Calculus: Late Transcendentals Multivariable
by Jon Rogawski, Colin Adams, Robert Franzosa
4th Edition
Publisher: W.H. Freeman & Company
Book Details
| Print ISBN | 9781319055783 |
| eText ISBN | 9781319281953 |
| Publisher | W.H. Freeman & Company |
| Publishing Year | 2019 |
| Edition | 4th Edition |
| Language | English |
Calculus: Late Transcendentals Multivariable, 4th Edition, is a textbook designed to support students through their study of calculus. The presentation coordinates clear exposition, visual figures, and structured layout to encourage engagement with the subject. The authors approach mathematical instruction as a form of storytelling intended to explain concepts clearly at a measured pace.
Coverage focuses on three main areas: infinite series, multivariable differentiation, and multiple integration. The chapters guide students from the behavior of series through multivariable differential techniques and integral calculus across higher dimensions.
To support student understanding and reasoning, the volume incorporates highlighted Conceptual Insight sections alongside practice exercises that reinforce core problem-solving techniques.
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
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