Calculus, 10ed, ISV

Before Calculus

0.1 Functions

0.2 New Functions from Old

0.3 Families of Functions

0.4 Inverse Functions

Limits and Continuity

1.1 Limits (An Intuitive Approach)

1.2 Computing Limits 62

1.3 Limits at Infinity; End Behavior of a Function

1.4 Limits (Discussed More Rigorously)

1.5 Continuity

1.6 Continuity of Trigonometric Functions

The Derivative

2.1 Tangent Lines and Rates of Change

2.2 The Derivative Function

2.3 Introduction to Techniques of Differentiation

2.4 The Product and Quotient Rules

2.5 Derivatives of Trigonometric Functions

2.6 The Chain Rule

2.7 Implicit Differentiation

2.8 Related Rates

2.9 Local Linear Approximation; Differentials

The Derivative in Graphing and Applications

3.1 Analysis of Functions I: Increase, Decrease and Concavity

3.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials

3.3 Analysis of Functions III: Rational Functions, Cusps and Vertical Tangents

3.4 Absolute Maxima and Minima

3.5 Applied Maximum and Minimum Problems

3.6 Rectilinear Motion

3.7 Newton's Method

3.8 Rolle's Theorem; Mean-Value Theorem

Integration

4.1 An Overview of the Area Problem

4.2 The Indefinite Integral

4.3 Integration by Substitution

4.4 The Definition of Area as a Limit; Sigma Notation

4.5 The Definite Integral

4.6 The Fundamental Theorem of Calculus

4.7 Rectilinear Motion Revisited Using Integration

4.8 Average Value of a Function and its Applications

4.9 Evaluating Definite Integrals by Substitution

Applications of The Definite Integral in Geometry, Science and Engineering

5.1 Area Between Two Curves

5.2 Volumes by Slicing; Disks and Washers

5.3 Volumes by Cylindrical Shells

5.4 Length of a Plane Curve

5.5 Area of a Surface of Revolution

5.6 Work

5.7 Moments, Centers of Gravity and Centroids

5.8 Fluid Pressure and Force

Exponential, Logarithmic and Inverse Trigonometric Functions

6.1 Exponential and Logarithmic Functions

6.2 Derivatives and Integrals Involving Logarithmic Functions

6.3 Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions

6.4 Graphs and Applications Involving Logarithmic and Exponential Functions

6.5 L'Hôpital's Rule; Indeterminate Forms

6.6 Logarithmic and Other Functions Defined by Integrals

6.7 Derivatives and Integrals Involving Inverse Trigonometric Functions

6.8 Hyperbolic Functions and Hanging Cables

Principles of Integral Evaluation

7.1 An Overview of Integration Methods

7.2 Integration by Parts

7.3 Integrating Trigonometric Functions

7.4 Trigonometric Substitutions

7.5 Integrating Rational Functions by Partial Fractions

7.6 Using Computer Algebra Systems and Tables of Integrals

7.7 Numerical Integration; Simpson's Rule

7.8 Improper Integrals

Mathematical Modeling with Differential Equations

8.1 Modeling with Differential Equations

8.2 Separation of Variables

8.3 Slope Fields; Euler's Method

8.4 First-Order Differential Equations and Applications

Infinite Series

9.1 Sequences

9.2 Monotone Sequences

9.3 Infinite Series

9.4 Convergence Tests

9.5 The Comparison, Ratio and Root Tests

9.6 Alternating Series; Absolute and Conditional Convergence

9.7 Maclaurin and Taylor Polynomials

9.8 Maclaurin and Taylor Series; Power Series

9.9 Convergence of Taylor Series

9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series

Parametric and Polar Curves; Conic Sections

10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves

10.2 Polar Coordinates

10.3 Tangent Lines, Arc Length and Area for Polar Curves

10.4 Conic Sections

10.5 Rotation of Axes; Second-Degree Equations

10.6 Conic Sections in Polar Coordinates

Three-Dimensional Space; Vectors

11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces

11.2 Vectors

11.3 Dot Product; Projections

11.4 Cross Product

11.5 Parametric Equations of Lines

11.6 Planes in 3-Space

11.7 Quadric Surfaces

11.8 Cylindrical and Spherical Coordinates

Vector-Valued Functions

12.1 Introduction to Vector-Valued Functions

12.2 Calculus of Vector-Valued Functions

12.3 Change of Parameter; Arc Length

12.4 Unit Tangent, Normal and Binormal Vectors

12.5 Curvature

12.6 Motion Along a Curve

12.7 Kepler's Laws of Planetary Motion

Partial Derivatives

13.1 Functions of Two or More Variables

13.2 Limits and Continuity

13.3 Partial Derivatives

13.4 Differentiability, Differentials and Local Linearity

13.5 The Chain Rule

13.6 Directional Derivatives and Gradients

13.7 Tangent Planes and Normal Vectors

13.8 Maxima and Minima of Functions of Two Variables

13.9 Lagrange Multipliers

Multiple Integrals

14.1 Double Integrals

14.2 Double Integrals over Nonrectangular Regions

14.3 Double Integrals in Polar Coordinates

14.4 Surface Area; Parametric Surfaces

14.5 Triple Integrals

14.6 Triple Integrals in Cylindrical and Spherical Coordinates

14.7 Change of Variables in Multiple Integrals; Jacobians

14.8 Centers of Gravity using Multiple Integrals

Topics In Vector Calculus

15.1 Vector Fields

15.2 Line Integrals

15.3 Independence of Path; Conservative Vector Fields

15.4 Green's Theorem

15.5 Surface Integrals

15.6 Applications of Surface Integrals; Flux

15.7 The Divergence Theorem

15.8 Stokes' Theorem

A Appendices

A Graphing Functions Using Calculators and Computer Algebra Systems

B Trigonometry Review

C Solving Polynomial Equations

D Selected Proofs

Answers To Odd-Numbered Exercises

Index I

Web Appendices (Online Only)

E Real Numbers, Intervals and Inequalities

F Absolute Value

G Coordinate Planes, Lines and Linear Functions

H Distance, Circles and Quadratic Equations

I Early Parametric Equations Option

J Mathematical Models

K The Discriminant

L Second-Order Linear Homogeneous Differential Equations

Web Projects: Expanding The Calculus Horizon (Online Only)

Blammo The Human Cannonball

Comet Collision

Hurricane Modeling

Iteration and Dynamical Systems

Railroad Design

Robotics