Calculus with Early Transcendentals

2.1 Rates of Change and Tangents

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2.2 Limits All Around the Plane

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2.3 The Mathematical Definition of Limit

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2.4 Determining Limits of Functions

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2.5 Continuity

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2.6 Rate of Change Revisited: The Derivative

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3.1 Differentiation Notation and Consequences

3.2 Derivatives of Polynomials, Exponentials, Products, and Quotients

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3.3 Derivatives of Trigonometric Functions

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3.4 The Chain Rule

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3.5 Implicit Differentiation

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3.6 Derivatives of Inverse Functions

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3.7 Rates of Change in Use

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3.8 Related Rates

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3.9 Linearization and Differentials

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4.1 Extreme Values of Functions

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4.2 The Mean Value Theorem

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4.3 The First and Second Derivative Tests

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4.4 L'Hôpital's Rule

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4.5 Calculus and Curve Sketching

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4.6 Optimization Problems

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4.7 Antiderivatives

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5.1 Area, Distance, and Riemann Sums

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5.2 The Definite Integral

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5.3 The Fundamental Theorem of Calculus

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5.4 Indefinite Integrals and the Substitution Rule

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5.5 The Substitution Rule and Definite Integration

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6.1 Finding Volumes Using Slices

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6.2 Finding Volumes Using Cylindrical Shells

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6.3 Arc Length and Surface Area

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6.4 Moments and Centers of Mass

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6.5 Force, Work, and Pressure

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6.6 Hyperbolic Functions

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7.1 Integration by Parts

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7.2 The Partial Fractions Method

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7.3 Trigonometric Integrals

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7.4 Trigonometric Substitutions

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7.5 Integration Summary and Integration Using Computer Algebra Systems

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7.6 Numerical Integration

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7.7 Improper Integrals

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8.1 Separable Differential Equations

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8.2 First-Order Linear Differential Equations

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8.3 Autonomous Differential Equations and Slope Fields

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8.4 Second-Order Linear Differential Equations

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9.1 Parametric Equations

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9.2 Calculus and Parametric Equations

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9.3 Polar Coordinates

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9.4 Calculus in Polar Coordinates

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9.5 Conic Sections in Cartesian Coordinates

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9.6 Conic Sections in Polar Coordinates

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10.1 Sequences

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10.2 Infinite Series

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10.3 The Integral Test

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10.4 Comparison Tests

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10.5 The Ratio and Root Tests

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10.6 Absolute and Conditional Convergence

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10.7 Power Series

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10.8 Taylor and Maclaurin Series

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10.9 Further Applications of Series

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11.1 Three-Dimensional Cartesian Space

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11.2 Vectors and Vector Algebra

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11.3 The Dot Product

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11.4 The Cross Product

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11.5 Describing Lines and Planes

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11.6 Cylinders and Quadric Surfaces

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12.1 Vector-Valued Functions

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12.2 Arc Length and the Unit Tangent Vector

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12.3 The Unit Normal and Binormal Vectors, Curvature, and Torsion

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12.4 Planetary Motion and Kepler's Laws

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13.1 Functions of Several Variables

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13.2 Limits and Continuity of Multivariable Functions

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13.3 Partial Derivatives

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13.4 The Chain Rule

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13.5 Directional Derivatives and Gradient Vectors

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13.6 Tangent Planes and Differentials

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13.7 Extreme Values of Functions of Two Variables

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13.8 Lagrange Multipliers

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14.1 Double Integrals

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14.2 Applications of Double Integrals

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14.3 Double Integrals in Polar Coordinates

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14.4 Triple Integrals

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14.5 Triple Integrals in Cylindrical and Spherical Coordinates

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14.6 Substitutions and Multiple Integrals

15.1 Vector Fields

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15.2 Line Integrals

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15.3 The Fundamental Theorem for Line Integrals

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15.4 Green's Theorem

15.5 Parametric Surfaces and Surface Area

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15.6 Surface Integrals

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15.7 Stokes' Theorem

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15.8 The Divergence Theorem

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