Calculus All-in-One For Dummies (+ Chapter Quizzes Online)

Calculus All-in-One For Dummies (+ Chapter Quizzes Online)

by Mark Ryan
Released April 2023
Publisher(s): For Dummies
ISBN: 9781119909675

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Book description

Make calculus more manageable with simplified instruction and tons of practice

Calculus All-in-One For Dummies pairs no-nonsense explanations of calculus content with practical examples and practice problems, so you can untangle the difficult concepts and improve your score in any calculus class. Plus, this book comes with access to chapter quizzes online. Dummies makes differentiation, integration, and everything in between more manageable, so you can crush calculus with confidence. Review the foundational basics, then dive into calc lessons that track your class. This book takes you through a full year of high-school calculus or a first semester of college calculus, only explained more clearly.

  • Work through easy-to-understand lessons on everything in a typical calc class
  • Get the score you want and need on standardized tests like AP Calculus
  • Access online chapter quizzes for additional practice
  • Untangle tricky problems and discover clever ways to solve them

With clear definitions, concise explanations, and plenty of helpful information on everything from limits and vectors to integration and curve-sketching, Calculus All-in-One For Dummies is the must-have resource for students who want to review for exams or just need extra help understanding the concepts from class.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Introduction
    1. About This Book
    2. Foolish Assumptions
    3. Icons Used in This Book
    4. Beyond the Book
    5. Where to Go from Here
  5. Unit 1: An Overview of Calculus
    1. Chapter 1: What Is Calculus?
      1. What Calculus Is Not
      2. So What Is Calculus, Already?
      3. Real-World Examples of Calculus
    2. Chapter 2: The Two Big Ideas of Calculus: Differentiation and Integration — Plus Infinite Series
      1. Defining Differentiation
      2. Investigating Integration
      3. Sorting Out Infinite Series
    3. Chapter 3: Why Calculus Works
      1. The Limit Concept: A Mathematical Microscope
      2. What Happens When You Zoom In
      3. Two Caveats; or, Precision, Preschmidgen
  6. Unit 2: Warming Up with Calculus Prerequisites
    1. Chapter 4: Pre-Algebra, Algebra, and Geometry Review
      1. Fine-Tuning Your Fractions
      2. Miscellaneous Algebra
      3. Geometry Refresher
      4. Practice Questions Answers and Explanations
      5. Whaddya Know? Chapter 4 Quiz
      6. Answers to Chapter 4 Quiz
    2. Chapter 5: Funky Functions and Their Groovy Graphs
      1. What Is a Function?
      2. What Does a Function Look Like?
      3. Common Functions and Their Graphs
      4. Inverse Functions
      5. Shifts, Reflections, Stretches, and Shrinks
      6. Practice Questions Answers and Explanations
      7. Whaddya Know? Chapter 5 Quiz
      8. Answers to Chapter 5 Quiz
    3. Chapter 6: The Trig Tango
      1. Starting off with SohCahToa
      2. Two Important Trig Triangles
      3. Circling the Enemy with the Unit Circle
      4. Graphing Sine, Cosine, and Tangent
      5. Inverse Trig Functions
      6. Identifying with Trig Identities
      7. Practice Questions Answers and Explanations
      8. Whaddya Know? Chapter 6 Quiz
      9. Answers to Chapter 6 Quiz
  7. Unit 3: Limits
    1. Chapter 7: Limits and Continuity
      1. Take It to the Limit — NOT
      2. Linking Limits and Continuity
      3. The 33333 Limit Mnemonic
      4. Practice Questions Answers and Explanations
      5. Whaddya Know? Chapter 7 Quiz
      6. Answers to Chapter 7 Quiz
    2. Chapter 8: Evaluating Limits
      1. Easy Does It — Easy Limits
      2. The “Real Deal” Limit Problems
      3. Evaluating Limits at ±Infinity
      4. Practice Questions Answers and Explanations
      5. Whaddya Know? Chapter 8 Quiz
      6. Answers to Chapter 8 Quiz
  8. Unit 4: Differentiation
    1. Chapter 9: Differentiation Orientation
      1. Differentiating: It’s Just Finding the Slope
      2. The Derivative: It’s Just a Rate
      3. The Derivative of a Curve
      4. The Difference Quotient
      5. Average Rate and Instantaneous Rate
      6. To Be or Not to Be? Three Cases Where the Derivative Does Not Exist
      7. Practice Questions Answers and Explanations
      8. Whaddya Know? Chapter 9 Quiz
      9. Answers to Chapter 9 Quiz
    2. Chapter 10: Differentiation Rules — Yeah, Man, It Rules
      1. Basic Differentiation Rules
      2. Differentiation Rules for Experts — Oh, Yeah, I’m a Calculus Wonk
      3. Differentiating Implicitly
      4. Differentiating Inverse Functions
      5. Scaling the Heights of Higher-Order Derivatives
      6. Practice Questions Answers and Explanations
      7. Whaddya Know? Chapter 10 Quiz
      8. Answers to Chapter 10 Quiz
    3. Chapter 11: Differentiation and the Shape of Curves
      1. Taking a Calculus Road Trip
      2. Finding Local Extrema — My Ma, She’s Like, Totally Extreme
      3. Finding Absolute Extrema on a Closed Interval
      4. Finding Absolute Extrema over a Function’s Entire Domain
      5. Locating Concavity and Inflection Points
      6. Looking at Graphs of Derivatives Till They Derive You Crazy
      7. The Mean Value Theorem — Go Ahead, Make My Day
      8. Practice Questions Answers and Explanations
      9. Whaddya Know? Chapter 11 Quiz
      10. Answers to Chapter 11 Quiz
    4. Chapter 12: Your Problems Are Solved: Differentiation to the Rescue!
      1. Getting the Most (or Least) Out of Life: Optimization Problems
      2. Yo-Yo a Go-Go: Position, Velocity, and Acceleration
      3. Related Rates — They Rate, Relatively
      4. Practice Questions Answers and Explanations
      5. Whaddya Know? Chapter 12 Quiz
      6. Answers to Chapter 12 Quiz
    5. Chapter 13: More Differentiation Problems: Going Off on a Tangent
      1. Tangents and Normals: Joined at the Hip
      2. Straight Shooting with Linear Approximations
      3. Business and Economics Problems
      4. Practice Questions Answers and Explanations
      5. Whaddya Know? Chapter 13 Quiz
      6. Answers to Chapter 13 Quiz
  9. Unit 5: Integration and Infinite Series
    1. Chapter 14: Intro to Integration and Approximating Area
      1. Integration: Just Fancy Addition
      2. Finding the Area Under a Curve
      3. Approximating Area
      4. Getting Fancy with Summation Notation
      5. Finding Exact Area with the Definite Integral
      6. Approximating Area with the Trapezoid Rule and Simpson’s Rule
      7. Practice Questions Answers and Explanations
      8. Whaddya Know? Chapter 14 Quiz
      9. Answers to Chapter 14 Quiz
    2. Chapter 15: Integration: It’s Backwards Differentiation
      1. Antidifferentiation
      2. Vocabulary, Voshmabulary: What Difference Does It Make?
      3. The Annoying Area Function
      4. The Power and the Glory of the Fundamental Theorem of Calculus
      5. The Fundamental Theorem of Calculus: Take Two
      6. Finding Antiderivatives: Three Basic Techniques
      7. Finding Area with Substitution Problems
      8. Practice Questions Answers and Explanations
      9. Whaddya Know? Chapter 15 Quiz
      10. Answers to Chapter 15 Quiz
    3. Chapter 16: Integration Techniques for Experts
      1. Integration by Parts: Divide and Conquer
      2. Tricky Trig Integrals
      3. Your Worst Nightmare: Trigonometric Substitution
      4. The A’s, B’s, and Cx’s of Partial Fractions
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 16 Quiz
      7. Answers to Chapter 16 Quiz
    4. Chapter 17: Who Needs Freud? Using the Integral to Solve Your Problems
      1. The Mean Value Theorem for Integrals and Average Value
      2. The Area between Two Curves — Double the Fun
      3. Volumes of Weird Solids: No, You’re Never Going to Need This
      4. Analyzing Arc Length
      5. Surfaces of Revolution — Pass the Bottle ’Round
      6. Practice Questions Answers and Explanations
      7. Whaddya Know? Chapter 17 Quiz
      8. Answers to Chapter 17 Quiz
    5. Chapter 18: Taming the Infinite with Improper Integrals
      1. L’Hôpital’s Rule: Calculus for the Sick
      2. Improper Integrals: Just Look at the Way That Integral Is Holding Its Fork!
      3. Practice Questions Answers and Explanations
      4. Whaddya Know? Chapter 18 Quiz
      5. Answers to Chapter 18 Quiz
    6. Chapter 19: Infinite Series: Welcome to the Outer Limits
      1. Sequences and Series: What They’re All About
      2. Convergence or Divergence? That Is the Question
      3. Alternating Series
      4. Keeping All the Tests Straight
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 19 Quiz
      7. Answers to Chapter 19 Quiz
  10. Index
  11. About the Author
  12. Connect with Dummies
  13. End User License Agreement

Product information

  • Title: Calculus All-in-One For Dummies (+ Chapter Quizzes Online)
  • Author(s): Mark Ryan
  • Release date: April 2023
  • Publisher(s): For Dummies
  • ISBN: 9781119909675