# Calculus: Late Transcendentals Multivariable

## Fourth EditionJon Rogawski; Colin Adams; Robert Franzosa

©2019ISBN:9781319281953

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ISBN:9781319055783

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ISBN:9781319311070

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We see teaching mathematics as a form of story-telling, both when we present in a classroom and when we write materials for exploration and learning. The goal is to explain to you in a captivating manner, at the right pace, and in as clear a way as possible, how mathematics works and what it can do for you. We find mathematics to be intriguing and immensely beautiful. We want you to feel that way, too.

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Learn More## Table of Contents

**Chapter 11: Infinite Series**

11.1 Sequences

11.2 Summing an Infinite Series

11.3 Convergence of Series with Positive Terms

11.4 Absolute and Conditional Convergence

11.5 The Ratio and Root Tests and Strategies for Choosing Tests

11.6 Power Series

11.7 Taylor Polynomials

11.8 Taylor Series

Chapter Review Exercises

Chapter 12: Parametric Equations, Polar Coordinates, and Conic Sections

12.1 Parametric Equations

12.2 Arc Length and Speed

12.3 Polar Coordinates

12.4 Area and Arc Length in Polar Coordinates

12.5 Conic Sections

Chapter Review Exercises

**Chapter 13: Vector Geometry**

13.1 Vectors in the Plane

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

13.3 Dot Product and the Angle Between Two Vectors

13.4 The Cross Product

13.5 Planes in 3-Space

13.6 A Survey of Quadric Surfaces

13.7 Cylindrical and Spherical Coordinates

Chapter Review Exercises

**Chapter 14: Calculus of Vector-Valued Functions**

14.1 Vector-Valued Functions

14.2 Calculus of Vector-Valued Functions

14.3 Arc Length and Speed

14.4 Curvature

14.5 Motion in 3-Space

14.6 Planetary Motion According to Kepler and Newton

Chapter Review Exercises

**Chapter 15: Differentiation in Several Variables**

15.1 Functions of Two or More Variables

15.2 Limits and Continuity in Several Variables

15.3 Partial Derivatives

15.4 Differentiability, Tangent Planes, and Linear Approximation

15.5 The Gradient and Directional Derivatives

15.6 Multivariable Calculus Chain Rules

15.7 Optimization in Several Variables

15.8 Lagrange Multipliers: Optimizing with a Constraint

Chapter Review Exercises

**Chapter 16: Multiple Integration**

16.1 Integration in Two Variables

16.2 Double Integrals over More General Regions

16.3 Triple Integrals

16.4 Integration in Polar, Cylindrical, and Spherical Coordinates

16.5 Applications of Multiple Integrals

16.6 Change of Variables

Chapter Review Exercises

**Chapter 17: Line and Surface Integrals**

17.1 Vector Fields

17.2 Line Integrals

17.3 Conservative Vector Fields

17.4 Parametrized Surfaces and Surface Integrals

17.5 Surface Integrals of Vector Fields

Chapter Review Exercises

**Chapter 18: Fundamental Theorems of Vector Analysis**

18.1 Green’s Theorem

18.2 Stokes’ Theorem

18.3 Divergence Theorem

Chapter Review Exercises

**Appendices **A. The Language of Mathematics

B. Properties of Real Numbers

C. Induction and the Binomial Theorem

D. Additional Proofs

ANSWERS TO ODD-NUMBERED EXERCISES

REFERENCES

INDEX

Additional content can be accessed online at www.macmillanlearning.com/calculuset4e:

**Additional Proofs:**L’Hôpital’s Rule

Error Bounds for Numerical

Integration

Comparison Test for Improper

Integrals

**Additional Content:**Second-Order Differential

Equations

Complex Numbers