Table of Contents
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Table of Contents
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Licensing
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1: Functions and Graphs
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2: Limits
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3: Derivatives
- 3.0: Prelude to Derivatives
- 3.1: Defining the Derivative
- 3.2: The Derivative as a Function
- 3.3: Differentiation Rules
- 3.4: Derivatives as Rates of Change
- 3.5: Derivatives of Trigonometric Functions
- 3.6: The Chain Rule
- 3.7: Derivatives of Inverse Functions
- 3.8: Implicit Differentiation
- 3.9: Derivatives of Exponential and Logarithmic Functions
- 3.R: Chapter 3 Review Exercises
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4: Applications of Derivatives
- 4.0: Prelude to Applications of Derivatives
- 4.1: Related Rates
- 4.2: Linear Approximations and Differentials
- 4.3: Maxima and Minima
- 4.4: The Mean Value Theorem
- 4.5: Derivatives and the Shape of a Graph
- 4.6: Limits at Infinity and Asymptotes
- 4.7: Applied Optimization Problems
- 4.8: L’Hôpital’s Rule
- 4.9: Newton’s Method
- 4.10: Antiderivatives
- 4.R: Chapter 4 Review Exercises
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5: Integration
- 5.0: Prelude to Integration
- 5.1: Approximating Areas
- 5.2: The Definite Integral
- 5.3: The Fundamental Theorem of Calculus
- 5.4: Integration Formulas and the Net Change Theorem
- 5.5: Substitution
- 5.6: Integrals Involving Exponential and Logarithmic Functions
- 5.7: Integrals Resulting in Inverse Trigonometric Functions
- 5.7: Integrals Resulting in Inverse Trigonometric Functions
- 5.R: Chapter 5 Review Exercises
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6: Applications of Integration
- 6.0: Prelude to Applications of Integration
- 6.1: Areas between Curves
- 6.2: Determining Volumes by Slicing
- 6.3: Volumes of Revolution - Cylindrical Shells
- 6.4: Arc Length of a Curve and Surface Area
- 6.5: Physical Applications of Integration
- 6.6: Moments and Centers of Mass
- 6.7: Integrals, Exponential Functions, and Logarithms
- 6.8: Exponential Growth and Decay
- 6.9: Calculus of the Hyperbolic Functions
- 6.R: Chapter 6 Review Exercises
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7: Techniques of Integration
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8: Introduction to Differential Equations
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9: Sequences and Series
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10: Power Series
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11: Parametric Equations and Polar Coordinates
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12: Vectors in Space
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13: Vector-Valued Functions
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14: Differentiation of Functions of Several Variables
- 14.0: Prelude to Differentiation of Functions of Several Variables
- 14.1: Functions of Several Variables
- 14.2: Limits and Continuity
- 14.3: Partial Derivatives
- 14.4: Tangent Planes and Linear Approximations
- 14.5: The Chain Rule for Multivariable Functions
- 14.6: Directional Derivatives and the Gradient
- 14.7: Maxima/Minima Problems
- 14.8: Lagrange Multipliers
- 14.R: Chapter 14 Review Exercises
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15: Multiple Integration
- 15.0: Prelude to Multiple Integration
- 15.1: Double Integrals over Rectangular Regions
- 15.2: Double Integrals over General Regions
- 15.3: Double Integrals in Polar Coordinates
- 15.4: Triple Integrals
- 15.5: Triple Integrals in Cylindrical and Spherical Coordinates
- 15.6: Calculating Centers of Mass and Moments of Inertia
- 15.7: Change of Variables in Multiple Integrals
- 15.R: Chapter 15 Review Exercises
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16: Vector Calculus
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17: Second-Order Differential Equations
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Appendices
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Index
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Glossary
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Detailed Licensing