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# Calculus

## Third EditionJon Rogawski; Colin Adams

©2015
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The most successful calculus book of its generation, Jon Rogawski’s *Calculus* offers an ideal balance of formal precision and dedicated conceptual focus, helping students build strong computational skills while continually reinforcing the relevance of calculus to their future studies and their lives.

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Learn More## Table of Contents

**Rogawski/Adams: Calculus 3e 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 Technology: Calculators and Computers

Chapter Review Exercises

**Chapter 2: Limits **2.1 Limits, Rates of Change, and Tangent Lines

2.2 Limits: A Numerical and Graphical Approach

2.3 Basic Limit Laws

2.4 Limits and Continuity

2.5 Evaluating Limits Algebraically

2.6 Trigonometric Limits

2.7 Limits at Infinity

2.8 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 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 Shape of a Graph

4.5 Graph Sketching and Asymptotes

4.6 Applied Optimizations

4.7 Newton’s Method

Chapter Review Exercises

**Chapter 5: The Integral**

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

5.7 Substitution Method

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

6.4 The Method of Cylindrical Shells

6.5 Work and Energy

Chapter Review Exercises

**Chapter 7: Exponential Functions**7.1 Derivative of f(x)=bx and the Number

*e*

7.2 Inverse Functions

7.3 Logarithms and their Derivatives

7.4 Exponential Growth and Decay

7.5 Compound Interest and Present Value

7.6 Models Involving y’= k(y-b)

7.7 L’Hôpital’s Rule

7.8 Inverse Trigonometric Functions

7.9 Hyperbolic Functions

Chapter Review Exercises

**Chapter 8: Techniques of Integration**8.1 Integration by Parts

8.2 Trigonometric Integrals

8.3 Trigonometric Substitution

8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions

8.5 The Method of Partial Fractions

8.6 Strategies for Integration

8.7 Improper Integrals

8.8 Probability and Integration

8.9 Numerical Integration

Chapter Review Exercises

**Chapter 9: Further Applications of the Integral and Taylor Polynomials **9.1 Arc Length and Surface Area

9.2 Fluid Pressure and Force

9.3 Center of Mass

9.4 Taylor Polynomials

Chapter Review Exercises

**Chapter 10: Introduction to Differential Equations**10.1 Solving Differential Equations

10.2 Graphical and Numerical Methods

10.3 The Logistic Equation

10.4 First-Order Linear Equations

Chapter Review Exercises

**Chapter 11: Infinite Series**11.1 Sequences

11.2 Summing an Infinite Series

11.3 Convergence of Series with Positive Terms

11.4 Absolute and Conditional Convergence

11.5 The Ratio and Root Tests

11.6 Power Series

11.7 Taylor Series

Chapter Review Exercises

**Chapter 12: Parametric Equations, Polar Coordinates, and Conic Sections **12.1 Parametric Equations

12.2 Arc Length and Speed

12.3 Polar Coordinates

12.4 Area and Arc Length in Polar Coordinates

12.5 Conic Sections

Chapter Review Exercises

**Chapter 13: Vector Geometry**13.1 Vectors in the Plane

13.2 Vectors in Three Dimensions

13.3 Dot Product and the Angle Between Two Vectors

13.4 The Cross Product

13.5 Planes in Three-Space

13.6 A Survey of Quadric Surfaces

13.7 Cylindrical and Spherical Coordinates

Chapter Review Exercises

**Chapter 14: Calculus of Vector-Valued Functions **14.1 Vector-Valued Functions

14.2 Calculus of Vector-Valued Functions

14.3 Arc Length and Speed

14.4 Curvature

14.5 Motion in Three-Space

14.6 Planetary Motion According to Kepler and Newton

Chapter Review Exercises

**Chapter 15: Differentiation in Several Variables**15.1 Functions of Two or More Variables

15.2 Limits and Continuity in Several Variables

15.3 Partial Derivatives

15.4 Differentiability and Tangent Planes

15.5 The Gradient and Directional Derivatives

15.6 The Chain Rule

15.7 Optimization in Several Variables

15.8 Lagrange Multipliers: Optimizing with a Constraint

Chapter Review Exercises

**Chapter 16: Multiple Integration**16.1 Integration in Variables

16.2 Double Integrals over More General Regions

16.3 Triple Integrals

16.4 Integration in Polar, Cylindrical, and Spherical Coordinates

16.5 Applications of Multiplying Integrals

16.6 Change of Variables

Chapter Review Exercises

**Chapter 17: Line and Surface Integrals**17.1 Vector Fields

17.2 Line Integrals

17.3 Conservative Vector Fields

17.4 Parametrized Surfaces and Surface Integrals

17.5 Surface Integrals of Vector Fields

Chapter Review Exercises

**Chapter 18: Fundamental Theorems of Vector Analysis**18.1 Green’s Theorem

18.2 Stokes’ Theorem

18.3 Divergence Theorem

**Appendices**A. The Language of Mathematics

B. Properties of Real Numbers

C. Mathematical Induction and the Binomial Theorem

D. Additional Proofs of Theorems

Answers to Odd-Numbered Exercises

References

Index