Calculus Essentials for Dummies

ISBN-10: 0470618353

ISBN-13: 9780470618356

Edition: 2010

Authors: Mark Ryan

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A new series extension of the For Dummies brand, The Essentials For Dummies will appeal to the huge number of readers who seek out focused, short form consumer reference books at the $9.99 price point. Positioned for students (and parents) who just want the key concepts and a few examples without the review, ramp-up, and anecdotal content The Essentials For Dummies series is a perfect solution for exam-cramming, homework help, and reference.
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Book details

List price: $13.95
Copyright year: 2010
Publisher: John Wiley & Sons, Incorporated
Publication date: 4/30/2010
Binding: Paperback
Pages: 192
Size: 5.50" wide x 8.75" long x 0.50" tall
Weight: 0.440

About This Book
Conventions Used in This Book
Foolish Assumptions
Icons Used in This Book
Where to Go from Here
Calculus: No Big Deal
So What Is Calculus Already?
Real-World Examples of Calculus
Why Calculus Works
Limits: Math microscopes
What happens when you zoom in
Limits and Continuity
Taking It to the Limit
Three functions with one limit
One-sided limits
Limits and vertical asymptotes
Limits and horizontal asymptotes
Instantaneous speed
Limits and Continuity
The hole exception
Evaluating Limits
Easy Limits
Limits to memorize
Plug-and-chug limits
"Real" Limit Problems
Conjugate multiplication
Miscellaneous algebra
Limits at Infinity
Horizontal asymptotes
Solving limits at infinity
Differentiation Orientation
The Derivative: It's Just Slope
The slope of a line
The derivative of a line
The Derivative: It's Just a Rate
Calculus on the playground
The rate-slope connection
The Derivative of a Curve
The Difference Quotient
Average and Instantaneous Rate
Three Cases Where the Derivative Does Not Exist
Differentiation Rules
Basic Differentiation Rules
The constant rule
The power rule
The constant multiple rule
The sum and difference rules
Differentiating trig functions
Exponential and logarithmic functions
Derivative Rules for Experts
The product and quotient rules
The chain rule
Differentiating Implicitly
Differentiation and the Shape of Curves
A Calculus Road Trip
Local Extrema
Finding the critical numbers
The First Derivative Test
The Second Derivative Test
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
Differentiation Problems
Optimization Problems
The maximum area of a corral
Position, Velocity, and Acceleration
Velocity versus speed
Maximum and minimum height
Velocity and displacement
Speed and distance traveled
Tying it all together
Related Rates
A calculus crossroads
Filling up a trough
Linear Approximation
Introduction to Integration
Integration: Just Fancy Addition
Finding the Area under a Curve
Dealing with negative area
Approximating Area
Approximating area with left sums
Approximating area with right sums
Approximating area with midpoint sums
Summation Notation
Summing up the basics
Writing Riemann sums with sigma notation
Finding Exact Area with the Definite Integral
Integration: Backwards Differentiation
Antidifferentiation: Reverse Differentiation
The Annoying Area Function
The Fundamental Theorem
Fundamental Theorem: Take Two
Antiderivatives: Basic Techniques
Reverse rules
Guess and check
Integration for Experts
Integration by Parts
Picking your u
Tricky Trig Integrals
Sines and cosines
Secants and tangents
Cosecants and cotangents
Trigonometric Substitution
Partial Fractions
The denominator contains only linear factors
The denominator contains unfactorable quadratic factors
The denominator contains repeated factors
Equating coefficients
Using the Integral to Solve Problems
The Mean Value Theorem for Integrals and Average Value
The Area between Two Curves
Volumes of Weird Solids
The meat-slicer method
The disk method
The washer method
The matryoshka doll method
Arc Length
Improper Integrals
Improper integrals with vertical asymptotes
Improper integrals with infinite limits of integration
Eight Things to Remember
a<sup>2</sup> - b<sup>2</sup> = (a - b)(a + b)
0/5 = 0 But 5/0 Is Undefined
Trig Values to Know
sin<sup>2</sup> � + cos<sup>2</sup> � = 1
The Product Rule
The Quotient Rule
Your Sunglasses
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