Calculus Essentials For Dummies

Book description

Calculus Essentials For Dummies (9781119591207) was previously published as Calculus Essentials For Dummies (9780470618356). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.


Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, Calculus Essentials For Dummies sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.

The Essentials For Dummies Series
Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Table of contents

  1. Cover
  2. Introduction
    1. About This Book
    2. Conventions Used in This Book
    3. Foolish Assumptions
    4. Icons Used in This Book
    5. Where to Go from Here
  3. Chapter 1: Calculus: No Big Deal
    1. So What Is Calculus Already?
    2. Real-World Examples of Calculus
    3. Differentiation
    4. Integration
    5. Why Calculus Works
  4. Chapter 2: Limits and Continuity
    1. Taking It to the Limit
    2. Limits and Continuity
  5. Chapter 3: Evaluating Limits
    1. Easy Limits
    2. “Real” Limit Problems
    3. Limits at Infinity
  6. Chapter 4: Differentiation Orientation
    1. The Derivative: It’s Just Slope
    2. The Derivative: It’s Just a Rate
    3. The Derivative of a Curve
    4. The Difference Quotient
    5. Average and Instantaneous Rate
    6. Three Cases Where the Derivative Does Not Exist
  7. Chapter 5: Differentiation Rules
    1. Basic Differentiation Rules
    2. Derivative Rules for Experts
    3. Differentiating Implicitly
  8. Chapter 6: Differentiation and the Shape of Curves
    1. A Calculus Road Trip
    2. Local Extrema
    3. Finding Absolute Extrema on a Closed Interval
    4. Finding Absolute Extrema over a Function’s Entire Domain
    5. Concavity and Inflection Points
    6. Graphs of Derivatives
    7. The Mean Value Theorem
  9. Chapter 7: Differentiation Problems
    1. Optimization Problems
    2. Position, Velocity, and Acceleration
    3. Acceleration
    4. Related Rates
    5. Linear Approximation
  10. Chapter 8: Introduction to Integration
    1. Integration: Just Fancy Addition
    2. Finding the Area under a Curve
    3. Approximating Area
    4. Summation Notation
    5. Finding Exact Area with the Definite Integral
  11. Chapter 9: Integration: Backwards Differentiation
    1. Antidifferentiation: Reverse Differentiation
    2. The Annoying Area Function
    3. The Fundamental Theorem
    4. Fundamental Theorem: Take Two
    5. Antiderivatives: Basic Techniques
  12. Chapter 10: Integration for Experts
    1. Integration by Parts
    2. Tricky Trig Integrals
    3. Trigonometric Substitution
    4. Partial Fractions
  13. Chapter 11: Using the Integral to Solve Problems
    1. The Mean Value Theorem for Integrals and Average Value
    2. The Area between Two Curves
    3. Volumes of Weird Solids
    4. Arc Length
    5. Improper Integrals
  14. Chapter 12: Eight Things to Remember
    1. But Is Undefined
    2. SohCahToa
    3. Trig Values to Know
    4. The Product Rule
    5. The Quotient Rule
    6. Your Sunglasses
  15. Index
  16. About the Author
  17. Advertisement Page
  18. Connect with Dummies
  19. End User License Agreement

Product information

  • Title: Calculus Essentials For Dummies
  • Author(s): Mark Ryan
  • Release date: May 2019
  • Publisher(s): For Dummies
  • ISBN: 9781119591207