Calculus Early Transcendentals 9th Edition by James Stewart, Daniel K Clegg, Saleem Watson ISBN 9780357128916 0357128915

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ISBN 10: 0357128915
ISBN 13: 9780357128916
Author: James Stewart, Daniel K Clegg, Saleem Watson

James Stewart’s Calculus series provides students with the strongest foundation for a STEM future by building problem-solving skills and developing critical thinking and conceptual understanding. Selected and mentored by Stewart, Daniel Clegg and Saleem Watson continue his precision, accuracy, and outstanding examples and problem sets. Careful refinements such as scaffolded exercises that build student confidence make the 9th edition an even more effective learning and teaching tool. WebAssign reinforces concepts and enables students to apply them with new Proof Problems, Expanded Problems, and Explore It interactive learning modules. Showing that Calculus is both practical and beautiful, the Stewart approach and WebAssign resources enhance understanding and build confidence for millions of students worldwide.

Calculus Early Transcendentals 9th Edition Table of contents:

1. Functions and Models

1.1. Four Ways to Represent a Function

Functions

Representations of Functions

Which Rules Define Functions?

Piecewise Defined Functions

Even and Odd Functions

Increasing and Decreasing Functions

1.1. Exercises

1.2. Mathematical Models: A Catalog of Essential Functions

Linear Models

Polynomials

Power Functions

Rational Functions

Algebraic Functions

Trigonometric Functions

Exponential Functions

Logarithmic Functions

1.2. Exercises

1.3. New Functions from Old Functions

Transformations of Functions

Combinations of Functions

1.3. Exercises

1.4. Exponential Functions

Exponential Functions and Their Graphs

Applications of Exponential Functions

The Number e

1.4. Exercises

1.5. Inverse Functions and Logarithms

Inverse Functions

Logarithmic Functions

Natural Logarithms

Graph and Growth of the Natural Logarithm

Inverse Trigonometric Functions

1.5. Exercises

1. Review

Principles of Problem Solving

2. Limits and Derivatives

2.1. The Tangent and Velocity Problems

The Tangent Problem

The Velocity Problem

2.1. Exercises

2.2. The Limit of a Function

Finding Limits Numerically and Graphically

One-Sided Limits

How Can a Limit Fail to Exist?

Infinite Limits; Vertical Asymptotes

2.2. Exercises

2.3. Calculating Limits Using the Limit Laws

Properties of Limits

Evaluating Limits by Direct Substitution

Using One-Sided Limits

The Squeeze Theorem

2.3. Exercises

2.4. The Precise Definition of a Limit

The Precise Definition of a Limit

One-Sided Limits

The Limit Laws

Infinite Limits

2.4. Exercises

2.5. Continuity

Continuity of a Function

Properties of Continuous Functions

The Intermediate Value Theorem

2.5. Exercises

2.6. Limits at Infinity; Horizontal Asymptotes

Limits at Infinity and Horizontal Asymptotes

Evaluating Limits at Infinity

Infinite Limits at Infinity

Precise Definitions

2.6. Exercises

2.7. Derivatives and Rates of Change

Tangents

Velocities

Derivatives

Rates of Change

2.7. Exercises

Writing Project. Early Methods for Finding Tangents

2.8. The Derivative as a Function

The Derivative Function

Other Notations

How Can a Function Fail to Be Differentiable?

Higher Derivatives

2.8. Exercises

2. Review

Problems Plus

3. Differentiation Rules

3.1. Derivatives of Polynomials and Exponential Functions

Constant Functions

Power Functions

New Derivatives from Old

Exponential Functions

3.1. Exercises

Applied Project. Building a Better Roller Coaster

3.2. The Product and Quotient Rules

The Product Rule

The Quotient Rule

3.2. Exercises

3.3. Derivatives of Trigonometric Functions

Derivatives of the Trigonometric Functions

Two Special Trigonometric Limits

3.3. Exercises

3.4. The Chain Rule

The Chain Rule

Derivatives of General Exponential Functions

How to Prove the Chain Rule

3.4. Exercises

Applied Project. Where Should a Pilot Start Descent?

3.5. Implicit Differentiation

Implicitly Defined Functions

Implicit Differentiation

Second Derivatives of Implicit Functions

3.5. Exercises

Discovery Project. Families of Implicit Curves

3.6. Derivatives of Logarithmic and Inverse Trigonometric Functions

Derivatives of Logarithmic Functions

Logarithmic Differentiation

The Number e as a Limit

Derivatives of Inverse Trigonometric Functions

3.6. Exercises

3.7. Rates of Change in the Natural and Social Sciences

Physics

Chemistry

Biology

Economics

Other Sciences

A Single Idea, Many Interpretations

3.7. Exercises

3.8. Exponential Growth and Decay

Population Growth

Radioactive Decay

Newton’s Law of Cooling

Continuously Compounded Interest

3.8. Exercises

Applied Project. Controlling Red Blood Cell Loss during Surgery

3.9. Related Rates

3.9. Exercises

3.10. Linear Approximations and Differentials

Linearization and Approximation

Applications to Physics

Differentials

3.10. Exercises

Discovery Project. Polynomial Approximations

3.11. Hyperbolic Functions

Hyperbolic Functions and Their Derivatives

Inverse Hyperbolic Functions and Their Derivatives

3.11. Exercises

3. Review

Problems Plus

4. Applications of Differentiation

4.1. Maximum and Minimum Values

Absolute and Local Extreme Values

Critical Numbers and the Closed Interval Method

4.1. Exercises

Applied Project. The Calculus of Rainbows

4.2. The Mean Value Theorem

Rolle’s Theorem

The Mean Value Theorem

4.2. Exercises

4.3. What Derivatives Tell Us about the Shape of a Graph

What Does f ′ Say about f ?

The First Derivative Test

What Does f ″ Say about f ?

The Second Derivative Test

Curve Sketching

4.3. Exercises

4.4. Indeterminate Forms and l’Hospital’s Rule

Indeterminate Forms (Types 0 0 , ∞ ∞ )

L’Hospital’s Rule

Indeterminate Products (Type 0 · ∞ )

Indeterminate Differences (Type ∞ – ∞ )

Indeterminate Powers (Types 0 0 , ∞ 0 , 1 ∞ )

4.4. Exercises

Writing Project. The Origins of L’Hospital’s Rule

4.5 . Summary of Curve Sketching

Guidelines for Sketching a Curve

Slant Asymptotes

4.5 . Exercises

4.6. Graphing with Calculus and Technology

4.6. Exercises

4.7. Optimization Problems

Applications to Business and Economics

4.7. Exercises

Applied Project. The Shape of a Can

Applied Project. Planes and Birds: Minimizing Energy

4.8. Newton’s Method

4.8. Exercises

4.9. Antiderivatives

The Antiderivative of a Function

Antidifferentiation Formulas

Graphing Antiderivatives

Linear Motion

4.9. Exercises

4. Review

Problems Plus

5. Integrals

5.1. The Area and Distance Problems

The Area Problem

The Distance Problem

5.1. Exercises

5.2. The Definite Integral

The Definite Integral

Evaluating Definite Integrals

The Midpoint Rule

Properties of the Definite Integral

5.2. Exercises

Discovery Project. Area Functions

5.3. The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus, Part 1

The Fundamental Theorem of Calculus, Part 2

Differentiation and Integration as Inverse Processes

5.3. Exercises

5.4. Indefinite Integrals and the Net Change Theorem

Indefinite Integrals

The Net Change Theorem

5.4. Exercises

Writing Project. Newton, Leibniz, and the Invention of Calculus

5.5. The Substitution Rule

Substitution: Indefinite Integrals

Substitution: Definite Integrals

Symmetry

5.5. Exercises

5. Review

Problems Plus

6. Applications of Integration

6.1. Areas between Curves

Area between Curves: Integrating with Respect to x

Area between Curves: Integrating with Respect to y

Applications

6.1. Exercises

Applied Project. The Gini Index

6.2. Volumes

Definition of Volume

Volumes of Solids of Revolution

Finding Volume Using Cross-Sectional Area

6.2. Exercises

6.3. Volumes by Cylindrical Shells

The Method of Cylindrical Shells

Disks and Washers versus Cylindrical Shells

6.3. Exercises

6.4. Work

6.4. Exercises

6.5. Average Value of a Function

6.5. Exercises

Applied Project. Calculus and Baseball

Applied Project. Where to Sit at the Movies

6. Review

Problems Plus

7. Techniques of Integration

7.1. Integration by Parts

Integration by Parts: Indefinite Integrals

Integration by Parts: Definite Integrals

Reduction Formulas

7.1. Exercises

7.2. Trigonometric Integrals

Integrals of Powers of Sine and Cosine

Integrals of Powers of Secant and Tangent

Using Product Identities

7.2. Exercises

7.3. Trigonometric Substitution

7.3. Exercises

7.4. Integration of Rational Functions by Partial Fractions

The Method of Partial Fractions

Rationalizing Substitutions

7.4. Exercises

7.5. Strategy for Integration

Guidelines for Integration

Can We Integrate All Continuous Functions?

7.5. Exercises

7.6. Using Tables and Technology

Tables of Integrals

Integration Using Technology

7.6. Exercises

Discovery Project. Patterns in Integrals

7.7. Approximate Integration

The Midpoint and Trapezoidal Rules

Error Bounds for the Midpoint and Trapezoidal Rules

Simpson’s Rule

Error Bound for Simpson’s Rule

7.7. Exercises

7.8. Improper Integrals

Type 1: Infinite Intervals

Type 2: Discontinuous Integrands

A Comparison Test for Improper Integrals

7.8. Exercises

7. Review

Problems Plus

8. Further Applications of Integration

8.1. Arc Length

Arc Length of a Curve

The Arc Length Function

8.1. Exercises

Discovery Project. Arc Length Contest

8.2. Area of a Surface of Revolution

8.2. Exercises

Discovery Project. Rotating on a Slant

8.3. Applications to Physics and Engineering

Hydrostatic Pressure and Force

Moments and Centers of Mass

Theorem of Pappus

8.3. Exercises

Discovery Project. Complementary Coffee Cups

8.4. Applications to Economics and Biology

Consumer Surplus

Blood Flow

Cardiac Output

8.4. Exercises

8.5. Probability

Probability Density Functions

Average Values

Normal Distributions

8.5. Exercises

8. Review

Problems Plus

9. Differential Equations

9.1. Modeling with Differential Equations

Models for Population Growth

A Model for the Motion of a Spring

General Differential Equations

9.1. Exercises

9.2. Direction Fields and Euler’s Method

Direction Fields

Euler’s Method

9.2. Exercises

9.3. Separable Equations

Separable Differential Equations

Orthogonal Trajectories

Mixing Problems

9.3. Exercises

Applied Project. How Fast Does a Tank Drain?

9.4. Models for Population Growth

The Law of Natural Growth

The Logistic Model

Comparison of the Natural Growth and Logistic Models

Other Models for Population Growth

9.4. Exercises

9.5. Linear Equations

Linear Differential Equations

Application to Electric Circuits

9.5. Exercises

Applied Project. Which Is Faster, Going Up or Coming Down?

9.6. Predator-Prey Systems

9.6. Exercises

9. Review

Problems Plus

10. Parametric Equations and Polar Coordinates

10.1. Curves Defined by Parametric Equations

Parametric Equations

Graphing Parametric Curves with Technology

The Cycloid

Families of Parametric Curves

10.1. Exercises

Discovery Project. Running Circles around Circles

10.2. Calculus with Parametric Curves

Tangents

Areas

Arc Length

Surface Area

10.2. Exercises

Applied Project. Bézier Curves

10.3. Polar Coordinates

The Polar Coordinate System

Relationship between Polar and Cartesian Coordinates

Polar Curves

Symmetry

Graphing Polar Curves with Technology

10.3. Exercises

Discovery Project. Families of Polar Curves

10.4. Calculus in Polar Coordinates

Area

Arc Length

Tangents

10.4. Exercises

10.5. Conic Sections

Parabolas

Ellipses

Hyperbolas

Shifted Conics

10.5. Exercises

10.6. Conic Sections in Polar Coordinates

A Unified Description of Conics

Polar Equations of Conics

Kepler’s Laws

10.6. Exercises

10. Review

Problems Plus

11. Sequences, Series, and Power Series

11.1. Sequences

Infinite Sequences

The Limit of a Sequence

Properties of Convergent Sequences

Monotonic and Bounded Sequences

11.1. Exercises

Discovery Project. Logistic Sequences

11.2. Series

Infinite Series

Sum of a Geometric Series

Test for Divergence

Properties of Convergent Series

11.2. Exercises

11.3. The Integral Test and Estimates of Sums

The Integral Test

Estimating the Sum of a Series

Proof of the Integral Test

11.3. Exercises

11.4. The Comparison Tests

The Direct Comparison Test

Limit Comparison Test

Estimating Sums

11.4. Exercises

11.5. Alternating Series and Absolute Convergence

Alternating Series

Estimating Sums of Alternating Series

Absolute Convergence and Conditional Convergence

Rearrangements

11.5. Exercises

11.6. The Ratio and Root Tests

The Ratio Test

The Root Test

11.6. Exercises

11.7. Strategy for Testing Series

11.7. Exercises

11.8. Power Series

Power Series

Interval of Convergence

11.8. Exercises

11.9. Representations of Functions as Power Series

Representations of Functions using Geometric Series

Differentiation and Integration of Power Series

Functions Defined by Power Series

11.9. Exercises

11.10. Taylor and Maclaurin Series

Definitions of Taylor Series and Maclaurin Series

When Is a Function Represented by Its Taylor Series?

Taylor Series of Important Functions

New Taylor Series from Old

Multiplication and Division of Power Series

11.10. Exercises

Discovery Project. An Elusive Limit

Writing Project. How Newton Discovered the Binomial Series

11.11. Applications of Taylor Polynomials

Approximating Functions by Polynomials

Applications to Physics

11.11. Exercises

Applied Project. Radiation from the Stars

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Tags: James Stewart, Daniel K Clegg, Saleem Watson, Early Transcendentals