# Calculus: Early Transcendentals

## Fourth EditionJon Rogawski; Colin Adams; Robert Franzosa

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We see teaching mathematics as a form of story-telling, both when we present in a classroom and when we write materials for exploration and learning. The goal with *Calculus: Early Transcendentals 4th edition* is to explain to you in a captivating manner, at the right pace, and in as clear a way as possible, how mathematics works and what it can do for you. We find mathematics to be intriguing and immensely beautiful. We want you to feel that way, too.

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Learn More## Table of Contents

Chapter 1: Precalculus Review

1.1 Real Numbers, Functions, and Graphs

1.2 Linear and Quadratic Functions

1.3 The Basic Classes of Functions

1.4 Trigonometric Functions

1.5 Inverse Functions

1.6 Exponential and Logarithmic Functions

1.7 Technology: Calculators and Computers

Chapter Review Exercises Chapter 2: Limits

2.1 The Limit Idea: Instantaneous Velocity and Tangent Lines

2.2 Investigating Limits

2.3 Basic Limit Laws

2.4 Limits and Continuity

2.5 Indeterminate Forms

2.6 The Squeeze Theorem and Trigonometric Limits

2.7 Limits at Infinity

2.8 The Intermediate Value Theorem

2.9 The Formal Definition of a Limit

Chapter Review Exercises Chapter 3: Differentiation

3.1 Definition of the Derivative

3.2 The Derivative as a Function

3.3 Product and Quotient Rules

3.4 Rates of Change

3.5 Higher Derivatives

3.6 Trigonometric Functions

3.7 The Chain Rule

3.8 Implicit Differentiation

3.9 Derivatives of General Exponential and Logarithmic Functions

3.10 Related Rates

Chapter Review Exercises Chapter 4: Applications of the Derivative

4.1 Linear Approximation and Applications

4.2 Extreme Values

4.3 The Mean Value Theorem and Monotonicity

4.4 The Second Derivative and Concavity

4.5 L’Hôpital’s Rule

4.6 Analyzing and Sketching Graphs of Functions

4.7 Applied Optimization

4.8 Newton’s Method

Chapter Review Exercises Chapter 5: Integration

5.1 Approximating and Computing Area

5.2 The Definite Integral

5.3 The Indefinite Integral

5.4 The Fundamental Theorem of Calculus, Part I

5.5 The Fundamental Theorem of Calculus, Part II

5.6 Net Change as the Integral of a Rate of Change

5.7 The Substitution Method

5.8 Further Integral Formulas

Chapter Review Exercises Chapter 6: Applications of the Integral

6.1 Area Between Two Curves

6.2 Setting Up Integrals: Volume, Density, Average Value

6.3 Volumes of Revolution: Disks and Washers

6.4 Volumes of Revolution: Cylindrical Shells

6.5 Work and Energy

Chapter Review Exercises Chapter 7: Techniques of Integration

7.1 Integration by Parts

7.2 Trigonometric Integrals

7.3 Trigonometric Substitution

7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions

7.5 The Method of Partial Fractions

7.6 Strategies for Integration

7.7 Improper Integrals

7.8 Numerical Integration

Chapter Review Exercises Chapter 8: Further Applications of the Integral

8.1 Probability and Integration

8.2 Arc Length and Surface Area

8.3 Fluid Pressure and Force

8.4 Center of Mass

Chapter Review Exercises Chapter 9: Introduction to Differential Equations

9.1 Solving Differential Equations

9.2 Models Involving y=k(y-b)

9.3 Graphical and Numerical Methods

9.4 The Logistic Equation

9.5 First-Order Linear Equations

Chapter Review Exercises Chapter 10: Infinite Series

10.1 Sequences

10.2 Summing an Infinite Series

10.3 Convergence of Series with Positive Terms

10.4 Absolute and Conditional Convergence

10.5 The Ratio and Root Tests and Strategies for Choosing Tests

10.6 Power Series

10.7 Taylor Polynomials

10.8 Taylor Series

Chapter Review Exercises Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections

11.1 Parametric Equations

11.2 Arc Length and Speed

11.3 Polar Coordinates

11.4 Area and Arc Length in Polar Coordinates

11.5 Conic Sections

Chapter Review Exercises Chapter 12: Vector Geometry

12.1 Vectors in the Plane

12.2 Three-Dimensional Space: Surfaces, Vectors, and Curves

12.3 Dot Product and the Angle Between Two Vectors

12.4 The Cross Product

12.5 Planes in 3-Space

12.6 A Survey of Quadric Surfaces

12.7 Cylindrical and Spherical Coordinates

Chapter Review Exercises Chapter 13: Calculus of Vector-Valued Functions

13.1 Vector-Valued Functions

13.2 Calculus of Vector-Valued Functions

13.3 Arc Length and Speed

13.4 Curvature

13.5 Motion in 3-Space

13.6 Planetary Motion According to Kepler and Newton

Chapter Review Exercises Chapter 14: Differentiation in Several Variables

14.1 Functions of Two or More Variables

14.2 Limits and Continuity in Several Variables

14.3 Partial Derivatives

14.4 Differentiability, Tangent Planes, and Linear Approximation

14.5 The Gradient and Directional Derivatives

14.6 The Chain Rule

14.7 Optimization in Several Variables

14.8 Lagrange Multipliers: Optimizing with a Constraint

Chapter Review Exercises Chapter 15: Multiple Integration

15.1 Integration in Two Variables

15.2 Double Integrals Over More General Regions

15.3 Triple Integrals

15.4 Integration in Polar, Cylindrical, and Spherical Coordinates

15.5 Applications of Multiple Integrals

15.6 Change of Variables

Chapter Review Exercises Chapter 16: Line and Surface Integrals

16.1 Vector Fields

16.2 Line Integrals

16.3 Conservative Vector Fields

16.4 Parametrized Surfaces and Surface Integrals

16.5 Surface Integrals of Vector Fields

Chapter Review Exercises Chapter 17: Fundamental Theorems of Vector Analysis

17.1 Green’s Theorem

17.2 Stokes’ Theorem

17.3 Divergence Theorem

Chapter Review Exercises