# Single Variable Calculus

## Second EditionJon Rogawski

©2012What’s the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching—supported by Rogawski’s

Widely adopted in its first edition, Rogawski’s

Now Rogawski’s

*Calculus,*Second Edition—the most successful new calculus text in 25 years!Widely adopted in its first edition, Rogawski’s

*Calculus*worked for instructors and students by balancing formal precision with a guiding conceptual focus. Rogawski engages students while reinforcing the relevance of calculus to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus.Now Rogawski’s

*Calculus*success continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning experience.**This hardcover volume includes chapters 1-12 of the Second Edition, for instructors who just want the book's coverage of topics in single variable calculus.**

## 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 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 3: Differentiation**3.1 Definition of the Derivative

3.2 The Derivative as a Function

3.3 Product and Quotient Rates

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 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

4.8 Antiderivatives

**Chapter 5: The Integral**

5.1 Approximating and Computing Area

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus, Part I

5.4 The Fundamental Theorem of Calculus, Part II

5.5 Net Change as the Integral of a Rate

5.6 Substitution Method

**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 7: The Exponential Function**

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 8: Techniques of Integration**

8.1 Integration by Parts

8.2 Trigonometric Integral

8.3 Trigonometric Substitution

8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions

8.5 The Method of Partial Fractions

8.6 Improper Integrals

8.7 Probability and Integration

8.8 Numerical Integration

**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 10: Introduction to Differential Equations**

10.1 Solving Differential Equations

10.2 Graphical and Numerical Method

10.3 The Logistic Equation

10.4 First-Order Linear Equations

**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 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