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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.
(Practice Exercises Additional Exercises and Questions to Guide Your Review appear at the end of each chapter.)
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
''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
(Practice Exercises Additional Exercises and Questions to Guide Your Review appear at the end of each chapter.)
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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