INSTRUCTOR S OLUTIONS MANUAL M

Thomas Calculus 13th Edition Thomas Solutions Manual Full Download:

INSTRUCTOR'S SOLUTIONS MANUAL

MULTIVARIABLE

ELKA BLOCK

FRANK PURCELL

THOMAS' CALCULUS

THIRTEENTH EDITION

AND

THOMAS' CALCULUS

EARLY TRANSCENDENTALS

THIRTEENTH EDITION

Based on the original work by

George B. Thomas, Jr

Massachusetts Institute of Technology

as revised by

Maurice D. Weir

Naval Postgraduate School

Joel Hass

University of California, Davis

with the assistance of

Christopher Heil

Georgia Institute of Technology

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The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs.

Reproduced by Pearson from electronic files supplied by the author.

Copyright ? 2014, 2010, 2008 Pearson Education, Inc. Publishing as Pearson, 75 Arlington Street, Boston, MA 02116.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.

ISBN-13: 978-0-321-87901-1 ISBN-10: 0-321-87901-5

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TABLE OF CONTENTS

10 Infinite Sequences and Series 701

10.1 Sequences 701 10.2 Infinite Series 712 10.3 The Integral Test 720 10.4 Comparison Tests 728 10.5 Absolute Convergence; The Ratio and Root Tests 738 10.6 Alternating Series and Conditional Convergence 744 10.7 Power Series 752 10.8 Taylor and Maclaurin Series 764 10.9 Convergence of Taylor Series 769 10.10 The Binomial Series and Applications of Taylor Series 777

Practice Exercises 786 Additional and Advanced Exercises 795

11 Parametric Equations and Polar Coordinates 801

11.1 Parametrizations of Plane Curves 801 11.2 Calculus with Parametric Curves 809 11.3 Polar Coordinates 819 11.4 Graphing Polar Coordinate Equations 825 11.5 Areas and Lengths in Polar Coordinates 832 11.6 Conic Sections 838 11.7 Conics in Polar Coordinates 849

Practice Exercises 860 Additional and Advanced Exercises 871

12 Vectors and the Geometry of Space 877

12.1 Three-Dimensional Coordinate Systems 877 12.2 Vectors 881 12.3 The Dot Product 886 12.4 The Cross Product 892 12.5 Lines and Planes in Space 898 12.6 Cylinders and Quadric Surfaces 906

Practice Exercises 912 Additional and Advanced Exercises 920

13 Vector-Valued Functions and Motion in Space 927

13.1 Curves in Space and Their Tangents 927 13.2 Integrals of Vector Functions; Projectile Motion 933 13.3 Arc Length in Space 941 13.4 Curvature and Normal Vectors of a Curve 945 13.5 Tangential and Normal Components of Acceleration 952

Thomas Calculus 13th Edition Thomas Solutions Manual Full Download:

13.6 Velocity and Acceleration in Polar Coordinates 959 Practice Exercises 962 Additional and Advanced Exercises 969

14 Partial Derivatives 973

14.1 Functions of Several Variables 973 14.2 Limits and Continuity in Higher Dimensions 984 14.3 Partial Derivatives 990 14.4 The Chain Rule 999 14.5 Directional Derivatives and Gradient Vectors 1008 14.6 Tangent Planes and Differentials 1014 14.7 Extreme Values and Saddle Points 1024 14.8 Lagrange Multipliers 1040 14.9 Taylor's Formula for Two Variables 1052 14.10 Partial Derivatives with Constrained Variables 1055

Practice Exercises 1059 Additional and Advanced Exercises 1076

15 Multiple Integrals 1083

15.1 Double and Iterated Integrals over Rectangles 1083 15.2 Double Integrals over General Regions 1086 15.3 Area by Double Integration 1100 15.4 Double Integrals in Polar Form 1105 15.5 Triple Integrals in Rectangular Coordinates 1112 15.6 Moments and Centers of Mass 1118 15.7 Triple Integrals in Cylindrical and Spherical Coordinates 1124 15.8 Substitutions in Multiple Integrals 1134

Practice Exercises 1142 Additional and Advanced Exercises 1149

16 Integrals and Vector Fields 1155

16.1 Line Integrals 1155 16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 1161 16.3 Path Independence, Conservative Fields, and Potential Functions 1172 16.4 Green's Theorem in the Plane 1178 16.5 Surfaces and Area 1185 16.6 Surface Integrals 1196 16.7 Stokes' Theorem 1206 16.8 The Divergence Theorem and a Unified Theory 1213

Practice Exercises 1219 Additional and Advanced Exercises 1230

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