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Elementary Differential Equations with Boundary Value Problems with IDE CD Package,9780321398505
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Elementary Differential Equations with Boundary Value Problems with IDE CD Package

by ;
Edition:
2nd
ISBN13:

9780321398505

ISBN10:
0321398505
Format:
Hardcover w/CD
Pub. Date:
1/1/2006
Publisher(s):
Addison Wesley
Includes 2-weeks free access to
step-by-step solutions for this book.
Step-by-Step solutions are actual worked out problems to the questions at the end of each chapter that help you understand your homework and study for your exams. Chegg and eCampus are providing you two weeks absolutely free. 81% of students said using Step-by-Step solutions prepared them for their exams.

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Summary

Elementary Differential Equations with Boundary Value Problems integrates the underlying theory, the solution procedures, and the numerical/computational aspects of differential equations in a seamless way. For example, whenever a new type of problem is introduced (such as first-order equations, higher-order equations, systems of differential equations, etc.) the text begins with the basic existence-uniqueness theory. This provides the student the necessary framework to understand and solve differential equations. Theory is presented as simply as possible with an emphasis on how to use it. The Table of Contents is comprehensive and allows flexibility for instructors.

Table of Contents

Preface xi
Introduction to Differential Equations
1(14)
Introduction
1(1)
Examples of Differential Equations
1(7)
Direction Fields
8(7)
First Order Differential Equations
15(92)
Introduction
15(4)
First Order Linear Differential Equations
19(12)
Introduction to Mathematical Models
31(10)
Population Dynamics and Radioactive Decay
41(7)
First Order Nonlinear Differential Equations
48(6)
Separable First Order Equations
54(9)
Exact Differential Equations
63(7)
The Logistic Population Model
70(7)
Applications to Mechanics
77(12)
Euler's Method
89(18)
Review Exercises
100(1)
Projects
101(6)
Second and Higher Order Linear Differential Equations
107(106)
Introduction
108(7)
The General Solution of Homogeneous Equations
115(6)
Constant Coefficient Homogeneous Equations
121(6)
Real Repeated Roots; Reduction of Order
127(5)
Complex Roots
132(10)
Unforced Mechanical Vibrations
142(12)
The General Solution of a Linear Nonhomogeneous Equation
154(4)
The Method of Undetermined Coefficients
158(10)
The Method of Variation of Parameters
168(6)
Forced Mechanical Vibrations, Electrical Networks, and Resonance
174(14)
Higher Order Linear Homogeneous Differential Equations
188(7)
Higher Order Homogeneous Constant Coefficient Differential Equations
195(6)
Higher Order Linear Nonhomogeneous Differential Equations
201(12)
Review Exercises
206(1)
Projects
206(7)
First Order Linear Systems
213(104)
Introduction
213(10)
Existence and Uniqueness
223(5)
Homogeneous Linear Systems
228(10)
Constant Coefficient Homogeneous Systems; the Eigenvalue Problem
238(9)
Real Eigenvalues and the Phase Plane
247(9)
Complex Eigenvalues
256(10)
Repeated Eigenvalues
266(11)
Nonhomogeneous Linear Systems
277(11)
Numerical Methods for Systems of Linear Differential Equations
288(12)
The Exponential Matrix and Diagonalization
300(17)
Review Exercises
310(1)
Projects
311(6)
Laplace Transforms
317(74)
Introduction
317(12)
Laplace Transform Pairs
329(15)
The Method of Partial Fractions
344(6)
Laplace Transforms of Periodic Functions and System Transfer Functions
350(9)
Solving Systems of Differential Equations
359(9)
Convolution
368(9)
The Delta Function and Impulse Response
377(14)
Projects
385(6)
Nonlinear Systems
391(80)
Introduction
391(9)
Equilibrium Solutions and Direction Fields
400(13)
Conservative Systems
413(11)
Stability
424(9)
Linearization and the Local Picture
433(15)
Two-Dimensional Linear Systems
448(10)
Predator-Prey Population Models
458(13)
Projects
466(5)
Numerical Methods
471(44)
Introduction
471(2)
Euler's Method, Heun's Method, and the Modified Euler's Method
473(6)
Taylor Series Methods
479(14)
Runge-Kutta Methods
493(22)
Appendix 1: Convergence of One-Step Methods
506(1)
Appendix 2: Stability of One-Step Methods
507(3)
Projects
510(5)
Series Solutions of Linear Differential Equations
515(50)
Introduction
515(12)
Series Solutions Near an Ordinary Point
527(9)
The Euler Equation
536(6)
Solutions Near a Regular Singular Point and the Method of Frobenius
542(8)
The Method of Frobenius Continued: Special Cases and a Summary
550(15)
Projects
561(4)
Second Order Partial Differential Equations and Fourier Series
565(94)
Introduction
565(5)
Heat Flow in a Thin Bar; Separation of Variables
570(10)
Series Solutions
580(9)
Calculating the Solution
589(11)
Fourier Series
600(16)
The Wave Equation
616(12)
Laplace's Equation
628(13)
Higher-Dimensional Problems; Nonhomogeneous Equations
641(18)
Project
655(4)
First Order Partial Differential Equations and the Method of Characteristics
659(22)
Introduction
659(3)
The Cauchy Problem
662(6)
Existence and Uniqueness
668(3)
The Method of Characteristics
671(10)
Projects
679(2)
Linear Two-Point Boundary Value Problems
681
Introduction
681(1)
Existence and Uniqueness
682(11)
Two-Point Boundary Value Problems for Linear Systems
693(12)
Sturm-Liouville Boundary Value Problems
705
Project
715
Answers 1(1)
Index 1


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