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# Calculus: Early Transcendentals Single Variable

## Fourth EditionJon Rogawski; Colin Adams; Robert Franzosa

©2019ISBN:9781319270353

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ISBN:9781319405731

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ISBN:9781319254421

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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 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' 5 k(y 2 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

**Appendices A1**A. The Language of Mathematics

B. Properties of Real Numbers

C. Induction and the Binomial Theorem

D. Additional Proofs

ANSWERS TO ODD-NUMBERED EXERCISES

REFERENCES

INDEX

Additional content can be accessed online at www.macmillanlearning.com/calculuset4e:

**Additional Proofs:**

L’Hôpital’s Rule

Error Bounds for Numerical

Integration

Comparison Test for Improper

Integrals

**Additional Content:**

Second-Order Differential

Equations

Complex Numbers