Calculus Concepts and Contexts 5th Edition by James Stewart, Stephen Kokoska ISBN 9780357749104 0357749103

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ISBN 10: 0357749103
ISBN 13: 9780357749104
Author: James Stewart, Stephen Kokoska

Calculus Concepts and Contexts 5th Edition Table of contents:

1. Functions and Models

1.1. Four Ways to Represent a Function

Representations of Functions

Piecewise Defined Functions

Symmetry

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

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

1.5. Exercises

1.6. Parametric Curves

Parametric Equations and Graphs

Technology

The Cycloid

1.6. Exercises

Laboratory Project. Motion of a Point on a Circle

1. Review

Principles of Problem Solving

2. Limits

2.1. The Tangent and Velocity Problems

The Tangent Line Problem

The Velocity Problem

2.1. Exercises

2.2. The Limit of a Function

One-Sided Limits

2.2. Exercises

2.3. Calculating Limits Using the Limit Laws

2.3. Exercises

2.4. Continuity

Continuity of Combinations of Functions

The Intermediate Value Theorem

2.4. Exercises

2.5. Limits Involving Infinity

Infinite Limits

Limits at Infinity

Infinite Limits at Infinity

2.5. Exercises

2.6. Derivatives and Rates of Change

Tangents

Velocities

Derivatives

Rates of Change

2.6. Exercises

Writing Project. Early Methods for Finding Tangents

2.7. The Derivative as a Function

Other Notations

Differentiability on an Interval

Nondifferentiable Functions

Higher Order Derivatives

2.7. Exercises

2. Review

Focus on Problem Solving

3. Differentiation Rules

3.1. Derivatives of Polynomials and Exponential 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

3.3. Exercises

3.4. The Chain Rule

Tangents to Parametric Curves

Proving the Chain Rule

3.4. Exercises

Laboratory Project. Bézier Curves

Applied Project. Where Should a Pilot Start Descent?

3.5. Implicit Differentiation

3.5. Exercises

3.6. Inverse Trigonometric Functions and Their Derivatives

3.6. Exercises

3.7. Derivatives of Logarithmic Functions

Logarithmic Differentiation

The Number e as a Limit

3.7. Exercises

Discovery Project. Hyperbolic Functions

3.8. Rates of Change in the Natural and Social Sciences

Physics

Chemistry

Biology

Economics

Other Sciences

A Single Idea, Many Interpretations

3.8. Exercises

3.9. Linear Approximations and Differentials

Linear Approximations

Applications to Physics

Differentials

3.9. Exercises

Laboratory Project. Taylor Polynomials

3. Review

Focus on Problem Solving

4. Applications of Differentiation

4.1. Related Rates

4.1. Exercises

4.2. Maximum and Minimum Values

4.2. Exercises

Applied Project. The Calculus of Rainbows

4.3. Derivatives and the Shapes of Curves

The Mean Value Theorem

Increasing and Decreasing Functions

Local Extreme Values

Concavity

4.3. Exercises

4.4. Graphing with Calculus and Technology

4.4. Exercises

4.5. Indeterminate Forms and L’Hospital’s Rule

Indeterminate Products

Indeterminate Differences

Indeterminate Powers

4.5. Exercises

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

4.6. Optimization Problems

Applications to Business and Economics

4.6. Exercises

Applied Project. Tin Can Shape

4.7. Newton’s Method

4.7. Exercises

4.8. Antiderivatives

Rectilinear Motion

4.8. Exercises

4. Review

Focus on Problem Solving

5. Integrals

5.1. Areas and Distances

The Area Problem

The Distance Problem

5.1. Exercises

5.2. The Definite Integral

Evaluating Integrals

The Midpoint Rule

Properties of the Definite Integral

5.2. Exercises

5.3. Evaluating Definite Integrals

Indefinite Integrals

Applications

5.3. Exercises

Discovery Project. Area Functions

5.4. The Fundamental Theorem of Calculus

Differentiation and Integration as Inverse Processes

Proof of FTC1

5.4. Exercises

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

References

Sourcebooks

5.5. The Substitution Rule

Substitution: Indefinite Integrals

Definite Integrals

Symmetry

5.5. Exercises

5.6. Integration by Parts

Reduction Formulas

5.6. Exercises

5.7. Additional Techniques of Integration

Trigonometric Integrals

Trigonometric Substitution

Partial Fractions

5.7. Exercises

5.8. Integration Using Tables and Computer Algebra Systems

Tables of Integrals

Computer Algebra Systems

Can We Integrate All Continuous Functions?

5.8. Exercises

Discovery Project. Patterns in Integrals

5.9. Approximate Integration

Approximation Techniques

Error Bounds

Simpson’s Rule

5.9. Exercises

5.10. Improper Integrals

Type 1: Infinite Intervals

Type 2: Discontinuous Integrands

A Comparison Test for Improper Integrals

5.10. Exercises

5. Review

Focus on Problem Solving

6. Applications of Integration

6.1. More about Areas

Areas between Curves

Areas Enclosed by Parametric Curves

6.1. Exercises

6.2. Volumes

The Disk Method

The Washer Method

6.2. Exercises

Discovery Project. Rotating on a Slant

6.3. Volumes by Cylindrical Shells

Disks and Washers versus Cylindrical Shells

6.3. Exercises

6.4. Arc Length

Curve Defined in Terms of x and y

6.4. Exercises

Discovery Project. Arc Length Contest

6.5. Average Value of a Function

Mean Value Theorem for Integrals

6.5. Exercises

Applied Project. The Best Seat at the Movies

6.6. Applications to Physics and Engineering

Work

Hydrostatic Pressure and Force

Moments and Centers of Mass

6.6. Exercises

Discovery Project. Complementary Coffee Cups

6.7. Applications to Economics and Biology

Consumer Surplus

Blood Flow

Cardiac Output

6.7. Exercises

6.8. Probability

Continuous Random Variables

Average Values

Normal Distributions

6.8. Exercises

6. Review

Focus on Problem Solving

7. Differential Equations

7.1. Modeling with Differential Equations

Models of Population Growth

A Model for the Motion of a Spring

General Differential Equations

7.1. Exercises

7.2. Slope Fields and Euler’s Method

Slope Fields

Euler’s Method

7.2. Exercises

7.3. Separable Equations

Orthogonal Trajectories

Mixing Problems

7.3. Exercises

Applied Project. How Fast Does a Tank Drain?

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

7.4. Exponential Growth and Decay

Population Growth

Radioactive Decay

Newton’s Law of Cooling

Continuously Compounded Interest

7.4. Exercises

Applied Project. Calculus and Baseball

7.5. The Logistic Equation

The Logistic Model

Slope Fields

Euler’s Method

The Analytic Solution

Comparison of the Natural Growth and Logistic Models

Other Models for Population Growth

7.5. Exercises

7.6. Predator-Prey Systems

7.6. Exercises

7. Review

Focus on Problem Solving

A Preview of Calculus

The Area Problem

The Tangent Line Problem

Velocity

The Limit of a Sequence

The Sum of a Series

Summary

8. Infinite Sequences and Series

8.1. Sequences

Sequence Basics

Limit of a Sequence

Limit Laws

Sequence-Function Links

Sequence Characterizations

8.1. Exercises

Laboratory Project. Logistic Sequences

8.2. Series

Series Basics

Series Compilation

Convergent Series Behavior

Combining Series

8.2. Exercises

8.3. The Integral and Comparison Tests; Estimating Sums

Testing with an Integral

Testing by Comparing

Estimating the Sum of a Series

8.3. Exercises

8.4. Other Convergence Tests

Alternating Series

Estimating Sums

Absolute Convergence

The Ratio Test

8.4. Exercises

8.5. Power Series

Power Series Basics

Power Series Convergence

8.5. Exercises

8.6. Representations of Functions as Power Series

Using Geometric Series

Differentiation and Integration of Power Series

8.6. Exercises

8.7. Taylor and Maclaurin Series

Introduction

Functions Equal to Their Taylor Series

The Binomial Series

Series Summary

Multiplication and Division of Power Series

8.7. Exercises

Laboratory Project. An Elusive Limit

Writing Project. How Newton Discovered the Binomial Series

8.8. Applications of Taylor Polynomials

Approximating Functions by Polynomials

Application to Physics

8.8. Exercises

Applied Project. Radiation from the Stars

8. Review

Focus on Problem Solving

9. Vectors and the Geometry of Space

9.1. Three-Dimensional Coordinate Systems

Location in Space

Graphs in Space

Distance in Space

9.1. Exercises

9.2. Vectors

Definitions and Notation

Combining Vectors

Vector Components

Operations and Properties

Basis Vectors

Applications

9.2. Exercises

9.3. The Dot Product

Work and the Dot Product

The Dot Product in Component Form

Projections

9.3. Exercises

9.4. The Cross Product

Torque and the Cross Product

The Cross Product in Component Form

Triple Products

9.4. Exercises

Discovery Project. The Geometry of a Tetrahedron

9.5. Equations of Lines and Planes

Lines

Planes

Distances

9.5. Exercises

Laboratory Project. Putting 3D in Perspective

9.6. Functions and Surfaces

Functions of Two Variables

Graphs

Quadric Surfaces

9.6. Exercises

9.7. Cylindrical and Spherical Coordinates

Cylindrical Coordinates

Spherical Coordinates

9.7. Exercises

Laboratory Project. Families of Surfaces

9. Review

Focus on Problem Solving

10. Vector Functions

10.1. Vector Functions and Space Curves

Vector Functions

Limits and Continuity

Space Curves

Using Technology to Draw Space Curves

10.1. Exercises

10.2. Derivatives and Integrals of Vector Functions

Derivatives

Differentiation Rules

Integrals

10.2. Exercises

10.3. Arc Length and Curvature

Arc Length

Curvature

The Normal and Binormal Vectors

10.3. Exercises

10.4. Motion in Space: Velocity and Acceleration

Velocity, Speed, and Acceleration

Tangential and Normal Components of Acceleration

Kepler’s Laws of Planetary Motion

10.4. Exercises

Applied Project. Kepler’s Laws

10.5. Parametric Surfaces

Grid Curves

Finding Parametric Representations

Surfaces of Revolution

10.5. Exercises

10. Review

Focus on Problem Solving

11. Partial Derivatives

11.1. Functions of Several Variables

Functions of Two Variables

Visual Representations

Functions of Three or More Variables

11.1. Exercises

11.2. Limits and Continuity

Limits of Functions of Two Variables

Continuity

11.2. Exercises

11.3. Partial Derivatives

Partial Derivatives of Functions of Two Variables

Interpretations of Partial Derivatives

Functions of More Than Two Variables

Higher Derivatives

Partial Differential Equations

The Cobb–Douglas Production Function

11.3. Exercises

11.4. Tangent Planes and Linear Approximations

Tangent Planes

Linear Approximations

Differentials

Functions of Three or More Variables

Tangent Planes to Parametric Surfaces

11.4. Exercises

11.5. The Chain Rule

The Chain Rule: Case 1

The Chain Rule: Case 2

The Chain Rule: General Version

Implicit Differentiation

11.5. Exercises

11.6. Directional Derivatives and the Gradient Vector

Directional Derivatives

The Gradient Vector

Functions of Three Variables

Maximizing the Directional Derivative

Tangent Planes to Level Surfaces

Significance of the Gradient Vector

11.6. Exercises

11.7. Maximum and Minimum Values

Local Maximum and Minimum Values

Absolute Maximum and Minimum Values

11.7. Exercises

Applied Project. Designing a Dumpster

Laboratory Project. Quadratic Approximations and Critical Points

11.8. Lagrange Multipliers

Lagrange Multipliers: One Constraint

Lagrange Multipliers: Two Constraints

11.8. Exercises

Applied Project. Rocket Science

Applied Project. Hydro-Turbine Optimization

11. Review

Focus on Problem Solving

12. Multiple Integrals

12.1. Double Integrals over Rectangles

Review of the Definite Integral

Volumes and Double Integrals

The Midpoint Rule

Average Value

Properties of Double Integrals

12.1. Exercises

12.2. Iterated Integrals

12.2. Exercises

12.3. Double Integrals over General Regions

General Regions

Properties of Double Integrals

12.3. Exercises

12.4. Double Integrals in Polar Coordinates

12.4. Exercises

12.5. Applications of Double Integrals

Density and Mass

Moments and Centers of Mass

Moment of Inertia

Probability

Expected Values

12.5. Exercises

12.6. Surface Area

Area of a Parametric Surface

Surface Area of a Graph

12.6. Exercises

12.7. Triple Integrals

Triple Integrals over Rectangular Boxes

Triple Integrals over General Regions

Applications of Triple Integrals

12.7. Exercises

Discovery Project. Volumes of Hyperspheres

12.8. Triple Integrals in Cylindrical and Spherical Coordinates

Cylindrical Coordinates

Spherical Coordinates

12.8. Exercises

Applied Project. Roller Derby

Discovery Project. The Intersection of Three Cylinders

12.9. Change of Variables in Multiple Integrals

Change of Variables in Double Integrals

Triple Integrals

12.9. Exercises

12. Review

Focus on Problem Solving

13. Vector Calculus

13.1. Vector Fields

Vector Fields in ℝ 2 and ℝ 3

Gradient Fields

13.1. Exercises

13.2. Line Integrals

Line Integrals in the Plane

Line Integrals with Respect to x or y

Line Integrals in Space

Line Integrals of Vector Fields

13.2. Exercises

13.3. The Fundamental Theorem for Line Integrals

The Fundamental Theorem for Line Integrals

Independence of Path

Conservative Vector Fields and Potential Functions

Conservation of Energy

13.3. Exercises

13.4. Green’s Theorem

Green’s Theorem

Finding Areas with Green’s Theorem

Extended Versions of Green’s Theorem

13.4. Exercises

13.5. Curl and Divergence

Curl

Divergence

Vector Forms of Green’s Theorem

13.5. Exercises

13.6. Surface Integrals

Parametric Surfaces

Graphs

Oriented Surfaces

Surface Integrals of Vector Fields

13.6. Exercises

13.7. Stokes’ Theorem

Curl Vector Meaning

13.7. Exercises

13.8. The Divergence Theorem

Divergence Theorem Extended

13.8. Exercises

13.9. Summary

13. Review

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Tags: James Stewart, Stephen Kokoska, Calculus Concepts, Contexts