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# Calculus : Study Guide for AP Calculus AB/BC or University Calculus

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1 MB|300 pages
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Calculus Study Guide suitable for AP Calculus or First Year College Calculus Students. Main topics covered : Functions Limits and Continuity, Derivatives, Application of the Derivative, Indefinite integration, Definite Integration, Techniques of Integration, Sequences and Series, L’Hopitals Rule, Improper Integrals, Taylor Series, Short Introduction to Differential Equations.

Calculus without Limits is a self-study guide that can be used as a textbook/lecture supplement by students, as a source of homework problems by the instructor or as a source of lecture material. Covers most topics discussed in a first year calculus course (or AP Calculus). The emphasis is on solved problems that show students how to attack the types of problems they will encounter in homework and on exams. Discussion of concepts is informal followed by example problems. Many practice problems are also included for students.

1 - Function Review
What is a function - Graphing - Even and Odd Functions - Increasing and Decreasing Functions - One to One Functions - Powers and Polynomials - Absolute Value Function - Exponential Function - Logarithm - Trigonometric Functions
2- Limits
Definition - Tricks for Doing Limits - Properties of Limits and Rules - Limits at Infinity - One Sided Limits Continuity
3- Derivative
Notation and Definition in terms of limits - Slope of Tangent Line - Power Rule and Derivative of a constant - Chain Rule - Derivatives of Trig Functions - Product and Quotient Rules
4- Applications of the Derivative
Derivative of Inverse Function - Implicit Differentiation - Application: Rates of Change, Velocity and Acceleration - Finding Minima and Maxima First and Second Derivative Test - Inflection Points - The Mean Value Theorem - Related Rates
5- The Integral
Notation - Power Rule of Integration - Integration of Trig Functions - Integration of inverse function - Integrating Exponential Function - The substitution technique - Integrating Hyperbolic Functions - Definite Integration - Sums and Area Under a Curve - Area Between Two Curves -
6- U-Substitution
Solved Problems
7- Integration by Parts
Definition and When to Use - Examples
8- Integration of Rational Functions
Introduction - Examples
9- Integration Using the Method of Partial Fractions
Discussion - Examples
10- Integrating Powers of Trig Functions
Examples
11- Trig Substitution
Three Cases - Basic Technique -Examples
12 - Improper Integrals
Definition - Examples
13 - Sequences and Infinite Series
Sequences - Limits - Infinite Series
14 Ratio, Comparison, and Integral Tests
Examples
15 - Alternating Series
16 - Power Series and Radius of Convergence
17- Taylor Series Expansions
18- L’Hopital’s Rule
When to use and Definition - Examples
19- Introduction to Differential Equations
First Order Differential Equations - Second Order Differential Equations
Total Pages
300 pages
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Teaching Duration
1 Year
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