College Tutor logo Calculus 2016

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Online Calculus Course
for grades 10 to 12, plus college

Einstein: Calculus 2017 edition tutoring online Calculus course interactive textbook. 414 pages, plus videos and numerous practice problems. Bonus: Infinite Series.

Complies with US Common Core State Standards (CCSS).

Approved by the CLRN for high school classroom instruction.

Some school districts are drastically cutting classes offered and you may have trouble getting in. The College Tutor series comes to the rescue. Our textbooks can be used in the classroom or as stand-alone teaching substitutes. Our content covers more ground than a typical course does and at lower cost. If your school is reluctant to give credit for your work ask for and insist on a Challenge Test.

Prerequisites: Completion of Geometry, Trigonometry, and Algebra 2 or 3.  A Texas Instruments (TI)-type graphics calculator is recommended.

This textbook is written in a private tutoring fashion for grade levels 10 to 12 to earn advanced placement credits for college admission.  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.  The 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 in detail.  Between solutions, various tips are given at appropriate places about how to approach the problem.  The student may also click on various short videos for further explanations of concepts.  Students will get the feeling of having a discussion with the teacher.  Various queries, which could have arisen in such discussions, have been answered.  The stress is on the concept or general approach, not on the formula or a type-set approach.

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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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