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by Mark Ryan
Calculus Essentials For Dummies
Cover
Introduction
About This Book
Conventions Used in This Book
Foolish Assumptions
Icons Used in This Book
Where to Go from Here
Chapter 1: Calculus: No Big Deal
So What Is Calculus Already?
Real-World Examples of Calculus
Differentiation
Integration
Why Calculus Works
Chapter 2: Limits and Continuity
Taking It to the Limit
Limits and Continuity
Chapter 3: Evaluating Limits
Easy Limits
“Real” Limit Problems
Limits at Infinity
Chapter 4: Differentiation Orientation
The Derivative: It’s Just Slope
The Derivative: It’s Just a Rate
The Derivative of a Curve
The Difference Quotient
Average and Instantaneous Rate
Three Cases Where the Derivative Does Not Exist
Chapter 5: Differentiation Rules
Basic Differentiation Rules
Derivative Rules for Experts
Differentiating Implicitly
Chapter 6: Differentiation and the Shape of Curves
A Calculus Road Trip
Local Extrema
Finding Absolute Extrema on a Closed Interval
Finding Absolute Extrema over a Function’s Entire Domain
Concavity and Inflection Points
Graphs of Derivatives
The Mean Value Theorem
Chapter 7: Differentiation Problems
Optimization Problems
Position, Velocity, and Acceleration
Acceleration
Related Rates
Linear Approximation
Chapter 8: Introduction to Integration
Integration: Just Fancy Addition
Finding the Area under a Curve
Approximating Area
Summation Notation
Finding Exact Area with the Definite Integral
Chapter 9: Integration: Backwards Differentiation
Antidifferentiation: Reverse Differentiation
The Annoying Area Function
The Fundamental Theorem
Fundamental Theorem: Take Two
Antiderivatives: Basic Techniques
Chapter 10: Integration for Experts
Integration by Parts
Tricky Trig Integrals
Trigonometric Substitution
Partial Fractions
Chapter 11: Using the Integral to Solve Problems
The Mean Value Theorem for Integrals and Average Value
The Area between Two Curves
Volumes of Weird Solids
Arc Length
Improper Integrals
Chapter 12: Eight Things to Remember
But Is Undefined
SohCahToa
Trig Values to Know
The Product Rule
The Quotient Rule
Your Sunglasses
Index
About the Author
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End User License Agreement
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