Differential equations

A.N. Tikhonov, A.B. Vasileva, A.G. Sveshnikov ; translated from the Russian by A.B. Sossinskij

Translated from the Russian by Sossinskij, A.B.

「Nielsen BookData」より

[目次]

• I. Introduction.- x 1. The Concept of a Differential Equation.- x 2. Physical Problems Leading to Differential Equations.- II. General Theory.- x 1. Elementary Integration Methods.- x 2. Theorems on the Existence and Uniqueness of the Solution of the Initial Value Problem for a First Order Equation Resolved with Respect to the Derivative. The Euler Polygonal Line Algorithm.- x 3. Equations not Resolved with Respect to the Derivative.- x 4. Existence and Uniqueness Theorems for the Solution of Normal Systems.- x 5. Dependence of Solutions on Initial Values and Parameters.- x 6. The Method of Successive Approximations (Picard's Method).- x 7. The Contraction Mapping Theorem.- III. Linear Differential Equations.- x 1. The Pendulum Equation as an Example of a Linear Equation. The Main Properties of Linear Equations with Constant Coefficients.- x 2. General Properties of n-th Order Equations.- x 3. Homogeneous n-th Order Linear Equations.- x 4. Non-homogeneous Linear n-th Order Equations.- x 5. Linear n-th Order Equations with Constant Coefficients.- x 6. Systems of Linear Equations. General Theory.- x 7. Systems of Linear Differential Equations with Constant Coefficients.- x 8. The Solutions in Power Series Form of Linear Equations.- IV. Boundary Value Problems.- x 1. Formulation of Boundary Value Problems and their Physical Meaning.- x 2. Non-homogeneous Boundary Value Problems.- x 3. Eigenvalue Problems.- V. Stability Theory.- x 1. Statement of the Problem.- x 2. Study of Stability in the First Approximation.- x 3. The Method of Lyapunov Functions.- x 4. The Study of Trajectories in a Neighbourhood of a Stationary Point.- VI. Numerical Methods for the Solution of Ordinary Differential Equations.- x 1. Numerical Methods for Solving Initial Value Problems.- x 2. Boundary Value Problems.- VII. Asymptotics of Solutions of Differential Equations with Respect to a Small Parameter.- x 1. Regular Perturbations.- x 2. Singular Perturbations.- VIII. First Order Partial Differential Equations.- x 1. Linear Equations.- x 2. Quasilinear Equations.

「Nielsen BookData」より

書名 Differential equations Sosinskiĭ, A. B. Sveshnikov, A. G. Tikhonov, Andrei Nikolaevich Vasilʹeva, A. B. Sossinskij A. B. Sveshnikov A. G. Tikhonov Aleksandr N. Vasil'eva A.B. Tikhonov A N dok Different︠s︡ialʹnye uravnenii︠a︡ Springer series in Soviet mathematics Springer-Verlag 1984 Softcover reprint of the original 1st ed. 1985 238 p. 24 cm 3540130020 0387130020 BA00573372 ※クリックでCiNii Booksを表示 英語 ロシア語 ドイツ
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