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1.

図書

図書
William E. Boyce and Richard C. Di Prima
出版情報: New York : Wiley, c1969  xiv, 533, A-43, I-8 p ; 24 cm
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2.

図書

図書
William E. Boyce and Richard C. DiPrima
出版情報: New York : Wiley, c1965  xvi, 485 p. ill. ; 24 cm
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3.

図書

図書
William E. Boyce and Richard C. DiPrima
出版情報: New York : Wiley, c1977  xiv, 582, [56] p. ; 24 cm
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目次情報: 続きを見る
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:
4.

図書

図書
William E. Boyce, Richard C. DiPrima
出版情報: Hoboken, N.J. : Wiley, c2012  xix, 809 p. ; 27 cm
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