Calculus essentials for dummies

Calculus essentials for dummies

Mark Ryan, 1955-

Book - 2010

Introduces the basic principles of calculus, covering such topics as differentiation, integrals, limits and continuity, and integration, in a text that includes sample problems and detailed explanations.

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Subjects
Calculus.
Published
Hoboken, NJ : Wiley Pub., Inc [2010]
Language
English
Main Author
Mark Ryan, 1955- (-)
Item Description
Includes index.
Physical Description
x, 182 pages : illustrations ; 22 cm
ISBN
9780470618356
  • Introduction
  • About This Book
  • Conventions Used in This Book
  • Foolish Assumptions
  • Icons Used in This Book
  • Where to Go from Here
  • Chapter 1. Calculus: No Big Deal
  • So What Is Calculus Already?
  • Real-World Examples of Calculus
  • Differentiation
  • Integration
  • Why Calculus Works
  • Limits: Math microscopes
  • What happens when you zoom in
  • Chapter 2. Limits and Continuity
  • Taking It to the Limit
  • Three functions with one limit
  • One-sided limits
  • Limits and vertical asymptotes
  • Limits and horizontal asymptotes
  • Instantaneous speed
  • Limits and Continuity
  • The hole exception
  • Chapter 3. Evaluating Limits
  • Easy Limits
  • Limits to memorize
  • Plug-and-chug limits
  • "Real" Limit Problems
  • Factoring
  • Conjugate multiplication
  • Miscellaneous algebra
  • Limits at Infinity
  • Horizontal asymptotes
  • Solving limits at infinity
  • Chapter 4. Differentiation Orientation
  • The Derivative: It's Just Slope
  • The slope of a line
  • The derivative of a line
  • The Derivative: It's Just a Rate
  • Calculus on the playground
  • The rate-slope connection
  • The Derivative of a Curve
  • The Difference Quotient
  • Average and Instantaneous Rate
  • Three Cases Where the Derivative Does Not Exist
  • Chapter 5. Differentiation Rules
  • Basic Differentiation Rules
  • The constant rule
  • The power rule
  • The constant multiple rule
  • The sum and difference rules
  • Differentiating trig functions
  • Exponential and logarithmic functions
  • Derivative Rules for Experts
  • The product and quotient rules
  • The chain rule
  • Differentiating Implicitly
  • Chapter 6. Differentiation and the Shape of Curves
  • A Calculus Road Trip
  • Local Extrema
  • Finding the critical numbers
  • The First Derivative Test
  • The Second Derivative Test
  • Finding Absolute Extrema on a Closed Interval
  • Finding Absolute Extrema over a Function's Entire Domain
  • Concavity and Inflection Points
  • Graphs of Derivatives
  • The Mean Value Theorem
  • Chapter 7. Differentiation Problems
  • Optimization Problems
  • The maximum area of a corral
  • Position, Velocity, and Acceleration
  • Velocity versus speed
  • Maximum and minimum height
  • Velocity and displacement
  • Speed and distance traveled
  • Acceleration
  • Tying it all together
  • Related Rates
  • A calculus crossroads
  • Filling up a trough
  • Linear Approximation
  • Chapter 8. Introduction to Integration
  • Integration: Just Fancy Addition
  • Finding the Area under a Curve
  • Dealing with negative area
  • Approximating Area
  • Approximating area with left sums
  • Approximating area with right sums
  • Approximating area with midpoint sums
  • Summation Notation
  • Summing up the basics
  • Writing Riemann sums with sigma notation
  • Finding Exact Area with the Definite Integral
  • Chapter 9. Integration: Backwards Differentiation
  • Antidifferentiation: Reverse Differentiation
  • The Annoying Area Function
  • The Fundamental Theorem
  • Fundamental Theorem: Take Two
  • Antiderivatives: Basic Techniques
  • Reverse rules
  • Guess and check
  • Substitution
  • Chapter 10. Integration for Experts
  • Integration by Parts
  • Picking your u
  • Tricky Trig Integrals
  • Sines and cosines
  • Secants and tangents
  • Cosecants and cotangents
  • Trigonometric Substitution
  • Case 1. Tangents
  • Case 2. Sines
  • Case 3. Secants
  • Partial Fractions
  • Case 1. The denominator contains only linear factors
  • Case 2. The denominator contains unfactorable quadratic factors
  • Case 3. The denominator contains repeated factors
  • Equating coefficients
  • Chapter 11. Using the Integral to Solve Problems
  • The Mean Value Theorem for Integrals and Average Value
  • The Area between Two Curves
  • Volumes of Weird Solids
  • The meat-slicer method
  • The disk method
  • The washer method
  • The matryoshka doll method
  • Arc Length
  • Improper Integrals
  • Improper integrals with vertical asymptotes
  • Improper integrals with infinite limits of integration
  • Chapter 12. Eight Things to Remember
  • a 2 - b 2 = (a - b)(a + b)
  • 0/5 = 0 But 5/0 Is Undefined
  • SohCahToa
  • Trig Values to Know
  • sin 2 ¿ + cos 2 ¿ = 1
  • The Product Rule
  • The Quotient Rule
  • Your Sunglasses
  • Index

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