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Elementary Differential Equations, Enhanced eText, 11th Edition

ISBN: 978-1-119-32063-0
March 2017, ©2017
Elementary Differential Equations, Enhanced eText, 11th Edition (1119320631) cover image

Description

Elementary Differential Equations, 11th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications.

In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two‐ or three‐ semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.

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Table of Contents

1. Introduction
   1.1 Some Basic Mathematical Models; Direction Fields
   1.2 Solutions of Some Differential Equations
   1.3 Classification of Differential Equations

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

3. Second-Order Linear Differential Equations
    3.1 Homogeneous Differential Equations with Constant Coefficients
    3.2 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 Periodic Vibrations

4. Higher-Order Linear Differential Equations
    4.1 General Theory of nth Order Linear Differential Equations
    4.2 Homogeneous Differential Equations with Constant Coefficients
    4.3 The Method of Undetermined Coefficients
    4.4 The Method of Variation of Parameters

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

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

7. Systems of First-Order Linear Equations
    7.1 Introduction
    7.2 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-Valued Eigenvalues
    7.7 Fundamental Matrices
    7.8 Repeated Eigenvalues
    7.9 Nonhomogeneous Linear Systems

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

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
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The Wiley Advantage

  • 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.
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