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

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  • Edition: 11th
  • Format: Paperback
  • Copyright: 2007-01-05
  • Publisher: Pearson
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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
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
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
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
Table of Contents provided by Publisher. All Rights Reserved.

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