imfm.qxd 9/15/05 12:06 PM Page i
Solution manual for
Advanced Engineering Mathematics, International Adaptation
Author: Erwin Kreyszig
11th Edition
,imfm.qxd 9/15/05 12:06 PM Page ii
PREFACE
General Character And Purpose Of The Instructor’s Manual
This Manual Contains:
(I) Detailed Solutions Of The Even-Numbered Problems.
(II) General Comments On The Purpose Of Each Section And Its Classroom Use,
With Mathematical And Didactic Information On Teaching Practice And Pedagogical
Aspects. Some Of The Comments Refer To Whole Chapters (And Are Indicated
Accordingly).
Changes In Problem Sets
The Major Changes In This Edition Of The Text Are Listed And Explained In The
Preface Of The Book. They Include Global Improvements Produced By Updating And
Streamlining Chapters As Well As Many Local Improvements Aimed At Simplification
Of The Whole Text. Speedy Orientation Is Helped By Chapter Summaries At The End Of
Each Chapter, As In The Last Edition, And By The Subdivision Of Sections Into
Subsections With Unnumbered Headings. Resulting Effects Of These Changes On The
Problem Sets Are As Follows.
The Problems Have Been Changed. The Large Total Number Of More Than 4000 Problems
Has Been Retained, Increasing Their Overall Usefulness By The Following:
• Placing More Emphasis On Modeling And Conceptual Thinking And Less
Emphasis On Technicalities, To Parallel Recent And Ongoing Developments In
Calculus.
• Balancing By Extending Problem Sets That Seemed Too Short And Contracting
Others That Were Too Long, Adjusting The Length To The Relative Importance
Of The Material In A Section, So That Important Issues Are Reflected Sufficiently
Well Not Only In The Text But Also In The Problems. Thus, The Danger Of
Overemphasizing Minor Techniques And Ideas Is Avoided As Much As Possible.
• Simplification By Omitting A Small Number Of Very Difficult Problems That
Appeared In The Previous Edition, Retaining The Wide Spectrum Ranging From
Simple Routine Problems To More Sophisticated Engineering Applications, And
Taking Into Account The “Algorithmic Thinking” That Is Developing Along With
Computers.
• Amalgamation Of Text, Examples, And Problems By Including The Large Number
Of More Than 600 Worked-Out Examples In The Text And By Providing
Problems Closely Related To Those Examples.
• Addition Of TEAM PROJECTS, CAS PROJECTS, And WRITING PROJECTS,
Whose Role Is Explained In The Preface Of The Book.
• Addition Of CAS EXPERIMENTS, That Is, The Use Of The Computer In
“Experimental Mathematics” For Experimentation, Discovery, And Research,
Which Often Produces Unexpected Results For Open-Ended Problems, Deeper
Insights, And Relations Among Practical Problems.
These Changes In The Problem Sets Will Help Students In Solving Problems As Well
As In Gaining A Better Understanding Of Practical Aspects In The Text. It Will Also
Enable Instructors To Explain Ideas And Methods In Terms Of Examples Supplementing
And Illustrating Theoretical Discussions—Or Even Replacing Some Of Them If So
Desired.
,imfm.qxd 9/15/05 12:06 PM Page iii
Vi Instructor’s Manual
“Show The Details Of Your Work.”
This Request Repeatedly Stated In The Book Applies To All The Problem Sets. Of
Course, It Is Intended To Prevent The Student From Simply Producing Answers By A
CAS Instead Of Trying To Understand The Underlying Mathematics.
Orientation On Computers
Comments On Computer Use Are Included In The Preface Of The Book. Software
Systems Are Listed In The Book At The Beginning Of Chap. 19 On Numeric Analysis
And At The Beginning Of Chap. 24 On Probability Theory.
ERWIN KREYSZIG
, im01.qxd 9/21/05 10:17 AM Page 1
Part A. ORDINARY DIFFERENTIAL
EQUATIONS (Odes)
CHAPTER 1 First-Order Odes
Major Changes
There Is More Material On Modeling In The Text As Well As In The
Problem Set. Some Additions On Population Dynamics Appear In Sec.
1.5.
Electric Circuits Are Shifted To Chap. 2, Where Second-Order Odes Will Be
Available. This Avoids Repetitions That Are Unnecessary And Practically Irrelevant.
Team Projects, CAS Projects, And CAS Experiments Are Included In Most Problem Sets.
SECTION 1.1. Basic Concepts. Modeling, Page 2
Purpose. To Give The Students A First Impression What An ODE Is And What We Mean By
Solving It.
Background Material. For The Whole Chapter We Need Integration Formulas
And Techniques, Which The Student Should Review.
General Comments
This Section Should Be Covered Relatively Rapidly To Get Quickly To The Actual
Solution Methods In The Next Sections.
Equations (1)–(3) Are Just Examples, Not For Solution, But The Student Will
See That Solutions Of (1) And (2) Can Be Found By Calculus, And A Solution Y = Ex Of
(3) By Inspection.
Problem Set 1.1 Will Help The Student With The Tasks Of
Solving Y' = Ƒ(X) By Calculus
Finding Particular Solutions From Given General Solutions
Setting Up An ODE For A Given Function As Solution
Gaining A First Experience In Modeling, By Doing One Or Two
Problems Gaining A First Impression Of The Importance Of Odes
Without Wasting Time On Matters That Can Be Done Much Faster, Once Systematic
Methods Are Available.
Comment On “General Solution” And “Singular Solution”
Usage Of The Term “General Solution” Is Not Uniform In The Literature. Some Books
Use The Term To Mean A Solution That Includes All Solutions, That Is, Both The
Particular And The Singular Ones. We Do Not Adopt This Definition For Two Reasons.
First, It Is Frequently Quite Difficult To Prove That A Formula Includes All Solutions;
Hence, This Definition Of A General Solution Is Rather Useless In Practice. Second,
Linear Differential Equations (Satisfying Rather General Conditions On The Coefficients)
Have No Singular Solutions (As Mentioned In The Text), So That For These Equations A
General Solution As Defined Does Include All Solutions. For The Latter Reason, Some
Books Use The Term “General Solution” For Linear Equations Only; But This Seems
Very Unfortunate.
1
Solution manual for
Advanced Engineering Mathematics, International Adaptation
Author: Erwin Kreyszig
11th Edition
,imfm.qxd 9/15/05 12:06 PM Page ii
PREFACE
General Character And Purpose Of The Instructor’s Manual
This Manual Contains:
(I) Detailed Solutions Of The Even-Numbered Problems.
(II) General Comments On The Purpose Of Each Section And Its Classroom Use,
With Mathematical And Didactic Information On Teaching Practice And Pedagogical
Aspects. Some Of The Comments Refer To Whole Chapters (And Are Indicated
Accordingly).
Changes In Problem Sets
The Major Changes In This Edition Of The Text Are Listed And Explained In The
Preface Of The Book. They Include Global Improvements Produced By Updating And
Streamlining Chapters As Well As Many Local Improvements Aimed At Simplification
Of The Whole Text. Speedy Orientation Is Helped By Chapter Summaries At The End Of
Each Chapter, As In The Last Edition, And By The Subdivision Of Sections Into
Subsections With Unnumbered Headings. Resulting Effects Of These Changes On The
Problem Sets Are As Follows.
The Problems Have Been Changed. The Large Total Number Of More Than 4000 Problems
Has Been Retained, Increasing Their Overall Usefulness By The Following:
• Placing More Emphasis On Modeling And Conceptual Thinking And Less
Emphasis On Technicalities, To Parallel Recent And Ongoing Developments In
Calculus.
• Balancing By Extending Problem Sets That Seemed Too Short And Contracting
Others That Were Too Long, Adjusting The Length To The Relative Importance
Of The Material In A Section, So That Important Issues Are Reflected Sufficiently
Well Not Only In The Text But Also In The Problems. Thus, The Danger Of
Overemphasizing Minor Techniques And Ideas Is Avoided As Much As Possible.
• Simplification By Omitting A Small Number Of Very Difficult Problems That
Appeared In The Previous Edition, Retaining The Wide Spectrum Ranging From
Simple Routine Problems To More Sophisticated Engineering Applications, And
Taking Into Account The “Algorithmic Thinking” That Is Developing Along With
Computers.
• Amalgamation Of Text, Examples, And Problems By Including The Large Number
Of More Than 600 Worked-Out Examples In The Text And By Providing
Problems Closely Related To Those Examples.
• Addition Of TEAM PROJECTS, CAS PROJECTS, And WRITING PROJECTS,
Whose Role Is Explained In The Preface Of The Book.
• Addition Of CAS EXPERIMENTS, That Is, The Use Of The Computer In
“Experimental Mathematics” For Experimentation, Discovery, And Research,
Which Often Produces Unexpected Results For Open-Ended Problems, Deeper
Insights, And Relations Among Practical Problems.
These Changes In The Problem Sets Will Help Students In Solving Problems As Well
As In Gaining A Better Understanding Of Practical Aspects In The Text. It Will Also
Enable Instructors To Explain Ideas And Methods In Terms Of Examples Supplementing
And Illustrating Theoretical Discussions—Or Even Replacing Some Of Them If So
Desired.
,imfm.qxd 9/15/05 12:06 PM Page iii
Vi Instructor’s Manual
“Show The Details Of Your Work.”
This Request Repeatedly Stated In The Book Applies To All The Problem Sets. Of
Course, It Is Intended To Prevent The Student From Simply Producing Answers By A
CAS Instead Of Trying To Understand The Underlying Mathematics.
Orientation On Computers
Comments On Computer Use Are Included In The Preface Of The Book. Software
Systems Are Listed In The Book At The Beginning Of Chap. 19 On Numeric Analysis
And At The Beginning Of Chap. 24 On Probability Theory.
ERWIN KREYSZIG
, im01.qxd 9/21/05 10:17 AM Page 1
Part A. ORDINARY DIFFERENTIAL
EQUATIONS (Odes)
CHAPTER 1 First-Order Odes
Major Changes
There Is More Material On Modeling In The Text As Well As In The
Problem Set. Some Additions On Population Dynamics Appear In Sec.
1.5.
Electric Circuits Are Shifted To Chap. 2, Where Second-Order Odes Will Be
Available. This Avoids Repetitions That Are Unnecessary And Practically Irrelevant.
Team Projects, CAS Projects, And CAS Experiments Are Included In Most Problem Sets.
SECTION 1.1. Basic Concepts. Modeling, Page 2
Purpose. To Give The Students A First Impression What An ODE Is And What We Mean By
Solving It.
Background Material. For The Whole Chapter We Need Integration Formulas
And Techniques, Which The Student Should Review.
General Comments
This Section Should Be Covered Relatively Rapidly To Get Quickly To The Actual
Solution Methods In The Next Sections.
Equations (1)–(3) Are Just Examples, Not For Solution, But The Student Will
See That Solutions Of (1) And (2) Can Be Found By Calculus, And A Solution Y = Ex Of
(3) By Inspection.
Problem Set 1.1 Will Help The Student With The Tasks Of
Solving Y' = Ƒ(X) By Calculus
Finding Particular Solutions From Given General Solutions
Setting Up An ODE For A Given Function As Solution
Gaining A First Experience In Modeling, By Doing One Or Two
Problems Gaining A First Impression Of The Importance Of Odes
Without Wasting Time On Matters That Can Be Done Much Faster, Once Systematic
Methods Are Available.
Comment On “General Solution” And “Singular Solution”
Usage Of The Term “General Solution” Is Not Uniform In The Literature. Some Books
Use The Term To Mean A Solution That Includes All Solutions, That Is, Both The
Particular And The Singular Ones. We Do Not Adopt This Definition For Two Reasons.
First, It Is Frequently Quite Difficult To Prove That A Formula Includes All Solutions;
Hence, This Definition Of A General Solution Is Rather Useless In Practice. Second,
Linear Differential Equations (Satisfying Rather General Conditions On The Coefficients)
Have No Singular Solutions (As Mentioned In The Text), So That For These Equations A
General Solution As Defined Does Include All Solutions. For The Latter Reason, Some
Books Use The Term “General Solution” For Linear Equations Only; But This Seems
Very Unfortunate.
1
