The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you happen to be a direct descendant of Einstein. Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus.
Calculus For Dummies is intended for three groups of readers:
Students taking their first calculus course - If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.
Students who need to brush up on their calculus to prepare for other studies - If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course.
Adults of all ages who'd like a good introduction to the subject - Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth. This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more:
Real-world examples of calculus The two big ideas of calculus: differentiation and integration Why calculus works Pre-algebra and algebra review Common functions and their graphs Limits and continuity Integration and approximating area Sequences and series Don't buy the misconception. Sure calculus is difficult - but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off - it's simply the next step in a logical progression.
Author(s): Mark Ryan
Series: For Dummies
Edition: 2
Title Page
Copyright Page
Contents at a Glance
Table of Contents
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Part I: An Overview of Calculus
Chapter 1: What Is Calculus?
What Calculus Is Not
So What Is Calculus Already?
Real-World Examples of Calculus
Chapter 2: The Two Big Ideas of Calculus: Differentiation and Integration — plus Infinite Series
Defining Differentiation
Investigating Integration
Sorting Out Infinite Series
Chapter 3: Why Calculus Works
The Limit Concept: A Mathematical Microscope
What Happens When You Zoom In
Two Caveats, or Precision, Preschmidgen
Part II: Warming Up with Calculus Prerequisites
Chapter 4: 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
Chapter 5: 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
Chapter 6: 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
Part III: Limits
Chapter 7: Limits and Continuity
Take It to the Limit — NOT
Linking Limits and Continuity
The 33333 Limit Mnemonic
Chapter 8: Evaluating Limits
Easy Limits
The “Real Deal” Limit Problems
Evaluating Limits at Infinity
Part IV: Differentiation
Chapter 9: 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
Chapter 10: Differentiation Rules — Yeah, Man, It Rules
Basic Differentiation Rules
Differentiation Rules for Experts — Oh, Yeah, I’m a Calculus Wonk
Differentiating Implicitly
Getting into the Rhythm with Logarithmic Differentiation
Differentiating Inverse Functions
Scaling the Heights of Higher Order Derivatives
Chapter 11: 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
Chapter 12: 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
Chapter 13: More Differentiation Problems: Going Off on a Tangent
Tangents and Normals: Joined at the Hip
Straight Shooting with Linear Approximations
Business and Economics Problems
Part V: Integration and Infinite Series
Chapter 14: Intro to Integration and Approximating Area
Integration: Just Fancy Addition
Finding the Area Under a Curve
Approximating Area
Getting Fancy with Summation Notation
Finding Exact Area with the Definite Integral
Approximating Area with the Trapezoid Rule and Simpson’s Rule
Chapter 15: Integration: It’s Backwards Differentiation
Antidifferentiation
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
Chapter 16: 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
Chapter 17: 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
The Washer Method
Analyzing Arc Length
Surfaces of Revolution — Pass the Bottle ’Round
Chapter 18: Taming the Infinite with Improper Integrals
L’Hôpital’s Rule: Calculus for the Sick
Improper Integrals: Just Look at the Way That Integral Is Holding Its Fork!
Chapter 19: Infinite Series
Sequences and Series: What They’re All About
Convergence or Divergence?That Is the Question
Alternating Series
Keeping All the Tests Straight
Part VI: The Part of Tens
Chapter 20: Ten Things to Remember
Your Sunglasses
a2−b2 = (a−b)(a+b)
0/5 = 0, but 5/0 Is Undefined
Anything0 = 1
SohCahToa
Trig Values for 30, 45, and 60 Degrees
sin2θ + cos2θ = 1
The Product Rule
The Quotient Rule
Where You Put Your Keys
Chapter 21: Ten Things to Forget
(a+b)2 = a2+b2 — Wrong!
√a2+b2 = a+b — Wrong!
Slope = x2−x1/y2−y1 — Wrong!
3a+b/3a+c = b/c — Wrong!
d/dxП3 = 3П2 — Wrong!
If k Is a Constant, d/dxkx = k’x+kx’ — Wrong!
The Quotient Rule Is d/dx(u/v) = v’u−vu’/v2 — Wrong!
∫x2dx = 1/3x3 — Wrong!
∫(sinx)dx = cosx+C — Wrong!
Green’s Theorem
Chapter 22: 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 Low Grade
Tell Your Teacher You Need an “A” in Calculus to Impress Your Significant Other
Claim 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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