Instructor Solutions Manual Multivariable For Thomas Calculus 12th Edition revised by Weir and Hass

Instructor Solutions Manual Multivariable For Thomas Calculus 12th Edition revised by Weir and Hass

TABLE OF CONTENTS

10 Infinite Sequences and Series   569

10.1 Sequences   569

10.2 Infinite Series   577

10.3 The Integral Test   583

10.4 Comparison Tests   590

10.5 The Ratio and Root Tests   597

10.6 Alternating Series, Absolute and Conditional Convergence   602

10.7 Power Series   608

10.8 Taylor and Maclaurin Series   617

10.9 Convergence of Taylor Series   621

10.10 The Binomial Series and Applications of Taylor Series   627

Practice Exercises   634

Additional and Advanced Exercises   642

11 Parametric Equations and Polar Coordinates 647

11.1 Parametrizations of Plane Curves   647

11.2 Calculus with Parametric Curves   654

11.3 Polar Coordinates   662

11.4 Graphing in Polar Coordinates   667

11.5 Areas and Lengths in Polar Coordinates   674

11.6 Conic Sections   679

11.7 Conics in Polar Coordinates   689

Practice Exercises   699

Additional and Advanced Exercises   709

12 Vectors and the Geometry of Space   715

12.1 Three-Dimensional Coordinate Systems    715

12.2 Vectors   718

12.3 The Dot Product   723

12.4 The Cross Product   728

12.5 Lines and Planes in Space   734

12.6 Cylinders and Quadric Surfaces   741

Practice Exercises   746

Additional Exercises   754

13 Vector-Valued Functions and Motion in Space   759

13.1 Curves in Space and Their Tangents   759

13.2 Integrals of Vector Functions; Projectile Motion   764

13.3 Arc Length in Space   770

13.4 Curvature and Normal Vectors of a Curve   773

13.5 Tangential and Normal Components of Acceleration   778

13.6 Velocity and Acceleration in Polar Coordinates   784

Practice Exercises   785

Additional Exercises   791

14 Partial Derivatives   795

14.1 Functions of Several Variables   795

14.2 Limits and Continuity in Higher Dimensions   804

14.3 Partial Derivatives   810

14.4 The Chain Rule   816

14.5 Directional Derivatives and Gradient Vectors   824

14.6 Tangent Planes and Differentials   829

14.7 Extreme Values and Saddle Points   836

14.8 Lagrange Multipliers   849

14.9 Taylor's Formula for Two Variables   857

14.10 Partial Derivatives with Constrained Variables   859

Practice Exercises   862

Additional Exercises   876

15 Multiple Integrals   881

15.1 Double and Iterated Integrals over Rectangles   881

15.2 Double Integrals over General Regions   882

15.3 Area by Double Integration   896

15.4 Double Integrals in Polar Form   900

15.5 Triple Integrals in Rectangular Coordinates   904

15.6 Moments and  Centers of Mass   909

15.7 Triple Integrals in Cylindrical and Spherical Coordinates   914

15.8 Substitutions in Multiple Integrals   922

Practice Exercises   927

Additional Exercises   933

16 Integration in Vector Fields   939

16.1 Line Integrals   939

16.2 Vector Fields and Line Integrals; Work, Circulation, and Flux   944

16.3 Path Independence, Potential Functions, and Conservative Fields   952

16.4 Green's Theorem in the Plane   957

16.5 Surfaces and  Area   963

16.6 Surface Integrals   972

16.7 Stokes's Theorem   980

16.8 The Divergence Theorem and a Unified Theory   984

Practice Exercises   989

Additional Exercises   997