Elementary Differential Equations

This new edition of Boyce & DiPrima’s Elementary Differential Equations, 8/e, and the accompanying supplements have been carefully developed to give you the support you need to succeed in your course.  The Eighth Edition gives you a CD-ROM with powerful ODE Architect modeling software and an array of web-based learning tools to support your studies.

The CD-ROM includes:

• The award-winning ODE Architect software. The software’s 14 modules enable you to build and solve your own ODEs, and to use simulations and multimedia to develop detailed mathematical models and concepts in a truly interactive environment.
• The ODE Architect Companion. The Companion extends the ideas featured in each multimedia module.

The web-based learning tools include:

• Review & Study Guidelines. The Chapter Review Guidelines will help you prepare for quizzes and exams.
• Online Review Quizzes. The quizzes enable you to test your knowledge of key concepts and provide diagnostic feedback that references appropriate sections in the text.
• PowerPoint Slides. You can print these slides out for in-class note taking.
• Getting Started with ODE Architect. This guide will help you get up-and-running with ODE Architect’s simulations and multimedia.

Richard C. DiPrima (deceased) received his B.S., M.S., and Ph.D. degrees in Mathematics from Carnegie-Mellon University. He joined the faculty of Rensselaer Polytechnic Institute after holding research positions at MIT, Harvard, and Hughes Aircraft. He held the Eliza Ricketts Foundation Professorship of Mathematics at Rensselaer, was a fellow of the American Society of Mechanical Engineers, the American Academy of Mechanics, and the American Physical Society. He was also a member of the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. He served as the Chairman of the Department of Mathematical Sciences at Rensselaer, as President of the Society for Industrial and Applied Mathematics, and as Chairman of the Executive Committee of the Applied Mechanics Division of ASME. In 1980, he was the recipient of theWilliam H.Wiley Distinguished Faculty Award given by Rensselaer. He received Fulbright fellowships in 1964–65 and 1983 and a Guggenheim fellowship in 1982–83. He was the author of numerous technical papers in hydrodynamic stability and lubrication theory and two texts on differential equations and boundary value problems. Professor DiPrima died on September 10, 1984.

Chapter 1 Introduction.

1.1 Some Basic Mathematical Models; Direction Fields.

1.2 Solutions of Some Differential Equations.

1.3 Classi.cation 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 SecondOrd er Linear Equations.

3.1 Homogeneous Equations with Constant Coef.cients.

3.2 Fundamental Solutions of Linear Homogeneous Equations.

3.3 Linear Independence and the Wronskian.

3.4 Complex Roots of the Characteristic Equation.

3.5 Repeated Roots; Reduction of Order.

3.6 Nonhomogeneous Equations; Method of Undetermined Coeficients.

3.7 Variation of Parameters.

3.8 Mechanical and Electrical Vibrations.

3.9 Forced Vibrations.

Chapter 4 Higher Order Linear Equations.

4.1 General Theory of nth Order Linear Equations.

4.2 Homogeneous Equations with Constant Coeficients.

4.3 The Method of Undetermined Coeficients.

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 Regular Singular Points.

5.5 Euler Equations.

5.6 Series Solutions Near a Regular Singular Point, Part I.

5.7 Series Solutions Near a Regular Singular Point, Part II.

5.8 Bessel’s Equation.

Chapter 6 The Laplace Transform.

6.1 De.nition 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 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 Coef.cients.

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–Kutta Method.

8.4 Multistep Methods.

8.5 More on Errors; Stability.

8.6 Systems of First Order Equations.

Chapter 9 Nonlinear Differential Equations andStability.

9.1 The Phase Plane: Linear Systems.

9.2 Autonomous Systems and Stability.

9.3 Almost 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.

Answers to Problems.

Index.