Calculus For Dummies

Lýsing:Calculus For Dummies, 2nd Edition (9781119293491) was previously published as Calculus For...
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Calculus For Dummies

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Rafbók til eignar. Rafbók til eignar þarf að hlaða niður á þau tæki sem þú vilt nota innan eins árs frá því bókin er keypt. Útgáfa: 2

Efnisyfirlit

  • Cover
  • Introduction
    • About This Book
    • Foolish Assumptions
    • Icons Used in This Book
    • Beyond the Book
    • Where to Go from Here
  • Part 1: 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 2: 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 3: 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 4: 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 5: 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 6: The Part of Tens
    • Chapter 20: Ten Things to Remember
    • Chapter 21: Ten Things to Forget
    • 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
  • About the Author
  • Connect with Dummies
  • End User License Agreement

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