دانلود کتاب Approximation Procedures in Nonlinear Oscillation Theory

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Preface\nChapter I: Basic Concepts\n§ 1 Equations for oscillatory systems\n§ 2 The shift operator and first return function\n§ 3 Integral and integrofunctional operators for periodic problem\n§ 4 The harmonic balance method\n§ 5 The method of mechanical quadratures\n§ 6 The collocation method\n§ 7 The method of finite differences\n§ 8 Factor methods\nChapter II: Existence theorems for oscillatory regimes\n§ 1 Smooth manifolds and differential forms\n§ 2 Degree of a mapping\n§ 3 Rotation of vector fields\n§ 4 Completely continuous vector fields\n§ 5 Fixed point principles and solution of operator equations\n§ 6 Forced oscillations in systems with weak nonlinearities\n§ 7 Oscillations in systems with strong nonlinearities. Directing functions method\nChapter III: Convergence of numerical procedures\n§ 1 Projection methods\n§ 2 Factor methods\n§ 3 Convergence of the harmonic balance method and the collocation method in the problem of periodic oscillations\n§ 4 Convergence of the method of mechanical quadratures\n§ 5 Convergence of the method of finite differences\n§ 6 Numerical procedures of approximate construction of oscillatory regimes in autonomous systems\n§ 7 Affinity theory\n§ 8 Effective convergence criteria for numerical procedures\n§ 9 Effective estimates of the convergence rate for the harmonic balance method\nNotes on the References\nReferences\nIndex