Multivariable Calculus Early Transcendentals 4th Edition by Jon Rogawski, Colin Adams, Robert Franzosa ISBN 9781319055905 1319055907

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ISBN 10: 1319055907
ISBN 13: 9781319055905
Author: Jon Rogawski, Colin Adams, Robert Franzosa

Multivariable Calculus Early Transcendentals 4th Edition Table of contents:

Chapter 1: Precalculus Review

1.1 Real Numbers, Functions, and Graphs

Graphing

Mathematical Models

1.1 Summary

1.1 Exercises

1.2 Linear and Quadratic Functions

1.2 Summary

1.2 Exercises

1.3 The Basic Classes of Functions

Constructing New Functions

Elementary Functions

Piecewise-Defined Functions

1.3 Summary

1.3 Exercises

1.4 Trigonometric Functions

Trigonometric Identities

1.4 Summary

1.4 Exercises

1.5 Inverse Functions

Inverse Trigonometric Functions

1.5 Summary

1.5 Exercises

1.6 Exponential and Logarithmic Functions

The Number e

Logarithms

Hyperbolic Functions

Inverse Hyperbolic Functions

Einstein’s Law of Velocity Addition

1.6 Summary

1.6 Exercises

1.7 Technology: Calculators and Computers

1.7 Summary

1.7 Exercises

Chapter Review Exercises

Chapter 2: Limits

2.1 The Limit Idea: Instantaneous Velocity and Tangent Lines

2.1 Summary

2.1 Exercises

2.2 Investigating Limits

Definition of a Limit

Graphical and Numerical Investigation

One-Sided Limits

Infinite Limits

2.2 Summary

2.2 Exercises

2.3 Basic Limit Laws

2.3 Summary

2.3 Exercises

2.4 Limits and Continuity

Examples of Discontinuities

Building Continuous Functions

Substitution: Evaluating Limits Using Continuity

2.4 Summary

2.4 Exercises

2.5 Indeterminate Forms

2.5 Summary

2.5 Exercises

2.6 The Squeeze Theorem and Trigonometric Limits

The Squeeze Theorem

2.6 Summary

2.6 Exercises

2.7 Limits at Infinity

2.7 Summary

2.7 Exercises

2.8 The Intermediate Value Theorem

2.8 Summary

2.8 Exercises

2.9 The Formal Definition of a Limit

The Size of the Gap

Proving Limit Theorems

2.9 Summary

2.9 Exercises

Chapter Review Exercises

Chapter 3: Differentiation

3.1 Definition of the Derivative

Estimating the Derivative

3.1 Summary

3.1 Exercises

3.2 The Derivative as a Function

Leibniz Notation

The Derivative and Behavior of the Graph

The Derivative of f(x) = ex

Differentiability, Continuity, and Local Linearity

3.2 Summary

3.2 Exercises

3.3 Product and Quotient Rules

3.3 Summary

3.3 Exercises

3.4 Rates of Change

Marginal Cost in Economics

Linear Motion

Motion Under the Influence of Gravity

3.4 Summary

3.4 Exercises

3.5 Higher Derivatives

3.5 Summary

3.5 Exercises

3.6 Trigonometric Functions

3.6 Summary

3.6 Exercises

3.7 The Chain Rule

3.7 Summary

3.7 Exercises

3.8 Implicit Differentiation

Derivatives of Inverse Trigonometric Functions

Finding Higher Order Derivatives Implicitly

3.8 Summary

3.8 Exercises

3.9 Derivatives of General Exponential and Logarithmic Functions

The Derivative of f(x) = bx and f(x) = logb x

Logarithmic Differentiation

Derivatives of Hyperbolic Functions

Inverse Hyperbolic Functions

3.9 Summary

3.9 Exercises

3.10 Related Rates

3.10 Summary

3.10 Exercises

Chapter Review Exercises

Chapter 4: Applications of the Derivative

4.1 Linear Approximation and Applications

Linear Approximation

Linearization

Differential Form of Linear Approximation

The Size of the Error

4.1 Summary

4.1 Exercises

4.2 Extreme Values

Local Extrema and Critical Points

Optimizing on a Closed Interval

Rolle’s Theorem

4.2 Summary

4.2 Exercises

4.3 The Mean Value Theorem and Monotonicity

Increasing / Decreasing Behavior of Functions

Testing Critical Points

4.3 Summary

4.3 Exercises

4.4 The Second Derivative and Concavity

Second Derivative Test for Critical Points

4.4 Summary

4.4 Exercises

4.5 L’Hôpital’s Rule

Comparing Growth of Functions

Proof of L’Hôpital’s Rule

4.5 Summary

4.5 Exercises

4.6 Analyzing and Sketching Graphs of Functions

4.6 Summary

4.6 Exercises

4.7 Applied Optimization

Open Versus Closed Intervals

4.7 Summary

4.7 Exercises

4.8 Newton’s Method

How Many Iterations Are Required?

Which Root Does Newton’s Method Compute?

4.8 Summary

4.8 Exercises

Chapter Review Exercises

Chapter 5: Integration

5.1 Approximating and Computing Area

Approximating Area by Rectangles

Summation Notation

Computing Area as the Limit of Approximations

5.1 Summary

5.1 Exercises

5.2 The Definite Integral

The Definite Integral and Signed Area

Properties of the Definite Integral

5.2 Summary

5.2 Exercises

5.3 The Indefinite Integral

Integrals Involvingex

Differential Equations

5.3 Summary

5.3 Exercises

5.4 The Fundamental Theorem of Calculus, Part I

5.4 Summary

5.4 Exercises

5.5 The Fundamental Theorem of Calculus, Part II

5.5 Summary

5.5 Exercises

5.6 Net Change as the Integral of a Rate of Change

The Integral of Velocity

Total Versus Marginal Cost

5.6 Summary

5.6 Exercises

5.7 The Substitution Method

Substitution Using Differentials

Change of Variables Formula for Definite Integrals

5.7 Summary

5.7 Exercises

5.8 Further Integral Formulas

Integrals Involving

5.8 Summary

5.8 Exercises

Chapter Review Exercises

Chapter 6: Applications of the Integral

6.1 Area Between Two Curves

Integration Along the y-Axis

6.1 Summary

6.1 Exercises

6.2 Setting Up Integrals: Volume, Density, Average Value

Volume

Density

Flow Rate

Average Value

6.2 Summary

6.2 Exercises

6.3 Volumes of Revolution: Disks and Washers

6.3 Summary

6.3 Exercises

6.4 Volumes of Revolution: Cylindrical Shells

6.4 Summary

6.4 Exercises

6.5 Work and Energy

6.5 Summary

6.5 Exercises

Chapter Review Exercises

Chapter 7: Techniques of Integration

7.1 Integration by Parts

7.1 Summary

7.1 Exercises

7.2 Trigonometric Integrals

7.2 Summary

7.2 Exercises

7.3 Trigonometric Substitution

7.3 Summary

7.3 Exercises

7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions

7.4 Summary

7.4 Exercises

7.5 The Method of Partial Fractions

Quadratic Factors

Using a Computer Algebra System

7.5 Summary

7.5 Exercises

7.6 Strategies for Integration

7.6 Summary

7.6 Exercises

7.7 Improper Integrals

Unbounded Functions

Comparing Integrals

7.7 Summary

7.7 Exercises

7.8 Numerical Integration

The Midpoint Rule

The Trapezoidal Rule

Error Bounds

Simpson’s Rule

7.8 Summary

7.8 Exercises

Chapter Review Exercises

Chapter 8: Further Applications Of The Integral

8.1 Probability and Integration

8.1 Summary

8.1 Exercises

8.2 Arc Length and Surface Area

Surface Area

8.2 Summary

8.2 Exercises

8.3 Fluid Pressure and Force

8.3 Summary

8.3 Exercises

8.4 Center of Mass

Laminas (Thin Plates)

Historical Perspective

8.4 Summary

8.4 Exercises

Chapter Review Exercises

Chapter 9: Introduction to Differential Equations

9.1 Solving Differential Equations

Separation of Variables

Exponential Growth and Decay

9.1 Summary

9.1 Exercises

9.2 Models Involving y′ = k(y − b)

9.2 Summary

9.2 Exercises

9.3 Graphical and Numerical Methods

9.3 Euler’s Method

9.3 Summary

9.3 Exercises

9.4 The Logistic Equation

9.4 Summary

9.4 Exercises

9.5 First-Order Linear Equations

9.5 Summary

9.5 Exercises

Chapter Review Exercises

Chapter 10: Infinite Series

10.1 Sequences

10.1 Summary

10.1 Exercises

10.2 Summing an Infinite Series

10.2 Summary

10.2 Exercises

10.3 Convergence of Series with Positive Terms

10.3 Summary

10.3 Exercises

10.4 Absolute and Conditional Convergence

10.4 Summary

10.4 Exercises

10.5 The Ratio and Root Tests and Strategies for Choosing Tests

Determining Which Test to Apply

10.5 Summary

10.5 Exercises

10.6 Power Series

Power Series Solutions of Differential Equations

10.6 Summary

10.6 Exercises

10.7 Taylor Polynomials

The Error Bound

10.7 Summary

10.7 Exercises

10.8 Taylor Series

Shortcuts to Finding Taylor Series

Binomial Series

Euler’s Formulas

10.8 Summary

10.8 Exercises

Chapter Review Exercises

Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections

11.1 Parametric Equations

Tangent Lines to Parametric Curves

Area Under a Parametric Curve

11.1 Summary

11.1 Exercises

11.2 Arc Length and Speed

11.2 Summary

11.2 Exercises

11.3 Polar Coordinates

11.3 Summary

11.3 Exercises

11.4 Area and Arc Length in Polar Coordinates

11.4 Summary

11.4 Exercises

11.5 Conic Sections

Eccentricity

Reflective Properties of Conic Sections

General Equations of Degree 2

11.5 Summary

11.5 Exercises

Chapter Review Exercises

Chapter 12: Vector Geometry

12.1 Vectors in the Plane

Vector Algebra

12.1 Summary

12.1 Exercises

12.2 Three-Dimensional Space: Surfaces, Vectors, and Curves

Surfaces

Vectors in 3-Space

Curves and Lines

12.2 Summary

12.2 Exercises

12.3 Dot Product and the Angle Between two Vectors

12.3 Summary

12.3 Exercises

12.4 The Cross Product

Cross Products, Area, and Volume

Proofs of Cross-Product Properties

12.4 Summary

12.4 Exercises

12.5 Planes in 3-Space

12.5 Summary

12.5 Exercises

12.6 A Survey of Quadric Surfaces

12.6 Summary

12.6 Exercises

12.7 Cylindrical and Spherical Coordinates

Cylindrical Coordinates

Spherical Coordinates

12.7 Summary

12.7 Exercises

Chapter Review Exercises

Chapter 13: Calculus Of Vector-Valued Functions

13.1 Vector-Valued Functions

13.1 Summary

13.1 Exercises

13.2 Calculus of Vector-Valued Functions

The Derivative as a Tangent Vector

Vector-Valued Integration

13.2 Summary

13.2 Exercises

13.3 Arc Length and Speed

Arc Length Parametrization

13.3 Summary

13.3 Exercises

13.4 Curvature

The Normal Vector

The Frenet Frame

Plane and Circle

13.4 Summary

13.4 Exercises

13.5 Motion in 3-Space

Understanding the Acceleration Vector

13.5 Summary

13.5 Exercises

13.6 Planetary Motion According to Kepler and Newton

Kepler’s Second Law

Proof of the Law of Ellipses

13.6 Summary

13.6 Exercises

Chapter Review Exercises

Chapter 14: Differentiation in Several Variables

14.1 Functions of Two or More Variables

Graphing Functions of Two Variables

Traces

Level Curves and Contour Maps

More Than Two Variables

14.1 Summary

14.1 Exercises

14.2 Limits and Continuity in Several Variables

14.2 Summary

14.2 Exercises

14.3 Partial Derivatives

Higher Order Partial Derivatives

14.3 Summary

14.3 Exercises

14.4 Differentiability, Tangent Planes, and Linear Approximation

Assumptions Matter

14.4 Summary

14.4 Exercises

14.5 The Gradient and Directional Derivatives

Introduction to the Chain Rule for Paths

Directional Derivatives

Properties of the Gradient

14.5 Summary

14.5 Exercises

14.6 Multivariable Calculus Chain Rules

Implicit Differentiation

14.6 Summary

14.6 Exercises

14.7 Optimization in Several Variables

Global Extrema

14.7 Summary

14.7 Exercises

14.8 Lagrange Multipliers: Optimizing with a Constraint

14.8 Summary

14.8 Exercises

Chapter Review Exercises

Chapter 15: Multiple Integration

15.1 Integration in Two Variables

Iterated Integrals

15.1 Summary

15.1 Exercises

15.2 Double Integrals over More General Regions

Regions Between Two Graphs

Average Value

Decomposing the Domain into Smaller Domains

15.2 Summary

15.2 Exercises

15.3 Triple Integrals

The Volume of the Sphere in Higher Dimensions

15.3 Summary

15.3 Exercises

15.4 Integration in Polar, Cylindrical, and Spherical Coordinates

Double Integrals in Polar Coordinates

Triple Integrals in Cylindrical Coordinates

Triple Integrals in Spherical Coordinates

15.4 Summary

15.4 Exercises

15.5 Applications of Multiple Integrals

Probability Theory

15.5 Summary

15.5 Exercises

15.6 Change of Variables

Maps from R2 to R2

How Area Changes Under a Mapping: The Jacobian Determinant

The Change of Variables Formula

Change of Variables in Three Variables

15.6 Summary

15.6 Exercises

Chapter Review Exercises

Chapter 16: Line and Surface Integrals

16.1 Vector Fields

Operations on Vector Fields

Conservative Vector Fields

16.1 Summary

16.1 Exercises

16.2 Line Integrals

Scalar Line Integrals

Applications of the Scalar Line Integral

Vector Line Integrals

Applications of the Vector Line Integral

16.2 Summary

16.2 Exercises

16.3 Conservative Vector Fields

Conservative Fields in Physics

Finding Potential Functions

The Vortex Field

16.3 Summary

16.3 Exercises

16.4 Parametrized Surfaces and Surface Integrals

Grid Curves, Normal Vectors, and the Tangent Plane

Surface Area

Surface Integral

Gravitational Potential of a Sphere

16.4 Summary

16.4 Exercises

16.5 Surface Integrals of Vector Fields

Fluid Flux

Electric and Magnetic Fields

Types of Integrals

16.5 Summary

16.5 Exercises

Chapter Review Exercises

Chapter 17: Fundamental Theorems of Vector Analysis

17.1 Green’s Theorem

Area via Green’s Theorem

The Circulation Form of Green’s Theorem

Additivity of Circulation

More General Form of Green’s Theorem

Flux Form of Green’s Theorem

17.1 Summary

17.1 Exercises

17.2 Stokes’ Theorem

17.2 Summary

17.2 Exercises

17.3 Divergence Theorem

Applications to Electrostatics

17.3 Summary

17.3 Exercises

Chapter Review Exercises

Appendices

A The Language of Mathematics

B Properties of Real Numbers

C Induction and The Binomial Theorem

D Additional Proofs

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Jon Rogawski,Colin Adams,Robert Franzosa,Multivariable Calculus,Transcendentals