Textbook

# Elementary Differential Equations, Ninth Edition

For Instructors
This revision of Boyce & DiPrima's market-leading text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Like previous editions, the new 9th edition of Elementary Differential Equations is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. A perennial best seller designed for engineers and scientists who need to use Elementary Differential Equations in their work and studies, the text covers all the essential topics on differential equations, including series solutions, Laplace transforms, systems of equations, numerical methods and phase plane methods. The 9th edition offers additional clear explanations detailed with many current examples, as well as added problems and subsections for clarity and motivation.
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Preface
Chapter 1 Introduction 1
1.1  Some Basic Mathematical Models; Direction Fields
1.2  Solutions of Some Differential Equations
1.3  Classification of Differential Equations
1.4  Historical Remarks

Chapter 2 First Order Differential Equations
2.1  Linear Equations; Method of Integrating Factors
2.2 Separable Equations
2.3 Modeling with First Order Equations
2.4 Differences Between Linear and Nonlinear Equations
2.5 Autonomous Equations and Population Dynamics
2.6 Exact Equations and Integrating Factors
2.7 Numerical Approximations: Euler's Method
2.8 The Existence and Uniqueness Theorem
2.9 First Order Difference Equations

Chapter 3 SecondOrder Linear Equations 135
3.1 Homogeneous Equations with Constant Coef?cients
3.2 Fundamental Solutions of Linear Homogeneous Equations; The Wronskian
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots; Reduction of Order
3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
3.6 Variation of Parameters
3.7 Mechanical and Electrical Vibrations
3.8 Forced Vibrations

Chapter 4 Higher Order Linear Equations
4.1 General Theory of nth Order Linear Equations
4.2 Homogeneous Equations with Constant Coef?cients
4.3 The Method of Undetermined Coef?cients
4.4 The Method of Variation of Parameters

Chapter 5 Series Solutions of Second Order Linear Equations
5.1 Review of Power Series
5.2 Series Solutions Near an Ordinary Point, Part I
5.3 Series Solutions Near an Ordinary Point, Part II
5.4 Euler Equations; Regular Singular Points
5.5 Series Solutions Near a Regular Singular Point, Part I
5.6 Series Solutions Near a Regular Singular Point, Part II
5.7  Bessel's Equation

Chapter 6 The Laplace Transform
6.1 Definition of the Laplace Transform
6.2 Solution of Initial Value Problems
6.3 Step Functions
6.4 Differential Equations with Discontinuous Forcing Functions
6.5 Impulse Functions
6.6 The Convolution Integral

Chapter 7 Systems of First Order Linear Equations
7.1 Introduction
7.2 Review of Matrices
7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
7.4 Basic Theory of Systems of First Order Linear Equations
7.5 Homogeneous Linear Systems with Constant Coefficients
7.6 Complex Eigenvalues
7.7 Fundamental Matrices
7.8 Repeated Eigenvalues
7.9 Nonhomogeneous Linear Systems

Chapter 8 Numerical Methods
8.1 The Euler or Tangent Line Method
8.2 Improvements on the Euler Method
8.3 The Runge-KuttaMethod
8.4 Multistep Methods
8.5 More on Errors; Stability
8.6 Systems of First Order Equations

Chapter 9 Nonlinear Differential Equations and Stability
9.1 The Phase Plane: Linear Systems
9.2 Autonomous Systems and Stability
9.3 Locally Linear Systems
9.4 Competing Species
9.5 Predator-Prey Equations
9.6 Liapunov's Second Method
9.7 Periodic Solutions and Limit Cycles
9.8 Chaos and Strange Attractors: The Lorenz Equations
Index

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• New end of chapter problems for added practice
• Expanded sections for clarity and motivation (Chapters 2, 3, 5)
• Discussion of linear dependence and independence moved from Chapter 3 to Chapter 4
• More explanation of integrals of piecewise continuous
functions and how Laplace transforms are used to solve initial value problems (Chapter 6)
• Abel's formula explicitly stated, with itemized summary (Chapter 7)
• New subsection on the importance of critical points (Chapter 9)
• More emphasis on the Jacobian matrix
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• A Flexible approach to content. Self-contained chapters allow instructors to customize the selection, order, and depth of chapters.
• A Flexible approach to technology. Boyce/DiPrima is adaptable to courses having various levels of computer involvement, ranging from little or none to intensive.  More than 450 problems are marked with a technology icon to indicate those that are considered to be technology intensive.
• Sound and accurate exposition of theory. Special attention is made to methods of solution, analysis, and approximation.
• Outstanding exercise sets.  Boyce/DiPrima remains unrivaled in quantity, variety, and range providing great flexibility in homework assignments.
• Applied Problems. Many problems ask the student not only to solve a differential equation but also to draw conclusions from the solution, reflecting the usual situation in scientific or engineering applications.
• Historical footnotes.  The footnotes allow the student to trace the development of the discipline and identify outstanding individual contributions.
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Instructors Resources
Wiley Instructor Companion Site
Instructor's Solution Manual
ISM Elementary Diff Eq & Boundary 9e
A research-based online environment for learning and assessment.
Digital evaluation copy available for this title
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Students Resources
Wiley Student Companion Site
Available Materials
by William E. Boyce, Richard C. DiPrima
978-0-470-38335-3
December 2008, ©2009, Paperback (E-book also available)
SSM Elementary Diff Eq & Boundary 9e
A research-based online environment for learning and assessment.
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Purchase Options
Wiley E-Text
Elementary Differential Equations, 9th Edition
ISBN : 978-0-470-45710-8
\$89.50

Paperback
Elementary Differential Equations: Binder Ready Version, 9th Edition
ISBN : 978-0-470-40404-1
656 pages
\$155.95

Hardcover
Elementary Differential Equations, 9th Edition
ISBN : 978-0-470-03940-3
656 pages
\$239.95

Hardcover
Elementary Differential Equations 9th Edition with ODE Architecture 1.5 CD Set
ISBN : 978-0-470-62624-5