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Elementary Differential Equations and Boundary Value Problems - Boyce W.E.

Boyce W.E. Elementary Differential Equations and Boundary Value Problems - John Wiley & Sons, 2001. - 1310 p.
Download (direct link): elementarydifferentialequations2001.pdf
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singular, 656-663 continuous spectrum, 660 Successive approximations, method of, 106, 401
Index
745
Superposition principle, 140,
344, 368, 600, 663 Sylvester, James, 348 Systems: of algebraic equations, 357-360, 542-543 of differential equations, 18 autonomous, 471-472 existence and uniqueness theorem, 343 initial conditions, 342 linear, 343 nonlinear, 343 numerical solution of, 455-458 reduction to, 341-342 solution of, 342 of linear first order equations, 368-418 definition of, 343 diagonalization, 398-400, 411-413 Euler, 382, 391, 408 existence and uniqueness theorem, 343 fundamental matrix, 393-401, 405-406 fundamental set of solutions, 370
general solution of, 370 homogeneous, 343,
368-372 homogeneous with constant coefficients, 373-410 complex eigenvalues, 384-393, 464-467 real and unequal eigenvalues, 373-383, 460-462
repeated eigenvalues, 401-410, 462-464 nonhomogeneous, 343, 411-418 superposition of solutions, 368
undetermined coefficients,
413-414 variation of parameters,
414-416
T
Tangent line method, see Euler method Tautochrone, 336-337 Taylor, Brook, 234 Taylor series, 154, 234
for functions of two variables,
434
Telegraph equation, 619, 627, 653 Thermal diffusivity, 574, 616 Threshold models, 81-84 Trajectories, 342, 373, 460, 467-468, 475-477 almost linear systems,
483-484 linear systems, 460-467 Transfer function, 335 Transient solution, 203, 583 Translation of function, 311 Transpose of matrix, 348 Triangular wave, 551-552, 553-555, 571 Truncation error, global, 424,
426, 445-447 local, 424
U
Undetermined coefficients, 171-178, 222-226 for systems of equations,
413-414 Uniqueness theorems, see
Existence and uniqueness theorems Unit step function, 310 Laplace transform of, 311
V
Van der Pol equation, 478, 526-530 Variation of parameters, 25, 39, 179-185, 226-230
for systems of equations,
414-416 Vector space, 151 Vectors, 151, 349 inner product, 351 length, 351
linear dependence and independence of,
360-362 magnitude, 351 multiplication of, 351 orthogonality, 351 Verhulst, Pierre F., 76 Verhulst equation, 76 Vibrations:
of elastic bar, 628-629 of elastic membrane, 604, 664-666 of elastic string, 591-604, 617-619 of spring-mass system,
186-195,200-207,306,
392
two degrees of freedom, 220,
345, 393 Volterra, Vito, 504 Volterra integral equation, 336
W
Wave equation, 17, 591, 617-619 in polar coordinates, 664, 667 solution of, 602 see also Elastic string, derivation of wave equation Wavelength, of vibrating string, 594
Wave velocity, 591, 601, 619 Wronski, Jozef, 141 Wronskian, 141, 211 Abelís identity for, 149, 213 for systems of equations, 369 Abelís identity, 370
Y
Yield, maximum sustainable, 87
Student Solutions Manual
Charles W. Haines
Rochester Institute of Technology
to accompany
Elementary Differential Equations, 7e and
Elementary Differential Equations and Boundary Value Problems, 7e
William E. Boyce Richard C. DiPrima
Rensselaer Polytechnic Institute
John Wiley & Sons, Inc.
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Copyright © 2001 John Wiley & Sons, Inc. 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, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (508) 750-8400, fax (508) 750-4470. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ@WILEY.COM.
ISBN 0-471-39114-X
Printed in the United States of America
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PREFACE
This supplement has been prepared for use in conjunction with the seventh editions of ELEMENTARY DIFFERNTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS and ELEMENTARY DIFFERENTIAL EQUATIONS, both by W.E. Boyce and R.C. DiPrima. The supplement contains a sampling of the problems from each section of the text. In most cases the complete details in determining the solutions are given while in the remainder of the problems helpful hints are provided. The problems chosen in each section represent, wherever possible, the variety of applications and types of examples that are covered in the written material of the text, thereby providing the student a complete set of examples from which to learn.
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