A First Course in Differential Equations with Modeling Applications

✍ Scribed by Dennis G. Zill

• Publisher: Cengage Learning
• Year: 2012
• Tongue: English
• Leaves: 489
• Edition: 10
• Category: Library

✦ Synopsis

A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 10th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible book speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, the book provides a thorough treatment of boundary-value problems and partial differential equations.

✦ Table of Contents

Cover
EPP2
EPP3
Title Page
Copyright
Statement
Contents
Preface
To the Student
To the Instructor
Student Resources
Instructor Resources
Acknowledgments
Reviewers of Past Editions
Reviewers of the Current Editions
Project for Section 3.1
Is AIDS an Invariably Fatal Disease?
Related Problems
References
About the Author
Project for Section 3.2
The Allee Effect
Related Problems
References
About the Author
Project for Section 3.3
Wolf Population Dynamics
Related Problems
About the Author
Project for Section 5.1
Bungee Jumping
Related Problems
About the Author
Project for Section 5.3
The Collapse of the Tacoma Narrows Suspension Bridge
Related Problems
References
About the Author
Project for Section 7.3
Murder at the Mayfair Diner
Related Problems
About the Author
Project for Section 8.2
Earthquake Shaking of Multistory Buildings
Related Problems
Project for Section 8.3
Modeling Arms Races
Related Problems
References
About the Author
Ch 1: Introduction to Differential Equations
Introduction
1.1 Definitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models
Chapter 1 in Review
Ch 2: First-Order Differential Equations
Introduction
2.1 Solution Curves Without a Solution
2.1.1 Direction Fields
2.1.2 Autonomous First-Order DEs
2.2 Separable Equations
2.3 Linear Equations
2.4 Exact Equations
2.5 Solutions by Substitutions
2.6 A Numerical Method
Chapter 2 in Review
Ch 3: Modeling with First-Order Differential Equations
Introduction
3.1 Linear Models
3.2 Nonlinear Models
3.3 Modeling with Systems of First-Order DEs
Chapter 3 in Review
Ch 4: Higher-Order Differential Equations
Introduction
4.1 Preliminary Theory—Linear Equations
4.1.1 Initial-Value and Boundary-Value Problems
4.1.2 Homogeneous Equations
4.1.3 Nonhomogeneous Equations
4.2 Reduction of Order
4.3 Homogeneous Linear Equations with Constant Coefficients
4.4 Undetermined Coefficients—Superposition Approach
4.5 Undetermined Coefficients—Annihilator Approach
4.6 Variation of Parameters
4.7 Cauchy-Euler Equation
4.8 Green’s Functions
4.8.1 Initial-Value Problems
4.8.2 Boundary-Value Problems
4.9 Solving Systems of Linear DEs by Elimination
4.10 Nonlinear Differential Equations
Chapter 4 in Review
Ch 5: Modeling with Higher-Order Differential Equations
Introduction
5.1 Linear Models: Initial-Value Problems
5.1.1 Spring/Mass Systems: Free Undamped Motion
5.1.2 Spring/Mass Systems: Free Damped Motion
5.1.3 Spring/Mass Systems: Driven Motion
5.1.4 Series Circuit Analogue
5.2 Linear Models: Boundary-Value Problems
5.3 Nonlinear Models
Chapter 5 in Review
Ch 6: Series Solutions of Linear Equations
Introduction
6.1 Review of Power Series
6.2 Solutions About Ordinary Points
6.3 Solutions About Singular Points
6.4 Special Functions
Chapter 6 in Review
Ch 7: The Laplace Transform
Introduction
7.1 Definition of the Laplace Transform
7.2 Inverse Transforms and Transforms of Derivatives
7.2.1 Inverse Transforms
7.2.2 Transforms of Derivatives
7.3 Operational Properties I
7.3.1 Translation on the s-Axis
7.3.2 Translation on the t-Axis
7.4 Operational Properties II
7.4.1 Derivatives of a Transform
7.4.2 Transforms of Integrals
7.4.3 Transform of a Periodic Function
7.5 The Dirac Delta Function
7.6 Systems of Linear Differential Equations
Chapter 7 in Review
Ch 8: Systems of Linear First-Order Differential Equations
Introduction
8.1 Preliminary Theory—Linear Systems
8.2 Homogeneous Linear Systems
8.2.1 Distinct Real Eigenvalues
8.2.2 Repeated Eigenvalues
8.2.3 Complex Eigenvalues
8.3 Nonhomogeneous Linear Systems
8.3.1 Undetermined Coefficients
8.3.2 Variation of Parameters
8.4 Matrix Exponential
Chapter 8 in Review
Ch 9: Numerical Solutions of Ordinary Differential Equations
Introduction
9.1 Euler Methods and Error Analysis
9.2 Runge-Kutta Methods
9.3 Multistep Methods
9.4 Higher-Order Equations and Systems
9.5 Second-Order Boundary-Value Problems
Chapter 9 in Review
Appendix I: Gamma Function
Appendix II: Matrices
Appendix III: Laplace Transforms
Answers for Selected Odd-Numbered Problems
Index
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
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