College Tutor logo Calculus 2017

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Ace your Calculus Course the Easy Way

Online Interactive Textbook

for grades 10 and up to 2 yrs college

Einstein: Calculus

Do you want to get into college but have not had Calculus?  Only a few high schools even teach it.  Here is your chance to catch up or to take it as a remedial course.  Do it now!  Just thinking about it does not help.

Our guarantee

Full money-back guarantee if you follow our learning instructions, score at least 85% correct on five of our Final tests, and you are still not accepted at a college or university.

This Calculus course textbook works with any computing device that is connected to the Internet.  That can be a desktop-, laptop-, tablet-computer, or even a smartphone with a screen resolution of 640 pixels or higher.   Modern smartphones have high resolution.

The program is portable; it works at school, on the road, or at home.  One can even use the computer at a friend’s house.  All one needs is an Internet connection.  It expires after one academic year.

But, you say, “I like printed textbooks better.”  Yes, you like to underline and highlight text in the book that you think is important, and read the text five times over.

Problem: Research by Prof. John Dunlovsky, Kent State University, shows that is actually the worst method to learn anything. 95% of students are struggling in this incorrect way, 4% happen to do it correctly by instinct, the remaining 1% of you are geniuses and don’t need any help. Which group are you in? Join the others NOW!

How are you supposed to learn efficiently and with a minimum of effort?  You’ll find the answer in our inexpensive online interactive textbooks.

This Calculus textbook is written for grade levels 10 to 14 (incl. 2 years College make-up work) with all problems worked out in detail.  Newer and faster methods, and tools for learning and problem solving with memory aids are introduced that become helpful to memorize the concepts.  Our emphasis is on basic concepts and their proper application to everyday problems.

Our approach is interactive and problems are not solved in textbook style; rather they are handled here as they would be solved in a classroom by defining each step and why that step has been chosen.  For example, if a Calculus problem requires 5, 10, or 15 steps to reach the final answer then the College Tutor shows those 5, 10, or 15 steps.  Between solutions, various tips are given at appropriate places about how to approach the problem.

This approach is particularly useful to American students wishing to attend college or university in any one of the STEM (Science, Technology, Engineering, Math) disciplines because fellow students from Europe, India, China, Peru and others are at least two years advanced and you have to compete with them from day one. Don’t believe it?  Click on U.S. math preparedness

This textbook aims to eradicate the difference and to bring a student to equal footing with foreign students.

In our book the student may click on various short videos for further explanations of Calculus concepts.  The stress is on the concept or general approach, not on the formula– or type-set approach.  Print and frame your Certificate of Accomplishments after successful completion.

Online Calculus interactive textbook for high school and community college students. Has 414 pages, plus videos and numerous practice problems. Free Bonus: Infinite Series.

Teachers click here for further information.

Contents

1. Functions, Limits, and Continuity
Equations and Graphs * Graphing Calculator * Modeling * Relations and Functions * Models and Data * The Calculus * Finding Limits * Squeeze Theorem * Evaluating Limits * Continuity * Infinite Limits
2. Derivatives
Tangent Lines and Rates of Change * The Derivative * Techniques of Differentiation * Derivatives of parametrically defined functions * Derivatives of Trigonometric Functions * Linearization and Newton’s Method
3. Applications of Derivatives
Problems Involving Related Rates * Extrema and the Mean Value Theorem * The First Derivative Test * The Second Derivative Test * Limits at Infinity * Analyzing the Graph of a Function * Optimization * Approximation Errors * Wavy Curve Method
4. Integration
Indefinite– and Definite Integrals * Differential Equations * Useful Summation Formulas * Definite Integrals * The Fundamental Theorem of Calculus * Integration by Substitution * Numerical Integration * Trapezoidal Rule * Simpson’s Rule * ILATE Rule * Estimate Definite Integrals with TI-83/84 Calculator
5. Applications of Definite Integrals
The Area between two Curves * Volumes * The Volume Formula * Volumes of Solids of Revolution * The Length of a Plane Curve * Area of a Surface of Revolution * Physics, Engineering, & Statistics Applications * Normal Probabilities
6. Integration Techniques
Basic Integration Formulas * Using u-Substitution * Integration By Parts * Solving Unknown Integrals * Integration by Partial Fractions * Trigonometric Integrals * Trigonometric Substitutions * Integration of Rational Functions, Completing the Square * Partial Fractions * Improper Integrals * Ordinary Differential Equations * Differential Equations and Integration
7. Transcendental Functions
Inverse Functions * Exponential and Logarithmic Functions * Exponential Growth and Decay * Derivatives and Integrals involving Inverse Trigonometric Functions * L’Hospital’s Rule
8. Infinite Series
Sequences (rules, terms, indices) * Infinite Series * Geometric Series * Other Convergent Series * Rules for Convergent Series, Reindexing * Series Without Negative Terms * Series with Odd or Even Negative Terms * Convergence Ratio Test and Root Test * Power Series * Taylor and Maclaurin Series * Calculations with Series * Frequently Used Maclaurin Series Formulas



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