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Systems of Units. Some Important Conversion Factors
The most important systems o...
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Differentiation
(cu)Ј ϭ cuЈ

(c constant)

Integration

͵ uvЈ dx ϭ uv Ϫ ͵ uЈv dx...
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Page i
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ADVANCED
ENGINEERING
MATHEMATICS
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Page v

10

TH EDITION

ADVANCED
ENGINEERING
MATHEMATICS
ERWIN KREYSZIG
Professor of Mathemat...
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PUBLISHER
PROJECT EDITOR
MARKETING MANAGER
CONTENT MANAGER
PRODUCTION EDITOR
MEDIA ...
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PREFACE
See also http://www.wiley.com/college/kreyszig

Purpose and Structure of th...
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Page viii

Preface

PARTS AND CHAPTERS OF THE BOOK

PART A

PART B

Chaps. 1–6
Ordinary...
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Preface

ix

Four Underlying Themes of the Book
The driving force in engineering mat...
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Preface

4. To clearly identify the conceptual structure of subject matters. For e...
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Preface

xi

to the field of engineering mathematics. It should encourage the studen...
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Preface

data, outliers, and the z-score (Sec. 24.1). Furthermore, new example...
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Preface

xiii

Vector Algebra and Calculus (Chaps. 9–10)
Fourier Series and PDEs (...
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CONTENTS
PART A

Ordinary Differential Equations (ODEs) 1
CHAPTER 1 First-Order ODEs...
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xvi

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Contents

5.3 Extended Power Series Method: Frobenius Method 180
5.4 Bessel’s ...
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Contents

xvii

CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl
354
9.1 Ve...
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xviii

Page xviii

Contents

12.6 Heat Equation: Solution by Fourier Series.
Steady Two-Dimen...
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Contents

xix

CHAPTER 17 Conformal Mapping
736
17.1 Geometry of Analytic Functions...
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Page xx

Contents

21.4 Methods for Elliptic PDEs 922
21.5 Neumann and Mixed Problems. Ir...
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Contents

xxi

25.4 Testing Hypotheses. Decisions 1077
25.5 Quality Control 1087
25...
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Page xxii
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Page 1

PART

A

Ordinary
Differential
Equations (ODEs)
CHAPTER
CHAPTER
CHAPTER
CHAPTER
CHAPTER...
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Page 2

CHAPTER

1

First-Order ODEs
Chapter 1 begins the study of ordinary differential equati...
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Page 3

SEC. 1.1 Basic Concepts. Modeling

3

y

h
Velocity
v
Water level h
Falling stone

Para...
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4

Page 4

CHAP. 1 First-Order ODEs

are ordinary differential equations (ODEs). Here, as in ca...
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SEC. 1.1 Basic Concepts. Modeling
EXAMPLE 2

5

Solution by Calculus. Solution Curves
T...
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6

Page 6

CHAP. 1 First-Order ODEs

We see that each ODE in these examples has a solution that...
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SEC. 1.1 Basic Concepts. Modeling

7

And Step 2 requires a solid knowledge and good un...
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Page 8

8

CHAP. 1 First-Order ODEs

PROBLEM SET 1.1
1–8

CALCULUS

17–20

Solve the ODE by int...
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SEC. 1.2 Geometric Meaning of yЈ ϭ ƒ(x, y). Direction Fields, Euler’s Method

1.2

9

G...
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CHAP. 1 First-Order ODEs

If you have no CAS, first draw a few level curves f (x, ...
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SEC. 1.2 Geometric Meaning of yЈ ϭ ƒ(x, y). Direction Fields, Euler’s Method

11

Tabl...
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12

Page 12

CHAP. 1 First-Order ODEs

16. CAS PROJECT. Direction Fields. Discuss direction
fie...
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SEC. 1.3 Separable ODEs. Modeling
EXAMPLE 2

13

Separable ODE
The ODE y r ϭ (x ϩ 1)e؊...
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14

Page 14

CHAP. 1 First-Order ODEs
Next we use the half-life H ϭ 5715 to determine k. When t...
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SEC. 1.3 Separable ODEs. Modeling
EXAMPLE 6

15

Heating an Office Building (Newton’s ...
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16

Page 16

CHAP. 1 First-Order ODEs
Step 5. Answer and interpretation. 6 A.M. is t ϭ 8 (namel...
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SEC. 1.3 Separable ODEs. Modeling

17

Step 3. Particular solution. The initial height...
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18

Page 18

CHAP. 1 First-Order ODEs
EXAMPLE 8

Reduction to Separable Form
Solve
2xyy r ϭ y 2...
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SEC. 1.3 Separable ODEs. Modeling
19–36

MODELING, APPLICATIONS

19. Exponential growt...
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CHAP. 1 First-Order ODEs

33. Rope. To tie a boat in a harbor, how many times
must...
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SEC. 1.4 Exact ODEs. Integrating Factors

21

an ODE that we can solve by going backwa...
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22

Page 22

CHAP. 1 First-Order ODEs

This condition is not only necessary but also sufficient...
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SEC. 1.4 Exact ODEs. Integrating Factors

23

Step 3. Checking an implicit solution. W...
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24

Page 24

CHAP. 1 First-Order ODEs

This example gives the idea. All we did was to multiply ...
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SEC. 1.4 Exact ODEs. Integrating Factors

25

This proves the following theorem.
THEOR...
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Page 26

CHAP. 1 First-Order ODEs
Test for exactness; you will get 1 on both sides of the e...
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