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## Elementary differential equations and boundary value problems / William E. Boyce and Richard C. Di Prima.

Editor: New York : Wiley, c1969Edición: 2nd edDescripción: xiv, 533, A-43, I-8 p. : il. ; 24 cmISBN: 0471093319Otra clasificación: 34-01
Contenidos:
```1. INTRODUCTION 
1.1 Ordinary Differential Equations 
1.2 Historical Remarks 
2. FIRST ORDER DIFFERENTIAL EQUATIONS 
2.1 Linear Equations 
2.2 Further Discussion of Linear Equations 
2.3 Nonlinear Equations 
2.4 Separable Equations 
2.5 Exact Equations 
2.6 Integrating Factors 
2.7 Homogeneous Equations 
2.8 Miscellaneous Problems 
2.9 Applications of First Order Equations 
2.10 Elementary Mechanics 
2.11 The Existence and Uniqueness Theorem 
2.12 The Existence Theorem from a More Modern Viewpoint 
Appendix. Derivation of Equation of Motion of Body with Variable Mass 
3. SECOND ORDER LINEAR EQUATIONS 
3.1 Introduction 
3.2 Fundamental Solutions of the Homogeneous Equation 
3.3 Linear Independence 
3.4 Reduction of Order 
3.5 Homogeneous Equations with Constant Coefficients 
3.5.1 Complex Roots 
3.6 The Nonhomogeneous Problem 
3.6.1 The Method of Undetermined Coefficients 
3.6.2 The Method of Variation of Parameters 
3.7 Mechanical Vibrations 
3.7.1 Free Vibrations 
3.7.2 Forced Vibrations 
3.8 Electrical Networks 
4. SERIES SOLUTIONS OF SECOND ORDER LINEAR EQUATIONS 
4.1 Introduction. Review of Power Series 
4.2 Series Solutions near an Ordinary Point, Part I 
4.2.1 Series Solutions near an Ordinary Point, Part II 
4.3 Regular Singular Points 
4.4 Euler Equations 
4.5 Series Solutions near a Regular Singular Point, Part I 
4.5.1 Series Solutions near a Regular Singular Point, Part II 
*4.6 Series Solutions near a Regular Singular Point; r1 = r2 and r1 — r2 = N 
*4.7 Bessel’s Equation 
5. HIGHER ORDER LINEAR EQUATIONS 
5.1 Introduction 
5.2 General Theory of //th Order Linear Equations 
5.3 The Homogeneous Equation with Constant Coefficients 
5.4 The Method of Undetermined Coefficients 
5.5 The Method of Variation of Parameters 
6. THE LAPLACE TRANSFORM 
6.1 Introduction. Definition of the Laplace Transform 
6.2 Solution of Initial Value Problems 
6.3 Step Functions 
6.3.1 A Differential Equation with a Discontinuous Forcing Function 
6.4 Impulse Functions 
6.5 The Convolution Integral 
6.6 General Discussion and Summary 
7. SYSTEMS OF FIRST ORDER EQUATIONS 
7.1 Introduction 
7.2 Solution of Linear Systems by Elimination 
7.3 Review of Matrices 
7.4 Basic Theory of Systems of Linear First Order Equations 
7.5 Linear Homogeneous Systems with Constant Coefficients 
7.6 Inverses, Eigenvalues, and Eigenvectors 
7.7 Fundamental Matrices 
7.8 Complex Roots 
7.9 Repeated Roots 
7.10 Nonhomogeneous Linear Systems 
7.11 The Laplace Transform for Systems of Equations 
8. NUMERICAL METHODS 
8.1 Introduction 
8.2 The Euler or Tangent Line Method 
8.3 The Error 
8.4 An Improved Euler Method 
8.5 The Three-Term Taylor Series Method 
8.6 The Runge-Kutta Method 
8.7 Some Difficulties with Numerical Methods 
8.8 A Multistep Method 
8.9 Systems of First Order Equations 
9. NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY 
9.1 Introduction 
9.2 Solutions and Trajectories 
9.3 The Phase Plane: The Linear System 
9.4 Stability; Almost Linear Systems 
9.5 Liapounov's Second Method 
9.6 Periodic Solutions and Limit Cycles 
10. PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES 
10.1 Introduction 
10.2 Heat Conduction and Separation of Variables 
10.3 Fourier Series 
10.4 The Fourier Theorem 
10.5 Even and Odd Functions 
10.6 Solution of Other Heat Conduction Problems 
10.7 The Wave Equation; Vibrations of an Elastic String 
10.8 Laplace’s Equation 
Appendix A. Derivation of the Heat Conduction Equation 
Appendix B. Derivation of the Wave Equation 
11. BOUNDARY VALUE PROBLEMS AND
STURM-LIOUVILLE THEORY 
11.1 Introduction 
11.2 Linear Homogeneous Boundary Value Problems: Eigenvalues and Eigenfunctions 
11.3 Sturm-Liouville Boundary Value Problems 
11.4 Solution of Nonhomogeneous Boundary Value Problems 
11.5 Singular Sturm-Liouville Problems 
11.6 Further Remarks on the Method of Separation of Variables; A Bessel Series Expansion 
11.7 Series of Orthogonal Functions; Mean Convergence 
INDEX 1-1``` Average rating: 0.0 (0 votes)
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1. INTRODUCTION  --
1.1 Ordinary Differential Equations  --
1.2 Historical Remarks  --
2. FIRST ORDER DIFFERENTIAL EQUATIONS  --
2.1 Linear Equations  --
2.2 Further Discussion of Linear Equations  --
2.3 Nonlinear Equations  --
2.4 Separable Equations  --
2.5 Exact Equations  --
2.6 Integrating Factors  --
2.7 Homogeneous Equations  --
2.8 Miscellaneous Problems  --
2.9 Applications of First Order Equations  --
2.10 Elementary Mechanics  --
2.11 The Existence and Uniqueness Theorem  --
2.12 The Existence Theorem from a More Modern Viewpoint  --
Appendix. Derivation of Equation of Motion of Body with Variable Mass  --
3. SECOND ORDER LINEAR EQUATIONS  --
3.1 Introduction  --
3.2 Fundamental Solutions of the Homogeneous Equation  --
3.3 Linear Independence  --
3.4 Reduction of Order  --
3.5 Homogeneous Equations with Constant Coefficients  --
3.5.1 Complex Roots  --
3.6 The Nonhomogeneous Problem  --
3.6.1 The Method of Undetermined Coefficients  --
3.6.2 The Method of Variation of Parameters  --
3.7 Mechanical Vibrations  --
3.7.1 Free Vibrations  --
3.7.2 Forced Vibrations  --
3.8 Electrical Networks  --
4. SERIES SOLUTIONS OF SECOND ORDER LINEAR EQUATIONS  --
4.1 Introduction. Review of Power Series  --
4.2 Series Solutions near an Ordinary Point, Part I  --
4.2.1 Series Solutions near an Ordinary Point, Part II  --
4.3 Regular Singular Points  --
4.4 Euler Equations  --
4.5 Series Solutions near a Regular Singular Point, Part I  --
4.5.1 Series Solutions near a Regular Singular Point, Part II  --
*4.6 Series Solutions near a Regular Singular Point; r1 = r2 and r1 — r2 = N  --
*4.7 Bessel’s Equation  --
5. HIGHER ORDER LINEAR EQUATIONS  --
5.1 Introduction  --
5.2 General Theory of //th Order Linear Equations  --
5.3 The Homogeneous Equation with Constant Coefficients  --
5.4 The Method of Undetermined Coefficients  --
5.5 The Method of Variation of Parameters  --
6. THE LAPLACE TRANSFORM  --
6.1 Introduction. Definition of the Laplace Transform  --
6.2 Solution of Initial Value Problems  --
6.3 Step Functions  --
6.3.1 A Differential Equation with a Discontinuous Forcing Function  --
6.4 Impulse Functions  --
6.5 The Convolution Integral  --
6.6 General Discussion and Summary  --
7. SYSTEMS OF FIRST ORDER EQUATIONS  --
7.1 Introduction  --
7.2 Solution of Linear Systems by Elimination  --
7.3 Review of Matrices  --
7.4 Basic Theory of Systems of Linear First Order Equations  --
7.5 Linear Homogeneous Systems with Constant Coefficients  --
7.6 Inverses, Eigenvalues, and Eigenvectors  --
7.7 Fundamental Matrices  --
7.8 Complex Roots  --
7.9 Repeated Roots  --
7.10 Nonhomogeneous Linear Systems  --
7.11 The Laplace Transform for Systems of Equations  --
8. NUMERICAL METHODS  --
8.1 Introduction  --
8.2 The Euler or Tangent Line Method  --
8.3 The Error  --
8.4 An Improved Euler Method  --
8.5 The Three-Term Taylor Series Method  --
8.6 The Runge-Kutta Method  --
8.7 Some Difficulties with Numerical Methods  --
8.8 A Multistep Method  --
8.9 Systems of First Order Equations  --
9. NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY  --
9.1 Introduction  --
9.2 Solutions and Trajectories  --
9.3 The Phase Plane: The Linear System  --
9.4 Stability; Almost Linear Systems  --
9.5 Liapounov's Second Method  --
9.6 Periodic Solutions and Limit Cycles  --
10. PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES  --
10.1 Introduction  --
10.2 Heat Conduction and Separation of Variables  --
10.3 Fourier Series  --
10.4 The Fourier Theorem  --
10.5 Even and Odd Functions  --
10.6 Solution of Other Heat Conduction Problems  --
10.7 The Wave Equation; Vibrations of an Elastic String  --
10.8 Laplace’s Equation  --
Appendix A. Derivation of the Heat Conduction Equation  --
Appendix B. Derivation of the Wave Equation  --
11. BOUNDARY VALUE PROBLEMS AND --
STURM-LIOUVILLE THEORY  --
11.1 Introduction  --
11.2 Linear Homogeneous Boundary Value Problems: Eigenvalues and Eigenfunctions  --
11.3 Sturm-Liouville Boundary Value Problems  --
11.4 Solution of Nonhomogeneous Boundary Value Problems  --
11.5 Singular Sturm-Liouville Problems  --
11.6 Further Remarks on the Method of Separation of Variables; A Bessel Series Expansion  --
11.7 Series of Orthogonal Functions; Mean Convergence  --
INDEX 1-1 --

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