Painless calculus

Christina M. Pawlowski

Book - 2021

"Whether you're a student or an adult looking to refresh your knowledge, Barron's Painless Calculus provides review and practice in an easy, step-by-step format"--

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Subjects
Genres
Study guides
Published
New York, NY : Kaplan Inc., d/b/a Barron's Educational Series [2021]
Language
English
Main Author
Christina M. Pawlowski (author)
Item Description
"Learning calculus has never been so easy...or so painless!" -- Cover.
Physical Description
viii, 342 pages : illustrations ; 23 cm
Audience
Grades 6-9
Bibliography
Includes index.
ISBN
9781506273198
  • How to Use This Book
  • Chapter 1. Limits and Continuity
  • Definition of a Limit
  • Graphic Approach to Limits
  • Graphic Approach to Limits at Infinity
  • Properties of Limits
  • Algebraic Approach to Limits
  • Algebraic Approach to Limits at Infinity
  • Continuity
  • Intermediate Value Theorem
  • Brain Ticklers-The Answers
  • Chapter 2. Differentiation
  • Average Rate of Change
  • Slope of a Tangent Line
  • Definition of a Derivative Function
  • Differentiability
  • Continuity and Differentiability
  • Brain Ticklers-The Answers
  • Chapter 3. Derivatives
  • Notation
  • Properties of Derivatives
  • Power Rule
  • Product Rule
  • Quotient Rule
  • Chain Rule
  • Trigonometric Functions
  • Exponential Functions
  • Logarithmic Functions
  • Sneaky Derivatives
  • Implicit Differentiation
  • Logarithmic Differentiation
  • Inverse Functions
  • Brain Ticklers-The Answers
  • Chapter 4. Applications of Derivatives
  • Equation of a Tangent Line
  • Equation of a Normal Line
  • Local Linear Approximation
  • L'Hopital's Rule
  • Curve Sketching
  • Graphical Representation of the Derivative
  • Second Derivative Test
  • Absolute Maxima and Minima
  • Extreme Value Theorem
  • Optimization
  • Rectilinear Motion
  • Mean Value Theorem
  • Related Rates
  • Brain Ticklers-The Answers
  • Chapter 5. Antidifferentiation
  • Indefinite Integrals
  • Properties of Indefinite Integrals
  • Integral Formulas
  • Integration by U-Substitution
  • Integration by Parts
  • Integration by Partial Fraction Decomposition
  • Integration by Completing the Square
  • Integration with Powers of Trigonometric Functions
  • Integration by Trigonometric Substitutions
  • Brain Ticklers-The Answers
  • Chapter 6. Definite Integrals
  • Notation
  • Properties of Definite Integrals
  • Riemann Sum
  • Trapezoidal Sum
  • Fundamental Theorem of Calculus
  • Mean Value Theorem for Integrals
  • Average Function Value
  • Brain Ticklers-The Answers
  • Chapter 7. Applications of Definite Integrals
  • Area Between Curves
  • Volume of a Solid of Revolution
  • Volume of a Solid with a Known Cross Section
  • Arc Length
  • Rectilinear Motion
  • Brain Ticklers-The Answers
  • Chapter 8. Differential Equations
  • Understanding Differential Equations
  • Separation of Variables
  • Exponential Growth and Decay
  • Logistic Growth
  • Slope Fields
  • Euler's Method
  • Brain Ticklers-The Answers
  • Appendix: Important Derivatives, Formulas, Integrals, Limits, and Theorems
  • Important Derivatives
  • Important Formulas
  • Important Integrals
  • Important Limits
  • Important Theorems
  • Index