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Calculus for Dummies�

ISBN-10: 0764524984
ISBN-13: 9780764524981
Edition: 2003
Authors: Mark Ryan
List price: $19.99
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Description: With easy-to-understand explanations, memorable examples, and helpful shortcuts, maths teacher Mark Ryan takes the mystery out of calculus concepts and problems - everything from limits, derivatives, and integration to word problems, integral  More...

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Book details

List price: $19.99
Copyright year: 2003
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/9/2003
Binding: Paperback
Pages: 384
Size: 7.25" wide x 9.00" long x 1.00" tall
Weight: 1.518
Language: English

With easy-to-understand explanations, memorable examples, and helpful shortcuts, maths teacher Mark Ryan takes the mystery out of calculus concepts and problems - everything from limits, derivatives, and integration to word problems, integral theorems, and conic sections.

Introduction
About This Book
Conventions Used in This Book
How to Use This Book
Foolish Assumptions
How This Book Is Organized
Icons Used in This Book
Where to Go from Here
An Overview of Calculus
What Is Calculus?
What Calculus Is Not
So What Is Calculus Already?
Real-World Examples of Calculus
The Two Big Ideas of Calculus: Differentiation and Integration
Defining Differentiation
Investigating Integration
Sorting Out Infinite Series
Why Calculus Works
The Limit Concept: A Mathematical Microscope
What Happens When You Zoom In
Two Caveats--or Precision, Preschmidgen
Warming Up with Calculus Prerequisites
Pre-Algebra and Algebra Review
Fine-Tuning Your Fractions
Absolute Value: Absolutely Easy
Empowering Your Powers
Rooting for Roots
Logarithms--This Is Not an Event at a Lumberjack Competition
Factoring Schmactoring, When Am I Ever Going to Need It?
Solving Quadratic Equations
Funky Functions and Their Groovy Graphs
What Is a Function?
What Does a Function Look Like?
Common Functions and Their Graphs
Inverse Functions
Shifts, Reflections, Stretches, and Shrinks
The Trig Tango
Studying Trig at Camp SohCahToa
Two Special Right Triangles
Circling the Enemy with the Unit Circle
Graphing Sine, Cosine, and Tangent
Inverse Trig Functions
Identifying with Trig Identities
Limits
Limits and Continuity
Take It to the Limit--Not
Linking Limits and Continuity
The 33333 Limit Mnemonic
Evaluating Limits
Easy Limits
The "Real Deal" Limit Problems
Evaluating Limits at Infinity
Differentiation
Differentiation Orientation
Differentiating: It's Just Finding the Slope
The Derivative: It's Just a Rate
The Derivative of a Curve
The Difference Quotient
Average Rate and Instantaneous Rate
To Be or Not to Be? Three Cases Where the Derivative Does Not Exist
Differentiation Rules--Yeah, Man, It Rules
Basic Differentiation Rules
Differentiation Rules for Experts--Oh, Yeah, I'm a Calculus Wonk
Differentiating Implicity
Getting into the Rhythm with Logarithmic Differentiation
Differentiating Inverse Functions
Scaling the Heights of Higher Order Derivatives
Differentiation and the Shape of Curves
Taking a Calculus Road Trip
Finding Local Extrema--My Ma, She's Like, Totally Extreme
Finding Absolute Extrema on a Closed Interval
Finding Absolute Extrema over a Function's Entire Domain
Locating Concavity and Inflection Points
Looking at Graphs of Derivatives Till They Derive You Crazy
The Mean Value Theorem--GRRRRR
Your Problems Are Solved: Differentiation to the Rescue!
Getting the Most (or Least) Out of Life: Optimization Problems
Yo-Yo a Go-Go: Position, Velocity, and Acceleration
Related Rates--They Rate, Relatively
Tangents and Normals: Joined at the Hip
Straight Shooting with Linear Approximations
Business and Economics Problems
Integration and Infinite Series
Intro to Integration and Approximating Area
Integration: Just Fancy Addition
Finding the Area under a Curve
Dealing with Negative Area
Approximating Area
Getting Fancy with Summation Notation
Finding Exact Area with the Definite Integral
Approximating Area with the Trapezoid Rule and Simpson's Rule
Integration: It's Backwards Differentiation
Antidifferentiation--That's Differentiation in Reverse
Vocabulary, Voshmabulary: What Difference Does It Make?
The Annoying Area Function
The Power and the Glory of the Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus: Take Two
Finding Antiderivatives: Three Basic Techniques
Finding Area with Substitution Problems
Integration Techniques for Experts
Integration by Parts: Divide and Conquer
Tricky Trig Integrals
Your Worst Nightmare: Trigonometric Substitution
The As, Bs, and Cxs of Partial Fractions
Forget Dr. Phil: Use the Integral to Solve Problems
The Mean Value Theorem for Integrals and Average Value
The Area between Two Curves--Double the Fun
Finding the Volumes of Weird Solids
Analyzing Arc Length
Surfaces of Revolution--Pass the Bottle 'Round
L'Hopital's Rule: Calculus for the Sick
Improper Integrals: Just Look at the Way That Integral Is Holding Its Fork!
Infinite Series
Sequences and Series: What They're All About
Convergence or Divergence? That Is the Question
Alternating Series
Keeping All the Tests Straight
The Part of Tens
Ten Things to Remember
Your Sunglasses
a[superscript 2] - b[superscript 2] = (a - b)(a + b)
0/5 = 0, But 5/0 Is Undefined
Anything[superscript 0] = 1
SohCahToa
Trigonometric Values for 30, 45, and 60 Degree Angles
sin[superscript 2 theta] + cos[superscript 2 theta] = 1
The Product Rule
The Quotient Rule
Where You Put Your Keys
Ten Things to Forget
(a + b)[superscript 2] = a[superscript 2] + b[superscript 2]--Wrong!
[radical]a[superscript 2] + b[superscript 2] = a + b--Wrong!
Slope = x[subscript 2] - x[subscript 1]/y[subscript 2] - y[subscript 1]--Wrong!
3a + b/3a + c = b/c--Wrong!
d/dx[pi superscript 3] = 3[pi superscript 2]--Wrong!
If k Is a Constant, d/dx kx = k'x + kx'--Wrong!
The Quotient Rule Is d/dx (u/v) = v'u - vu'/v[superscript 2]--Wrong!
[function of] x[superscript 2] dx = 1/3x[superscript 3]--Wrong!
[function of] (sinx) dx = cosx + C--Wrong!
Green's Theorem
Ten Things You Can't Get Away With
Give Two Answers on Exam Questions
Write Illegibly on Exams
Don't Show Your Work on Exams
Don't Do All of the Exam Problems
Blame Your Study Partner for Your Low Exam Grade
Tell Your Teacher That You Need an "A" in Calculus to Impress Your Significant Other
Complain That Early-Morning Exams Are Unfair Because You're Not a "Morning Person"
Protest the Whole Idea of Grades
Pull the Fire Alarm During an Exam
Use This Book as an Excuse
Index

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