Elementary differential equations and boundary value problems

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Elementary differential equations and boundary value problems / William E. Boyce and Richard C. DiPrima

版:

3rd ed

資料種別:

図書

出版情報:

New York : Wiley, c1977

形態:

xiv, 582, [56] p. ; 24 cm

著者名:

ISBN:

9780471093343 [0471093343]
9780471831808 [0471831808] (: pbk)

書誌ID:

BA00532976

子書誌情報

フルテキスト

所蔵情報

他の版・巻

Elementary differential equations and boundary value problems. 6th ed (: cloth)
William E. Boyce, Richard C. DiPrima , Wiley , c1997

Elementary differential equations and boundary value problems. 10th ed (: [hardcover])
William E. Boyce, Richard C. DiPrima , Wiley, c2012 ,

Elementary differential equations and boundary value problems. 2nd ed
William E. Boyce and Richard C. Di Prima , Wiley , c1969

Elementary differential equations and boundary value problems
William E. Boyce and Richard C. DiPrima , Wiley , c1965

書誌詳細

注記:

Includes index

主題:

Boundary value problems; Differential equations

言語:

英語

目次情報:

Preface

Introduction / Chapter 1：

Some Basic Mathematical Models; Direction Fields / 1.1：

Solutions of Some Differential Equations / 1.2：

Classification of Differential Equations / 1.3：

Historical Remarks / 1.4：

First Order Differential Equations / Chapter 2：

Linear Equations with Variable Coefficients / 2.1：

Separable Equations / 2.2：

Modeling with First Order Equations / 2.3：

Differences Between Linear and Nonlinear Equations / 2.4：

Autonomous Equations and Population Dynamics / 2.5：

Exact Equations and Integrating Factors / 2.6：

Numerical Approximations: Euler's Method / 2.7：

The Existence and Uniqueness Theorem / 2.8：

First Order Difference Equations / 2.9：

Second Order Linear Equations / Chapter 3：

Homogeneous Equations with Constant Coefficients / 3.1：

Fundamental Solutions of Linear Homogeneous Equations / 3.2：

Linear Independence and 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 / 3.9：

Higher Order Linear Equations / Chapter 4：

General Theory of nth Order Linear Equations / 4.1：

Homogeneous Equations with Constant Coeffients / 4.2：

The Method of Undetermined Coefficients / 4.3：

The Method of Variation of Parameters / 4.4：

Series Solutions of Second Order Linear Equations / Chapter 5：

Review of Power Series / 5.1：

Series Solutions near an Ordinary Point, Part I / 5.2：

Series Solutions near an Ordinary Point, Part II / 5.3：

Regular Singular Points / 5.4：

Euler Equations / 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 / 5.8：

The Laplace Transform / Chapter 6：

Definition of the Laplace Transform / 6.1：

Solution of Initial Value Problems / 6.2：

Step Functions / 6.3：

Differential Equations with Discontinuous Forcing Functions / 6.4：

Impulse Functions / 6.5：

The Convolution Integral / 6.6：

Systems of First Order Linear Equations / Chapter 7：

Review of Matrices / 7.1：

Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors / 7.3：

Basic Theory of Systems of First Order Linear Equations / 7.4：

Homogeneous Linear Systems with Constant Coefficients / 7.5：

Complex Eigenvalues / 7.6：

Fundamental Matrices / 7.7：

Repeated Eigenvalues / 7.8：

Nonhomogeneous Linear Systems / 7.9：

Numerical Methods / Chapter 8：

The Euler or Tangent Line Method / 8.1：

Improvements on the Euler Method / 8.2：

The Runge-Kutta Method / 8.3：

Multistep Methods / 8.4：

More on Errors; Stability / 8.5：

Systems of First Order Equations / 8.6：

Nonlinear Differential Equations and Stability / Chapter 9：

The Phase Plane; Linear Systems / 9.1：

Autonomous Systems and Stability / 9.2：

Almost Linear Systems / 9.3：

Competing Species / 9.4：

Predator-Prey Equations / 9.5：

Liapunov's Second Method / 9.6：

Periodic Solutions and Limit Cycles / 9.7：

Chaos and Strange Attractors; the Lorenz Equations / 9.8：

Partial Differential Equations and Fourier Series / Chapter 10：

Two-Point Boundary Valve Problems / 10.1：

Fourier Series / 10.2：

The Fourier Convergence Theorem / 10.3：

Even and Odd Functions / 10.4：

Separation of Variables; Heat Conduction in a Rod / 10.5：

Other Heat Conduction Problems / 10.6：

The Wave Equation; Vibrations of an Elastic String / 10.7：

Laplace's Equation / 10.8：

Derivation of the Heat Conduction Equation / Appendix A.：

Derivation of the Wave Equation / Appendix B.：

Boundary Value Problems and Sturm-Liouville Theory / Chapter 11：

The Occurrence of Two Point Boundary Value Problems / 11.1：

Sturm-Liouville Boundary Value Problems / 11.2：

Nonhomogeneous Boundary Value Problems / 11.3：

Singular Sturm-Liouville Problems / 11.4：

Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion / 11.5：

Series of Orthogonal Functions: Mean Convergence / 11.6：

Answers to Problems

Index

Preface

Introduction / Chapter 1：

Some Basic Mathematical Models; Direction Fields / 1.1：

Solutions of Some Differential Equations / 1.2：

Classification of Differential Equations / 1.3：

Historical Remarks / 1.4：

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