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Elementary Differential Equations 10th Edition by William Boyce, Richard DiPrima ISBN 978-1118157398 1118157397

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Elementary Differential Equations 10th Edition William E. Boyce Digital Instant Download

Author(s): William E. Boyce, Richard C. DiPrima
ISBN(s): 9780470458327, 0470458321
Edition: 10
File Details: PDF, 4.21 MB
Year: 2012
Language: english
SKU: EB-4178322 Category: Tags: ,

Elementary Differential Equations 10th Edition by William E. Boyce, Richard C. DiPrima – Ebook PDF Instant Download/Delivery: 978-1118157398, 1118157397
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Product details: 

ISBN 10: 1118157397

ISBN 13: 978-1118157398

Author:  William E. Boyce, Richard C. DiPrima

Elementary Differential Equations, 10th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical and sometimes intensely practical. The authors have sought to combine a sound and accurate 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 10th edition includes new problems, updated figures and examples to help motivate students.

 

Table of contents: 

Chapter 1 – Introduction

  1. Some Basic Mathematical Models; Direction Fields

  2. Solutions of Some Differential Equations

  3. Classification of Differential Equations

  4. Historical Remarks

Chapter 2 – First Order Differential Equations

  1. Linear Equations; Method of Integrating Factors

  2. Separable Equations

  3. Modeling with First Order Equations

  4. Differences Between Linear and Nonlinear Equations

  5. Autonomous Equations and Population Dynamics

  6. Exact Equations and Integrating Factors

  7. Numerical Approximations: Euler’s Method

  8. The Existence and Uniqueness Theorem

  9. First Order Difference Equations

Chapter 3 – Second Order Linear Equations

  1. Homogeneous Equations with Constant Coefficients

  2. Solutions of Linear Homogeneous Equations; the Wronskian

  3. Complex Roots of the Characteristic Equation

  4. Repeated Roots; Reduction of Order

  5. Nonhomogeneous Equations; Method of Undetermined Coefficients

  6. Variation of Parameters

  7. Mechanical and Electrical Vibrations

  8. Forced Vibrations

Chapter 4 – Higher Order Linear Equations

  1. General Theory of nth Order Linear Equations

  2. Homogeneous Equations with Constant Coefficients

  3. The Method of Undetermined Coefficients

  4. The Method of Variation of Parameters

Chapter 5 – Series Solutions of Second Order Linear Equations

  1. Review of Power Series

  2. Series Solutions Near an Ordinary Point, Part I

  3. Series Solutions Near an Ordinary Point, Part II

  4. Euler Equations; Regular Singular Points

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

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

  7. Bessel’s Equation

Chapter 6 – The Laplace Transform

  1. Definition of the Laplace Transform

  2. Solution of Initial Value Problems

  3. Step Functions

  4. Differential Equations with Discontinuous Forcing Functions

  5. Impulse Functions

  6. The Convolution Integral

Chapter 7 – Systems of First Order Linear Equations

  1. Introduction

  2. Review of Matrices

  3. Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors

  4. Basic Theory of Systems of First Order Linear Equations

  5. Homogeneous Linear Systems with Constant Coefficients

  6. Complex Eigenvalues

  7. Fundamental Matrices

  8. Repeated Eigenvalues

  9. Nonhomogeneous Linear Systems

Chapter 8 – Numerical Methods

  1. The Euler or Tangent Line Method

  2. Improvements on the Euler Method

  3. The Runge-Kutta Method

  4. Multistep Methods

  5. Systems of First Order Equations

  6. More on Errors; Stability

Chapter 9 – Nonlinear Differential Equations and Stability

  1. The Phase Plane: Linear Systems

  2. Autonomous Systems and Stability

  3. Locally Linear Systems

  4. Competing Species

  5. Predator-Prey Equations

  6. Liapunov’s Second Method

  7. Periodic Solutions and Limit Cycles

  8. Chaos and Strange Attractors: The Lorenz Equations

Chapter 10 – Partial Differential Equations and Fourier Series

  1. Two-Point Boundary Value Problems

  2. Fourier Series

  3. The Fourier Convergence Theorem

  4. Even and Odd Functions

  5. Separation of Variables; Heat Conduction in a Rod

  6. Other Heat Conduction Problems

  7. The Wave Equation: Vibrations of an Elastic String

  8. Laplace’s Equation

Appendices

  • Appendix A – Derivation of the Heat Conduction Equation

  • Appendix B – Derivation of the Wave Equation

Chapter 11 – Boundary Value Problems and Sturm-Liouville Theory

  1. The Occurrence of Two-Point Boundary Value Problems

  2. Sturm-Liouville Boundary Value Problems

  3. Nonhomogeneous Boundary Value Problems

  4. Singular Sturm-Liouville Problems

  5. Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion

  6. Series of Orthogonal Functions: Mean Convergence

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Tags: William Boyce, Richard DiPrima, Elementary Differential Equations