Thomas' Calculus, Media Upgrade, Part Two (Multivariable, Chap 11-16)

by Thomas, George B., Jr.; Weir, Maurice D.; Hass, Joel R.; Giordano, Frank R.

• ISBN13: 9780321501035
• ISBN10: 0321501039
• Edition: 11th
• Format: Paperback
• Copyright: 2007-01-05
• Publisher: Pearson

Summary

Thomas'Calculus Part Two Media Upgrade, Eleventh Edition,responds to the needs of today's readers by developing their conceptual understanding while strengthening their skills in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. This book offers a full range of exercises, a precise and conceptual presentation, and a new media package designed specifically to meet the needs of today's readers. The exercises gradually increase in difficulty, helping readers learn to generalize and apply the concepts. The refined table of contents introduces the exponential, logarithmic, and trigonometric functions in Chapter 7 of the text.Infinite Sequences and Series, Vectors and the Geometry of Space, Vector-Valued Functions and Motion in Space, Partial Derivatives, Multiple Integrals, Integration in Vector Fields.For all readers interested in Calculus.

Table of Contents

Infinite Sequences and Series

Sequences

Infinite Series

The Integral Test

Comparison Tests

The Ratio and Root Tests

Alternating Series, Absolute and Conditional Convergence

Power Series

Taylor and Maclaurin Series

Convergence of Taylor Series; Error Estimates

Applications of Power Series

Fourier Series

Vectors and the Geometry of Space

Three-Dimensional Coordinate Systems

Vectors

The Dot Product

The Cross Product

Lines and Planes in Space

Cylinders and Quadric Surfaces

Vector-Valued Functions and Motion in Space

Vector Functions

Modeling Projectile Motion

Arc Length and the Unit Tangent Vector T

Curvature and the Unit Normal Vector N

Torsion and the Unit Binormal Vector B

Planetary Motion and Satellites

Partial Derivatives

Functions of Several Variables

Limits and Continuity in Higher Dimensions

Partial Derivatives

The Chain Rule

Directional Derivatives and Gradient Vectors

Tangent Planes and Differentials

Extreme Values and Saddle Points

Lagrange Multipliers

Partial Derivatives with Constrained Variables

Taylor's Formula for Two Variables

Multiple Integrals

Double Integrals

Areas, Moments and Centers of Mass

Double Integrals in Polar Form

Triple Integrals in Rectangular Coordinates

Masses and Moments in Three Dimensions

Triple Integrals in Cylindrical and Spherical Coordinates

Substitutions in Multiple Integrals

Integration in Vector Fields

Line Integrals

Vector Fields, Work, Circulation, and Flux

Path Independence, Potential Functions, and Conservative Fields

Green's Theorem in the Plane

Surface Area and Surface Integrals

Parametrized Surfaces

Stokes' Theorem

The Divergence Theorem and a Unified Theory

Appendices

Mathematical Induction

Proofs of Limit Theorems

Commonly Occurring Limits

Theory of the Real Numbers

Complex Numbers

The Distributive Law for Vector Cross Products

Determinants and Cramer's Rule

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