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Table of contents
  1. Preface
  2. 1 Functions and Graphs
    1. Introduction
    2. 1.1 Review of Functions
    3. 1.2 Basic Classes of Functions
    4. 1.3 Trigonometric Functions
    5. 1.4 Inverse Functions
    6. 1.5 Exponential and Logarithmic Functions
    7. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
      4. Review Exercises
  3. 2 Limits
    1. Introduction
    2. 2.1 A Preview of Calculus
    3. 2.2 The Limit of a Function
    4. 2.3 The Limit Laws
    5. 2.4 Continuity
    6. 2.5 The Precise Definition of a Limit
    7. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
      4. Review Exercises
  4. 3 Derivatives
    1. Introduction
    2. 3.1 Defining the Derivative
    3. 3.2 The Derivative as a Function
    4. 3.3 Differentiation Rules
    5. 3.4 Derivatives as Rates of Change
    6. 3.5 Derivatives of Trigonometric Functions
    7. 3.6 The Chain Rule
    8. 3.7 Derivatives of Inverse Functions
    9. 3.8 Implicit Differentiation
    10. 3.9 Derivatives of Exponential and Logarithmic Functions
    11. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
      4. Review Exercises
  5. 4 Applications of Derivatives
    1. Introduction
    2. 4.1 Related Rates
    3. 4.2 Linear Approximations and Differentials
    4. 4.3 Maxima and Minima
    5. 4.4 The Mean Value Theorem
    6. 4.5 Derivatives and the Shape of a Graph
    7. 4.6 Limits at Infinity and Asymptotes
    8. 4.7 Applied Optimization Problems
    9. 4.8 L’Hôpital’s Rule
    10. 4.9 Newton’s Method
    11. 4.10 Antiderivatives
    12. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
      4. Review Exercises
  6. 5 Integration
    1. Introduction
    2. 5.1 Approximating Areas
    3. 5.2 The Definite Integral
    4. 5.3 The Fundamental Theorem of Calculus
    5. 5.4 Integration Formulas and the Net Change Theorem
    6. 5.5 Substitution
    7. 5.6 Integrals Involving Exponential and Logarithmic Functions
    8. 5.7 Integrals Resulting in Inverse Trigonometric Functions
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
      4. Review Exercises
  7. 6 Applications of Integration
    1. Introduction
    2. 6.1 Areas between Curves
    3. 6.2 Determining Volumes by Slicing
    4. 6.3 Volumes of Revolution: Cylindrical Shells
    5. 6.4 Arc Length of a Curve and Surface Area
    6. 6.5 Physical Applications
    7. 6.6 Moments and Centers of Mass
    8. 6.7 Integrals, Exponential Functions, and Logarithms
    9. 6.8 Exponential Growth and Decay
    10. 6.9 Calculus of the Hyperbolic Functions
    11. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
      4. Review Exercises
  8. A | Table of Integrals
  9. B | Table of Derivatives
  10. C | Review of Pre-Calculus
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
  12. Index
I
implicit differentiation 3.8 Implicit Differentiation
increasing on the interval I I 1.1 Review of Functions
indefinite integral 4.10 Antiderivatives
independent variable 1.1 Review of Functions
indeterminate forms 4.8 L’Hôpital’s Rule
infinite discontinuity 2.4 Continuity
infinite limit at infinity 4.6 Limits at Infinity and Asymptotes
infinite limits 2.2 The Limit of a Function
initial-value problem 4.10 Antiderivatives
instantaneous rate of change 3.1 Defining the Derivative
integrable function 5.2 The Definite Integral
Integral calculus 2.1 A Preview of Calculus
integration by substitution 5.5 Substitution
Intermediate Value Theorem 2.4 Continuity
interval notation 1.1 Review of Functions
intuitive definition of the limit 2.2 The Limit of a Function
inverse function 1.4 Inverse Functions
inverse hyperbolic functions 1.5 Exponential and Logarithmic Functions
inverse trigonometric functions 1.4 Inverse Functions
iterative process 4.9 Newton’s Method
J
jump discontinuity 2.4 Continuity
M
Mandelbrot set 4.9 Newton’s Method
mathematical models 1.2 Basic Classes of Functions
Mean Value Theorem 4.4 The Mean Value Theorem
Mean Value Theorem for Integrals 5.3 The Fundamental Theorem of Calculus
method of cylindrical shells. 6.3 Volumes of Revolution: Cylindrical Shells
method of exhaustion 5.1 Approximating Areas
multivariable calculus 2.1 A Preview of Calculus
Q
quadratic function 1.2 Basic Classes of Functions
Quotient law for limits 2.3 The Limit Laws
T
table of values 1.1 Review of Functions
tangent line approximation 4.2 Linear Approximations and Differentials
Tangent Problem 2.1 A Preview of Calculus
theorem of Pappus for volume 6.6 Moments and Centers of Mass
transcendental functions 1.2 Basic Classes of Functions
transformation of a function 1.2 Basic Classes of Functions
trigonometric functions 1.3 Trigonometric Functions
trigonometric identity 1.3 Trigonometric Functions
Z
zeroes of functions 4.9 Newton’s Method
zeros of a function 1.1 Review of Functions
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