An Instructor’s Solutions Manual to Accompany
ADVANCED ENGINEERING MATHEMATICS,
8TH EDITION
PETER V. O’NEIL
,© 2018, 2012 Cengage Learning ISBN: 978-1-305-63515-9
WCN: 01-100-101 Cengage Learning
20 Channel Center Street
ALL RIGHTS RESERVED. No part of this work covered by the Boston, MA 02210
copyright herein may be reproduced, transmitted, stored, or USA
used in any form or by any means graphic, electronic, or
mechanical, including but not limited to photocopying, Cengage Learning is a leading provider of customized
recording, scanning, digitizing, taping, Web distribution, learning solutions with office locations around the globe,
information networks, or information storage and retrieval including Singapore, the United Kingdom, Australia,
systems, except as permitted under Section 107 or 108 of the Mexico, Brazil, and Japan. Locate your local office at:
1976 United States Copyright Act, without the prior written international.cengage.com/region.
permission of the publisher except as may be permitted by the
license terms below. Cengage Learning products are represented in
Canada by Nelson Education, Ltd.
For your course and learning solutions, visit
For product information and technology assistance, contact us at
www.cengage.com/engineering.
Cengage Learning Academic Resource Center,
1-800-423-0563.
Purchase any of our products at your local college
For permission to use material from this text or product, submit
store or at our preferred online store
all requests online at www.cengage.com/permissions. www.cengagebrain.com.
Further permissions questions can be emailed to
.
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: electronically must be through a password-protected site, with all
copy and download functionality disabled, and accessible solely by
Cengage Learning has provided you with this product (the your students who have purchased the associated textbook for the
“Supplement”) for your review and, to the extent that you adopt Course. You may not sell, license, auction, or otherwise redistribute
the associated textbook for use in connection with your course the Supplement in any form. We ask that you take reasonable
(the “Course”), you and your students who purchase the steps to protect the Supplement from unauthorized use,
textbook may use the Supplement as described below. reproduction, or distribution. Your use of the Supplement indicates
Cengage Learning has established these use limitations in your acceptance of the conditions set forth in this Agreement. If you
response to concerns raised by authors, professors, and other do not accept these conditions, you must return the Supplement
users regarding the pedagogical problems stemming from unused within 30 days of receipt.
unlimited distribution of Supplements.
All rights (including without limitation, copyrights, patents, and trade
Cengage Learning hereby grants you a nontransferable license secrets) in the Supplement are and will remain the sole and
to use the Supplement in connection with the Course, subject to exclusive property of Cengage Learning and/or its licensors. The
the following conditions. The Supplement is for your personal, Supplement is furnished by Cengage Learning on an “as is” basis
noncommercial use only and may not be reproduced, posted without any warranties, express or implied. This Agreement will be
electronically or distributed, except that portions of the governed by and construed pursuant to the laws of the State of
Supplement may be provided to your students IN PRINT FORM New York, without regard to such State’s conflict of law rules.
ONLY in connection with your instruction of the Course, so long
as such students are advised that they may not copy or Thank you for your assistance in helping to safeguard the integrity
distribute any portion of the Supplement to any third party. Test of the content contained in this Supplement. We trust you find the
banks and other testing materials may be made available in the Supplement a useful teaching tool.
classroom and collected at the end of each class session, or
posted electronically as described herein. Any material posted
,INSTRUCTOR'S SOLUTIONS MANUAL
TO ACCOMPANY
ADVANCED ENGINEERNG
MATHEMATICS
8th EDITION
PETER V. O’NEIL
UNIVERSITY OF ALABAMA AT BIRMINGHAM
, Contents
1 First-Order Differential Equations 1
1.1 Terminology and Separable Equations 1
1.2 The Linear First-Order Equation 12
1.3 Exact Equations 19
1.4 Homogeneous, Bernoulli and Riccati Equations 28
2 Second-Order Differential Equations 37
2.1 The Linear Second-Order Equation 37
2.2 The Constant Coefficient Homogeneous Equation 41
2.3 Particular Solutions of the Nonhomogeneous Equation 46
2.4 The Euler Differential Equation 53
2.5 Series Solutions 58
3 The Laplace Transform 69
3.1 Definition and Notation 69
3.2 Solution of Initial Value Problems 72
3.3 The Heaviside Function and Shifting Theorems 77
3.4 Convolution 86
3.5 Impulses and the Dirac Delta Function 92
3.6 Systems of Linear Differential Equations 93
iii
ADVANCED ENGINEERING MATHEMATICS,
8TH EDITION
PETER V. O’NEIL
,© 2018, 2012 Cengage Learning ISBN: 978-1-305-63515-9
WCN: 01-100-101 Cengage Learning
20 Channel Center Street
ALL RIGHTS RESERVED. No part of this work covered by the Boston, MA 02210
copyright herein may be reproduced, transmitted, stored, or USA
used in any form or by any means graphic, electronic, or
mechanical, including but not limited to photocopying, Cengage Learning is a leading provider of customized
recording, scanning, digitizing, taping, Web distribution, learning solutions with office locations around the globe,
information networks, or information storage and retrieval including Singapore, the United Kingdom, Australia,
systems, except as permitted under Section 107 or 108 of the Mexico, Brazil, and Japan. Locate your local office at:
1976 United States Copyright Act, without the prior written international.cengage.com/region.
permission of the publisher except as may be permitted by the
license terms below. Cengage Learning products are represented in
Canada by Nelson Education, Ltd.
For your course and learning solutions, visit
For product information and technology assistance, contact us at
www.cengage.com/engineering.
Cengage Learning Academic Resource Center,
1-800-423-0563.
Purchase any of our products at your local college
For permission to use material from this text or product, submit
store or at our preferred online store
all requests online at www.cengage.com/permissions. www.cengagebrain.com.
Further permissions questions can be emailed to
.
NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED,
OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN.
READ IMPORTANT LICENSE INFORMATION
Dear Professor or Other Supplement Recipient: electronically must be through a password-protected site, with all
copy and download functionality disabled, and accessible solely by
Cengage Learning has provided you with this product (the your students who have purchased the associated textbook for the
“Supplement”) for your review and, to the extent that you adopt Course. You may not sell, license, auction, or otherwise redistribute
the associated textbook for use in connection with your course the Supplement in any form. We ask that you take reasonable
(the “Course”), you and your students who purchase the steps to protect the Supplement from unauthorized use,
textbook may use the Supplement as described below. reproduction, or distribution. Your use of the Supplement indicates
Cengage Learning has established these use limitations in your acceptance of the conditions set forth in this Agreement. If you
response to concerns raised by authors, professors, and other do not accept these conditions, you must return the Supplement
users regarding the pedagogical problems stemming from unused within 30 days of receipt.
unlimited distribution of Supplements.
All rights (including without limitation, copyrights, patents, and trade
Cengage Learning hereby grants you a nontransferable license secrets) in the Supplement are and will remain the sole and
to use the Supplement in connection with the Course, subject to exclusive property of Cengage Learning and/or its licensors. The
the following conditions. The Supplement is for your personal, Supplement is furnished by Cengage Learning on an “as is” basis
noncommercial use only and may not be reproduced, posted without any warranties, express or implied. This Agreement will be
electronically or distributed, except that portions of the governed by and construed pursuant to the laws of the State of
Supplement may be provided to your students IN PRINT FORM New York, without regard to such State’s conflict of law rules.
ONLY in connection with your instruction of the Course, so long
as such students are advised that they may not copy or Thank you for your assistance in helping to safeguard the integrity
distribute any portion of the Supplement to any third party. Test of the content contained in this Supplement. We trust you find the
banks and other testing materials may be made available in the Supplement a useful teaching tool.
classroom and collected at the end of each class session, or
posted electronically as described herein. Any material posted
,INSTRUCTOR'S SOLUTIONS MANUAL
TO ACCOMPANY
ADVANCED ENGINEERNG
MATHEMATICS
8th EDITION
PETER V. O’NEIL
UNIVERSITY OF ALABAMA AT BIRMINGHAM
, Contents
1 First-Order Differential Equations 1
1.1 Terminology and Separable Equations 1
1.2 The Linear First-Order Equation 12
1.3 Exact Equations 19
1.4 Homogeneous, Bernoulli and Riccati Equations 28
2 Second-Order Differential Equations 37
2.1 The Linear Second-Order Equation 37
2.2 The Constant Coefficient Homogeneous Equation 41
2.3 Particular Solutions of the Nonhomogeneous Equation 46
2.4 The Euler Differential Equation 53
2.5 Series Solutions 58
3 The Laplace Transform 69
3.1 Definition and Notation 69
3.2 Solution of Initial Value Problems 72
3.3 The Heaviside Function and Shifting Theorems 77
3.4 Convolution 86
3.5 Impulses and the Dirac Delta Function 92
3.6 Systems of Linear Differential Equations 93
iii
