definite integrals
Integration by parts: one more example
M5: Trigonometric integrals and trigonometric substitutions
Powers of sine and cosine
Products of sine and cosine
(co)secant, (co)tangent and their powers
Trig substitutions
M6: Partial Fractions
Partial fractions: generalities; long division
only non-repeated linear factors
with repeated linear factors
with irreducible quadratic factors
with repeated irreducible quadratic factors
M7: Improper Integrals
Improper integrals of type I
Improper integrals of type II
Comparison for improper integrals
M8: Parametric Curves
Introduction to parametric curves
Tangent lines to parametric curves
Symmetry; concavity
plane areas
arc length
Surface area of surface of revolutions
M9: Polar Curves
Polar coordinates
Polar regions and polar curves
tangent lines to polar curves
arc length for polar curves
area enclosed by a sector of a polar curve
M10: Sequences and Series
Sequences
limit of sequences
abstract properties of sequences
limit of sequences defined inductively
fixed points and limits of sequences defined inductively
Series
Series: a criterion for divergence
Geometric Series
Telescoping sums
M11: Integral Test and Comparison Test
Integral Test
p-series
Estimating the sum
Direct Comparison Test
Limit Comparison Test
Estimating sums revisited
M12: Alternating Series Test
Alternating Series Test
Absolute and conditional convergence
Estimating sums with the Alternating Series Test
M13: Ratio and Root Tests
Ratio Test (Statement and proof)
Ratio Test: examples
Root Test
Strategies to test series for convergence (M14)
M15: Power Series and Taylor Series
Power series
Intervals of convergence
Representation of functions as power series
term-by-term differentiation and integration of power series
more power series representations
Power series and sums of numerical series
Taylor and MacLaurin series
Examples of Taylor Series
Convergence of Taylor Series
More examples of Taylor Series
M16: Applications of power series
Power series and sums of numerical series
Estimating integrals
Calculating limits
More power series: products
More power series: Binomial series
Notations
Index
Endnotes
ID Numbers
Links outside Open Library
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| October 13, 2015 | Edited by Alice Kirk | Edited without comment. |
| October 13, 2015 | Created by Alice Kirk | Added new book. |