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Bellman R. — Perturbation Techniques in Mathematics, Physics, and Engineering
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Название: Perturbation Techniques in Mathematics, Physics, and EngineeringАвтор: Bellman R. Аннотация: This three-part graduate-level treatment begins with classical perturbation techniques, discussing the Lagrange expansion theorem, matrix exponential, invariant imbedding, and dynamic programming. The second part concentrates on equations, presenting renormalization techniques of Lindstedt and Shohat and averaging techniques by Bellman and Richardson. The concluding chapter focuses on second-order linear differential equations, illustrating applications of the WKB-Liouville method and asymptotic series. Exercises, comments, and an annotated bibliography follow each demonstration of technique. A course in intermediate calculus and a basic understanding of ordinary differential equations are prerequisites
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1966Количество страниц: 118Добавлена в каталог: 05.12.2009Операции: Положить на полку |
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Предметный указатель
Abel — Schroeder functional equations 48 Adaptive control 76 Adjoint 38 Almost periodic 68 Altschuler, S. 23 91 Ambarzumian, S. 92 Analytic continuation 91 Asymptotic behavior 42 45 61 80 91 94 97 106 Asymptotic expansions 98 Asymptotic form 89 Asymptotic series 107 Asymptotic solutions 96 Atkinson, F. V. 35 102 Averaging techniques 69 Baker — Campbell — Hausdorff series 38 Baker — Hausdorff formula 37 Baker, H. F. 39 Beckenbach, E. F. 15 69 Bellman, R 15 22 23 27 31 32 35 37 38 39 42 45 47 48 49 53 63 64 67 69 71 72 76 86 94 97 102 106 109 114 Bessel function 11 113 Billings, J. H. 86 Bilodeau, G. G. 53 Birkhoff, G. D. 9 46 47 Bogoliuboff, N. 69 Borg, G. 92 Boundary layer phenomena 51 Branching processes 50 Bremmer series 101 102 Bremmer, H. 102 Brock, P. 63 Calogero, F 23 91 97 106 Cameron, R. H. 9 Cap, F. 35 Caplygin, S. 69 Carleman linearization 69 Cascade method 86 Cauchy integral theorem 6 Celestial mechanics 54 55 Cesari, L. 42 61 Characteristic functions 20 Characteristic value problems 23 Characteristic values 20 Chen, K 37 Classical perturbation techniques 44 Closure 71 Collision processes 32 Continued fractions 53 114 Cooke, K. L. 38 42 53 Coupling coefficient 3 DeBruijn, N. G. 113 Difference equations 48 Differential-difference equations 38 42 53 Diliberto, S. P. 69 Discontinuous behavior 51 Dreyfus, S. 109 Dynamic programming 23 27 31 74 76 97 Dynamical systems 47 Elliptic functions 63 64 78 Equilibrium point 40 Erdelyi, A. 51 98 114 Error function 114 Exponential integral 110 114 Feynman, R. P. 37 Finite closure 70 Flatto, L. 51 Fletcher, J. E. 64 Formal solution 4 47 Francis, L. 51 Fredholm equation 18 Fredholm, I. 35 Friedrichs, K. O. 27 Functional equations 43 Gelfand, I. M. 9 91 Good, I. J. 9 Goursat, E. 7 Green, G. 95 Green’s functions 31 Grobner, W. 34 Hadamard, J. 50 Harris, T. E. 50 Harris, W. A., Jr. 51 Hartman, P. 89 Heaviside, O. 110 Hedrick, E. R. 7 Heisenberg, E. 61 Hermite, C. 79 Hille, E. 50 Hsu, C. S. 64 Imbedding 5 Inequalities 15 69 Inhomogeneous linear equations 12 Invariant imbedding 28 31 91 102 103 Inverse problem 91 Inversion problem 91 Irregular perturbation 50 Iteration 47 49 Jordan, T. F. 37 Kalaba, R. 23 31 32 53 67 97 102 Kaplansky, I. 11 Keller, H. B. 102 Keller, J. B. 102 Kellogg, O. D 9 Kepler equation 7 Kolodner, I. I. 91 Kronecker products 47 Kryloff, N 69 Lagrange expansion 5 6 112 Lagrange, C. L. 7 Laguerre polynomials 7 Langer approximation 98 Langer, R. 92 98 Laplace cascade method 86 Laplace transform 12 111 113 LaSalle, J. P. 42 Lefschetz, S. 42 61 Lehman, R. S. 31 Letov, N. 42 Levin, J. J. 51 67 Levinson, N. 51 Levitan, B. M. 91 Lie group dynamical formalism 37 Lie series 35 Lighthill, M. J. 78 Limit cycles 61 Lindstedt expansion 62 Lindstedt, R. 57 Linear differential equations 9 Linear operation 2 Linear operator 3 Linear perturbation series 15 Linearization 69 Liouville change of variable 94 Liouville transformation 80 89 Liouville — Neumann series, l 7 102 Liouville, R. 11 87 95 97 Lippman, B. A. 91 Lochak, G. 61 Lowdin, P. — O. 37 Luke, Y. L. 113 Lyapunov, A. M. 46 MacCallum, C. J. 91 103 Magnus, W. 37 39 Maradudin, A. A. 37 Maslov, V. P. 96 Mathieu equation 64 Mathieu functions 78 Matrix analysis 15 Matrix exponential 33 Maximum operation 97 Method of continuity 5 Minorsky, N. 55 Mori, R. 61 Moroney, R. M. 23 Multidimensional Lagrange expansion 8 Multiple characteristic root 27 Multivibrator 54 Munakata, K. 64 Murray, F. J. 37 Myskis, D. 53 Nemytskii, V. V. 42 Neutron transport 29 Nikiforov, A. F. 95 98 Nonlinear differential equations 71 Nonlinear mechanics 63 69 Nonlinear oscillation 55 57 67 Nonlinear perturbation 39 Nonlinear spring 54 Nonlinear transformations 53 Nonlinear vibrators 61 Olech, C. 42 Olver, F. W. J. 95 Operator calculus 37 Orthogonal polynomials 113 Pade table 113 Periodic coefficients 79 Periodic solutions 54 Periodic surfaces 69 Perron, O. 48 Perturbation series 67 74 Perturbation techniques 23 25 69 Perturbation theorems 69 Perturbation theory 76 114 Phase shift 91 97 Phillippe, L. 61 Poincare — Lyapunov theorem 41 43 47 Poincare, H. 8 46 61 114 Potential scattering 91 Principle of localization 102 Pritulo, M. F 78 Projection operator formalism 37 quantum mechanics 26 Quasi-linearity 97 Quasilinearization 23 97 Quasiperiodic coefficients 79 Random walk 31 Recurrence relations 47 Rejto, P. A. 27 Relative invariants 45 Renormalization 57 Renormalization techniques 54 69 Retarded argument 53 Riccati equation 10 23 69 96 106 Richardson, J. M. 45 53 69 71 72 114 Ritt, J. F 11 Sack, R. A. 39 Sarsanov, A. A. 50 Scattering 31 Schiffer, M. 27 Schrodinger equation 95 98 Schwinger, J. 91 Second method of Lyapunov 42 Second solution 106 Secular term 55 56 Self-consistent techniques 67 72 Semigroups 50 Shah, S. M. 7 Shanks, D. 53 Shatz, S. S. 67 Shohat expansion 61 Shohat, J. 63 Shtokalo, J. 79 Silva, A. 61 Singular perturbations 51 Skalsky, M. 8 Smith, R. A. 57 64 Spectral function 91 Stability 41 Stability theory 15 42 86 Starzinsky, V. M. 79 Stekloff, O. 87 Stepanov, V. V. 42 Stieltjes, T. J. 8 114 Stoker, J. J. 61 Struble, R. A. 64 Sturm — Liouville equations 20 Sturm — Liouville problems 22 Sturrock, P. A. 8 Sudarshan, E. C. G. 37 Sugiyama, S. 53 Summability 53 Szego, G. 15 87 113 Taniuti, T. 55 Temple, G 5 78 Temple’s regularization technique 76 Time lags 52 Topfer, H. 50 Transition points 98 Transplantation 27 Tukey, J. W. 69 Two-point boundary-value problems 19 74 Urabe, M. 50 64 Uvarov, V. B. 95 98 van der Pol equation 59 64 67 70 Van der Pol, B. 54 Vandermonde’s convolution 8 Variation of parameters 12 Variational principles 23 31 97 Vasudevan, R. 67 Verde, M. 91 Volterra integral equation 17 von Karman, T. 5 Wasow, W. 47 51 Watson, G. N 8 11 113 Wave branching processes 102 Wave propagation 99 102 103 Weiss, G. H. 37 Whittaker, E. T. 8 113 Wiener’s integral 9 Wing, G. M. 31 32 Wintner, A. 55 89 WKB approximation 80 94 95 96 99 101 102 Wright, E. M 7 wronskian 13 Yaglom, A. M. 9
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