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299 pages

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English

This is a guide through a playlist of Calculus instructional videos. The format, level of details, and progression of topics are consistent with a semester long college level first Calculus course.

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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. 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 book can be used for self study, or as a textbook for a Calculus course following the “flipped classroom” model.

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:

- M1: Limits
- Definition of the limit of a function
- Limit laws
- Evaluating limits
- Squeeze Theorem
- Applications
- M1 Sample Quiz
- Solutions to M1 sample Quiz

- M2: One-sided limits; infinite limits and limits at infinity
- one-sided limits: definition
- one-sided limits: examples
- M2 Sample Quiz 1: one-sided limits
- Solutions to the M2 sample Quiz
- Definition of infinite limits
- Finding vertical asymptotes
- Limits at infinity and horizontal asymptotes
- Finding horizontal asymptotes
- Slant asymptotes
- 1M2 sample Quiz 2: infinite limits, limits at infinity, asymptotes
- 1Solutions to the M2 sample Quiz

- M3: Continuity and Derivatives
- Continuity: definition
- Finding discontinuities
- The Intermediate Value Theorem
- M3 Sample Quiz 1: continuity
- M3 Sample Quiz 1 Solutions
- Definition of the derivative
- Derivative as a function
- Derivative: Examples and applications
- M3 Sample Quiz 2: derivative
- 1M3 Sample Quiz 2 Solutions

- Review for the first 3 modules
- MOCK TEST
- Solutions to Mock Test

- M4: Differentiation Rules
- Power Rule for differentiation
- Constant multiple and Sum Rules for derivatives
- Product Rule for differentiation
- Quotient Rule for derivatives
- Differentiation Rules, examples and applications
- M4 Sample Quiz
- M4 Sample Quiz Solutions

- M5: Derivatives of Trigonometric functions; Chain Rule
- Derivatives of trig functions
- Derivatives of trig functions: Examples
- M5 Sample Quiz 1: derivatives of trig functions
- M5 Sample Quiz 1 Solutions
- Chain Rule
- Examples using the Chain Rule
- M5 Sample Quiz 2: Chain Rule
- M5 Sample Quiz 2 Solutions

- M6: Implicit Differentiation; Related Rates Problems
- Implicit Differentiation
- Implicit Differentiation: Examples
- M6 Sample Quiz 1: Implicit Differentiation
- M6 Sample Quiz 1 Solutions
- Related Rates: first problems
- Related Rates: filling up a tank
- Related Rates: Radar gun
- Related Rates: moving shadow
- M6 Sample Quiz 2: Related Rates
- 1M6 Sample Quiz 2 Solutions

- Review on modules M4 to M
- MOCK TEST
- MOCK TEST 2 Solutions

- M7: Extreme Values of a function
- Extrema
- local extrema and critical values
- Closed Interval Method
- M7 Sample Quiz
- M7 Sample Quiz Solutions

- M8: the Mean Value Theorem and first derivative Test
- Rolle’s Theorem
- The Mean Value Theorem
- Applications of the Mean Value Theorem
- M8 Sample Quiz 1: Mean Value Theorem
- M8 Sample Quiz 1 Solutions
- Intervals of increase and decrease
- First Derivative Test: further examples
- M8 Sample Quiz 2: Intervals of increase and decrease
- M8 Sample Quiz 2 Solutions

- M9: Curve Sketching
- Concavity and inflection points
- Second derivative Test
- Curve Sketching: Examples
- M9 Sample Quiz: Curve Sketching
- M9 Sample Quiz Solutions

- M10: Optimization
- Optimization: First examples and general method
- Example: an open box
- Example: the best poster
- Example: across the marshes
- Example: the best soda can
- M10 Sample Quiz: optimization
- M10 sample Quiz Solutions

- Review on modules 7 through 1
- MOCK TEST
- MOCK TEST 3 Solutions

- M11: Definite Integral
- Preliminaries: Sums
- The area problem
- Formal definition of the definite integral
- First examples of definite integrals
- Properties of integrals
- M11 Sample Quiz
- M11 Sample Quiz Solutions

- M12: Indefinite Integral
- Antiderivatives
- Antiderivatives: Examples
- M12 Sample Quiz: indefinite integrals
- M12 Sample Quiz Solutions

- M13: Calculating Integrals
- Fundamental Theorem of Calculus
- Proof of the Fundamental Theorem of Calculus
- M13 Sample Quiz 1: FTC applied
- M13 Sample Quiz 1 Solutions
- Substitution for indefinite integrals
- Substitution for definite integrals
- Integrals and symmetry
- M13 Sample Quiz 2: substitution
- M13 Sample Quiz 2 Solutions

- M14: areas and other applications
- Area between two curves
- M14 Sample Quiz 1: areas
- M14 Sample Quiz 1 Solutions
- Arc Length
- Work
- M14 Sample Quiz 2: applications
- M14 Sample Quiz 2 Solutions

- M15: Volumes
- Volume by cross-section
- Volume by cross-section: solids of revolution
- Volume by cylindrical Shells
- M15 Sample Quiz: volumes
- M15 Sample Quiz Solutions

- Review on Modules 11 through 1
- MOCK TEST
- MOCK TEST 4 Solutions

- Index
- Endnote

This textbook is definitely a five-star addition to the literature of mathematics. The topics and especially the excellent way they are presented do, indeed, cover the first semester (and perhaps a little more) of a university calculus course. Moreover, this book is an excellent resource for a first-time student in the subject or for the person who would like a refresher in the basic of calculus. This outstanding effort is even ideal for students not studying one of the mathematical sciences.

September 18, 2014 at 7:49 PM

Excellent, very useful.

March 11, 2014 at 2:30 PM

It's a great book, well-structured, easily implementing, could safe in class time for explanations. Gave to my students as a supplementary material, they like it.

January 30, 2014 at 6:35 PM

The author of this text presents the methods of AP Calculus AB in a readable and thorough manner. This book is ideal for self-study, use as a student study guide, or as a guide for instructors. There are several topics covered here that are not taught in the traditional American curriculum; most notably, the existence and uniqueness of the solution of a polynomial equation by use of the Intermediate Value Theorem. A refreshing addition to current books on the market.

January 16, 2014 at 7:14 AM

This Calculus project is very much student oriented. It is made having in mind a modern generation of students that grew up in the information age society and are on-line constantly. The explosion of content that is accessible on-line does not make it always easier to learn a large body of knowledge such as Calculus which is very much interconnected and requires consistency. On the contrary, jumping around and sorting through thousands of links can be exhausting and contra productive. These books and accompanied videos are an excellent example of using technology effectively to present classical material in new ways that modern, information-age students are more inclined to use and benefit from its consistency, rigor and efforts to develop critical thinking. These are universal goals of studying that are needed no less than before if not more in creating the future generation of workforce that will be creative, dynamic and flexible and will continue to learn throughout their careers.
In conclusion, this is easily the best Calculus resource I have seen in recent years and I strongly recommend it. I think that the projects of this type are much needed for other common undergraduate mathematics classes and more generally for science and engineering classes.

December 3, 2013 at 1:53 PM

A serious illustration of all the numerical skills needed to really master Calculus I.

November 5, 2013 at 3:00 PM

Very nice. The accent is funny but I love the videos.

October 30, 2013 at 2:10 PM

A really usefull book.

October 22, 2013 at 6:17 PM