Calculus: Single Variable - 2nd Edition Book

Preface.

Supplementary Resources.

Acknowledgments.

About the Authors.

C H A P T E R 1 Basics.

Preview.

1 Number Systems.

2 Planar Coordinates and Graphing in the Plane.

3 Lines and Their Slopes.

4 Functions and Their Graphs.

5 Combining Functions.

6 Trigonometry.

Summary of Key Topics.

Review Exercises.

Genesis & Development 1.

C H A P T E R 2 Limits.

Preview.

1 The Concept of Limit.

2 Limit Theorems.

3 Continuity.

4 Infinite Limits and Asymptotes.

5 Limits of Sequences.

6 Exponential Functions and Logarithms.

Summary of Key Topics.

Review Exercises.

Genesis & Development 2.

C H A P T E R 3 The Derivative.

Preview.

1 Rates of Change and Tangent Lines.

2 The Derivative.

3 Rules for Differentiation.

4 Differentiation of Some Basic Functions.

5 The Chain Rule.

6 Derivatives of Inverse Functions.

7 Higher Derivatives.

8 Implicit Differentiation.

9 Differentials and Approximation of Functions.

10 Other Transcendental Functions.

Summary of Key Topics.

Review Exercises.

Genesis & Development 3.

C H A P T E R 4 Applications of the Derivative.

Preview.

1 Related Rates.

2 The Mean Value Theorem.

3 Maxima and Minima of Functions.

4 Applied Maximum-Minimum Problems.

5 Concavity.

6 Graphing Functions.

7 l’Hoˆ pital’s Rule.

8 The Newton-Raphson Method.

9 Antidifferentiation and Applications.

Summary of Key Topics.

Review Exercises.

Genesis & Development 4.

C H A P T E R 5 The Integral.

Preview.

1 Introduction to Integration—The Area Problem.

2 The Riemann Integral.

3 Rules for Integration.

4 The Fundamental Theorem of Calculus.

5 A Calculus Approach to the Logarithm and Exponential Functions.

6 Integration by Substitution.

7 More on the Calculation of Area.

8 Numerical Techniques of Integration.

Summary of Key Topics.

Review Exercises.

Genesis & Development 5.

C H A P T E R 6 Techniques of Integration.

Preview.

1 Integration by Parts.

2 Powers and Products of Trigonometric Functions.

3 Trigonometric Substitution.

4 Partial Fractions—Linear Factors.

5 Partial Fractions—Irreducible Quadratic Factors.

6 Improper Integrals—Unbounded Integrands.

7 Improper Integrals—Unbounded Intervals.

Summary of Key Topics.

Review Exercises.

Genesis & Development 6.

C H A P T E R 7 Applications of the Integral.

Preview.

1 Volumes.

2 Arc Length and Surface Area.

3 The Average Value of a Function.

4 Center of Mass.

5 Work.

6 First Order Differential Equations—Separable Equations.

7 First Order Differential Equations—Linear Equations.

Summary of Key Topics.

Review Exercises.

Genesis & Development 7.

C H A P T E R 8 Infinite Series.

Preview.

1 Series.

2 The Divergence Test and the Integral Test.

3 The Comparison Tests.

4 Alternating Series.

5 The Ratio and Root Tests.

6 Introduction to Power Series.

7 Representing Functions by Power Series.

8 Taylor Series.

Summary of Key Topics.

Review Exercises.

Genesis & Development 8.

Table of Integrals.

Answers to Selected Exercises.

Index.