1

Limits, Derivatives, Integrals, and Integrals

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1-1

The Concept of Instantaneous Rate

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1-2

Rate of Change by Equation, Graph, or Table

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1-3

One Type of Integral of a Function

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1-4

Definite Integrals by Trapezoids, fromEquations and Data

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1-5

Calculus Journal

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1-6

Chapter Review and Test

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1-8

Algebraic Calculus Techniques for the Elementary Functions

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2

Properties of Limits

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2-1

Numerical Approach to the Definition of Limit

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2-2

Graphical and Algebraic Approaches to the Definition of Limit

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2-3

The Limit Theorems

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2-4

Continuity and Discontinuity

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2-5

Limits Involving Infinity

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2-6

The Intermediate Value Theorem and Its Consequences

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2-7

Chapter Review and Test

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4

Products, Quotients, and Parametric Functions

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4-1

Combinations of Two Functions

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4-10

Chapter Review and Test

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4-2

Derivative of a Product of Two Functions

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4-3

Derivative of a Quotient of Two Functions

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4-4

Derivatives of the Other Trigonometric Functions

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4-5

Derivatives of Inverse Trigonometric Functions

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4-6

Differentiability and Continuity

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4-7

Derivatives of a Parametric Function

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4-8

Graphs and Derivatives of Implicit Relations

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4-9

Related Rates

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5-1

A Definite Integral Problem

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5-2

Linear Approximations and Differentials

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5-3

Formal Definition of Antiderivative and Indefinite Integral

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5-4

Formal Definition of Antiderivative and Indefinite Integral

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5-5

The Mean Value Theorem and Rolles Theorem

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5-6

The Fundamental Theorem of Calculus

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5-7

Definite Integral Properties and Practice

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6

The Calculus of Exponential and Logarithmic Functions

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6-1

Integral of the Reciprocal Function:A Population Growth Problem

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6-2

Antiderivative of the Reciprocal Function and Another Form of the Fundamental Theorem

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6-3

The Uniqueness Theorem and Properties of Logarithmic Functions

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6-4

The Number e, Exponential Functions,and Logarithmic Differentiation

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6-5

Limits of Indeterminate Forms: lHospitals Rule

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6-6

Limits of Indeterminate Forms: lHospitals Rule

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6-7

Chapter Review and Test

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6-8

Cumulative Review: Chapters 16

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7-1

Direct Proportion Property of Exponential Functions

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7-2

Exponential Growth and Decay

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7-3

Other Differential Equations for Real-World Applications

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7-4

Graphical Solution of Differential Equations by Using Slope Fields

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7-5

Graphical Solution of Differential Equations by Using Slope Fields

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7-6

The Logistic Function, and Predator-Prey Population Problems

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7-7

Chapter Review and Test

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7-8

Cumulative Review: Chapters 17

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8-1

Cubic Functions and Their Derivatives

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8-2

Critical Points and Points of Inflection

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8-3

Maxima and Minima in Plane and Solid Figures

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8-4

Volume of a Solid of Revolution by Cylindrical Shells

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8-5

Length of a Plane CurveArc Length

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8-6

Length of a Plane CurveArc Length

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8-7

Lengths and Areas for Polar Coordinates

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8-8

Chapter Review and Test

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9-1

Introduction to the Integral of a Product of Two Functions

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9-10

Improper Integrals

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9-11

Miscellaneous Integrals and Derivatives

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9-12

Integrals in Journal

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9-13

Chapter Review and Test

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9-2

Integration by PartsA Way to Integrate Products

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9-3

Rapid Repeated Integration by Parts

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9-4

Reduction Formulas and Computer Algebra Systems

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9-5

Integrating Special Powers of Trigonometric Functions

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9-6

Integration by Trigonometric Substitution

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9-7

Integration of Rational Functions by Partial Fractions

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9-8

Integrals of the Inverse Trigonometric Functions

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9-9

Calculus of the Hyperbolic and Inverse Hyperbolic Functions

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10

The Calculus of MotionAverages, Extremes, and Vectors

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10-1

Introduction to Distance and Displacement for Motion Along a Line

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10-2

Distance, Displacement, and Acceleration for Linear Motion

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10-3

Average Value Problems in Motion and Elsewhere

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10-4

Minimal Path Problems

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10-5

Maximum and Minimum Problems in Motion and Elsewhere

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10-6

Vector Functions for Motion in a Plane

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10-7

Chapter Review and Test

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11

The Calculus of Variable-Factor Products

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11-1

Review of WorkForce Times Displacement

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11-2

Work Done by a Variable Force

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11-3

Mass of a Variable-Density Object

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11-4

Moments, Centroids, Center of Mass,and the Theorem of Pappus

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11-5

Force Exerted by a Variable PressureCenter of Pressure

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11-6

Other Variable-Factor Products

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11-7

Chapter Review and Test

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12

The Calculus of Functions Defined by Power Series

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12-1

Introduction to Power Series

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12-10

Cumulative Reviews

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12-2

Geometric Sequences and Series as Mathematical Models

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12-3

Power Series for an Exponential Function

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12-4

Power Series for Other Elementary Functions

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12-5

Taylor and Maclaurin Series, and Operations on These Series

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12-6

Interval of Convergence for a SeriesThe Ratio Technique

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12-7

Convergence of Series at the Ends of the Convergence Interval

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12-8

Error Analysis for SeriesThe Lagrange Error Bound

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12-9

Chapter Review and Test