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Davis H.T. Ч Introduction to nonlinear differential and integral equations
Davis H.T. Ч Introduction to nonlinear differential and integral equations

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Ќазвание: Introduction to nonlinear differential and integral equations

јвтор: Davis H.T.

јннотаци€:

topics covered include differential equations of the first order, the Riccati equation and existence theorems, second order equations, elliptic integrals and functions, the technique of continuous analysical continuation, the phenomena of the phase plane, nonlinear mechanics, nonlinear integral equations, problems from the calculus of variations and more. 1960 ed. 137 problems.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2010

 оличество страниц: 593

ƒобавлена в каталог: 01.12.2013

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel's equation      74Ч75
Abel, N.H.      74 145 545
Action, definition of      457
Adams Ч Bashfortli method      481
Adams, J.C.      481
Agnew, R.P.      545
Airey, J.R.      373
Airy, G.B.      368
Algebraic functions      7
Almost periodic functions      290Ч291
Ampere, A.M.      19
Analytic continuation      245 246 Chap.
Andrews, A.H.      61
Andronow, A.      545
Antosiewicz, H.A.      545
Appell, P.      545
Appleton, e.v.      545
Archibald, R.C.      114 545
Archimedes      439
Asymptotic series      5
Automorphic functions, definition of      222
Autonne, L.      545
Ayre, R.S.      551
Baggott, E.A.      31 553
Baker, E.D.      406Ч407
Balze, O.      443
Barocio, S.      545
Bashforth, F.      481
Bass, R.W.      545
Bateman, H.      20 21 455 545
Bautin, N.N.      344 346 545
Bellman, R.      545
Bendixson's theorem      354Ч355
Bendixson, I.      186 309 351Ч352 354Ч355 545
Bernhart, A.      545
Bernoulli numbers      473
Bernoulli's equation      49
Bernoulli, Daniel      58 546
Bernoulli, James      49 57 473
Bernoulli, John      57 546
Berry, A.      546
Besicovitch, A.S.      290
Bessel functions      4 5 68Ч70
Bieberbach, L.      21 546
Birkhoff, G.D.      285 546
Blasius equation      16 400Ч405
Blasius, H.      16 400Ч404 546
Block, H.      546
Blodgett, Katherine B.      552
Bocher, M.      83
Bochner, S.      546
Bogoliuboff, N.      365 367 552
Bohr, H.      290
Boltzmann, L.      284
Bompiani, E.      546
Boole, G.      115 546
Bouguer, P.      114Ч115
Bouquet, j.c.      79
Boutroux, M.P.      232 242 244 54
Branch points      14 185 225
Brassinne, E.      546
Bratu's equation      432Ч434
Bratu, G.      415 432Ч434 546
Briot, C.      79
Brocard, H.      114
Brodetsky, S.      26
Brown, E, W.      285
Brownell, F.H.      546
Brucht, G.      546
Burkhardt      161
Bush, V.      407 547
Bushaw, D.      547
C-discriminant      50 54
Cajori, F.      172
Calculus of limits      79Ч83 190Ч191
Calculus of variations      Chap. 14
Calculus of variations, Fundamental Lemma of      443
Calculus of variations, necessary conditions for extremals in      449Ч450
Caldwell, S.H.      407 547
Capture point      117 123Ч124
Caque, J.      83
Carleman, T.      454 547
Carlson, A.J.      61
Cartan, E.      20
Cartwright, Mary L.      368 547
Cauchy Ч Lipschitz, method of      88Ч93
Cauchy, A.L.      19 79 88 468
Cavalieri, F.B.      478
Cayley, A.      53 58 547
Center      322
Center, conditions for      350
Cepheid variable stars      368Ч371
Ceskro, E.      299
Chaikin, S.      545
Challis, H.W.      547
Chandrasekhar, S.      377 408 547
Characteristic equation      311 317
Chiellini, A.      547
Chrystal's equation      51Ч53
Chrystal, G.      51 55 547
Clairaut's equation      49Ч51
Clairaut, A.C.      49
Clebsch, R.F.A.      19
Coddington, E.A.      547
Coefficient of heredity      113
Collet, A.      547
Complementary elliptic integral      131
Complete elliptic integrals, definition of      131
Complete elliptic integrals, definition of, differential equations of      137
Complete elliptic integrals, definition of, expansions of      133Ч135
Continued fractions      70Ч72
Continuous analytic continuation      Chap. 9
Continuous analytic continuation, application around a singular point      263Ч266
Continuous analytic continuation, method of      251Ч256
Convolution, nonlinear      434Ч437
Copson, E.T.      547
Corbeiller, Ph.Le      547
Cotton, E.      414 547
Critical points      14 185 225
Curvature, method of      29Ч32 248Ч249
Curves of pursuit      see "Pursuit"
Cusp-locus      54Ч56
d'Adhemar, R.      545
D'Alembert      53
D'Alembert's equation      53
da Vinci, Leonado      95
Darboux, J.G.      19 53 547
Davis, H.T.      295 302 548
De Baggio, H.F.      548
de Maupertuis, P.L.M.      114 440 457
De Vogelaere, R.      548
Delaunay, C.      285
Dido's problem      439 445Ч447
Differential equation of third order, Blasius      16 400Ч405
Differential equations of first order      Chap. 2
Differential equations of first order, Abel's      74Ч75
Differential equations of first order, Bernoulli's      49
Differential equations of first order, Chrystal's      51Ч53
Differential equations of first order, Clairaut's      49Ч51
Differential equations of first order, d'Alembert's      53
Differential equations of first order, graphical method of solution      26Ч29
Differential equations of first order, homogeneous case of      36Ч45
Differential equations of first order, Riccati's      Chap. 3
Differential equations of first order, solution by isoclines and curvature      29Ч32
Differential equations of second order      Chap. 7 Chap.
Differential equations of second order of polynomial class      Chap. 8
Differential equations of second order with fixed critical points      184Ч185 225Ч228
Differential equations of second order with periodic solutions      186 297Ч308 339Ч351
Differential equations of second order, classification of      182Ч189
Differential equations of second order, Duffing's      15 180 271 386Ч400
Differential equations of second order, elliptic      14 179 183Ч184 194Ч211 270
Differential equations of second order, Emden type      381Ч386 408
Differential equations of second order, Emden's      15 181 371Ч377
Differential equations of second order, existence theorems for      189Ч192
Differential equations of second order, generalized Riccati      76Ч79 186 218Ч221
Differential equations of second order, Kidder's      16 410Ч411
Differential equations of second order, Langmuir's      16 181
Differential equations of second order, Painleve's      14 185 229Ч244 233Ч234 239Ч244 258Ч261 263Ч266 501Ч504
Differential equations of second order, Painleve's, values of      507Ч530
Differential equations of second order, Rayleigh's      15 181 186Ч187
Differential equations of second order, Thomas Ч Fermi's      16 405Ч407
Differential equations of second order, Van der Pol's      15 17 181 186Ч187 270 358Ч368
Differential equations of second order, Van der Pol's, values of      531Ч536
Differential equations of second order, Volterra's      102 180 270 324Ч327 355
Differential equations of second order, Volterra's, values of      537Ч542
Differential equations of second order, Volterra's, white dwarf      16 408
Diliberto, S.P.      548
Dirichlet, P.G.L.      291 455
Doetsch, G.      548
Dorodnicyn, A.A.      368 548
Douglas, J.      454
Duff, G.F.      548
Duffin, R.J.      548
Duffing's equation      15 180 271 386Ч400
Duffing, G.      15 180 271 386 395 548
Dulac, H.      343 548
Duncan, J.C.      368
Dunoyer, L.      114 548
Eckweiler, H.J.      548
Eddington, A.S.      376 548
Einstein, A.      180
Elliptic equations      14 179 183Ч184 194Ч211 270
Elliptic functions      Chap. 6 see elliptic "Weier-strass elliptic
Elliptic integrals      Chap. 6
Elliptic integrals, computation of      137Ч141
Elliptic integrals, expansions of      135Ч137
Elliptic integrals, first kind      131
Elliptic integrals, second kind      131
Elliptic integrals, tables of      142Ч143
Elliptic integrals, third kind      132
Elliptic modular functions      169Ч171
Elliptic modular functions, use in solving quintic      172Ч175
Emde, F.      203 551
Emden type equations      381Ч386 408
Emden's equation      15 181 371Ч377
Emden, R.      15 181 371 376Ч378 381 548
Equation, differential      see "Differential equations"
Equation, differential of continuity      21
Equation, differential, Euler's      15 443
Equation, differential, Liouville's      20 377
Equation, differential, Navier Ч Stokes      21
Equation, differential, Poisson's      19
Equations, integral      Chap. 13 see
Equations, numerical integration of      Chap. 15
Equations, numerical integration of by Adams Ч Bashforth method      481
Equations, numerical integration of by continuous analytic continuation      Chap. 9
Equations, numerical integration of by Milne method      486Ч488 491
Equations, numerical integration of by Runge Ч Kutta method      482Ч486
Equations, with fixed critical points      495Ч498
Equiharmonic case of elliptic functions      161
Equivalent linearization      367
Ergchorad      285
Ergodic theorem      285
Euler cordition      441Ч445
Euler cordition for double integrals      450Ч452
Euler cordition in isoperimetric case      445Ч447
Euler equation      15 443
Euler Ч Maclaurin formula      473
Euler's theorem on homogeneous functions      36
Euler, L.      1 15 36 58 162 440 441Ч447 473 548
Evans, G.C.      414 548
Excess function      441
Existence theorems      Chap. 4 189Ч192 415Ч416 424Ч425
Exponents, preservation of      215
Exponents, preservation of, theorems concerning      215Ч218
Extremal, definition of      443
Extremal, definition of, necessary conditions for      449Ч450
Falkenhagen, J.H.M.      548
Falkner, V.M.      400 548
Falling body, velocity of      60Ч62
Farnell, A.B.      552
Faulkner, J.E.      344 346
Fejer, L.      299
Fermat, P.      440 456Ч457
Fermi, E.      405 548
Finite differences, calculus of      468Ч472
Fisher, R.A.      61
Flanders, D.      549
Fletcher, A.      140
Floquet's theory      300Ч303
Floquet, O.      300Ч303
Focus      268 314 322
Forcing functions and phase curves      273Ч283
Ford, L.R.      214 222 549
Forsyth, A.R.      20 54 444 549
Fourier series, in pendulum problem      291Ч297
Fourier series, in pendulum problem in expansion of Jacobi's elliptic functions      167Ч169
Fourier series, in pendulum problem in problem of periodicity      298Ч300
Fourier series, in pendulum problem in solution of Duffing's equation      388Ч396
Fourier, J.      162 291 434
Fredholm's nonlinear integral equation      424Ч433
Fredholm's nonlinear integral equation, existence theorem for      424Ч425
Fredholm, I.      414 424Ч425
Friedricks, K.O.      549
Frommer's curve      341Ч342
Frommer's theorem      341
Frommer, M.      340Ч341 343 350 549
Fuchs, L.      83
Functions, automorphic      222
Functions, Bessel's      4 5 68Ч70
Functions, classification of      7
Functions, elliptic modular      169Ч171
Functions, homogeneous      36
Functions, Jacobi's elliptic      145Ч156
Functions, Mathieu's      303
Functions, theta      162Ч167
Functions, Weierstrass elliptic      156Ч161
Gambier, B.      183Ч185 223 225 493 549
Garnier, R.      549
Gas spheres, isothermal      377Ч378
Gas spheres, theory of      371Ч377
Gause, G.F.      102
Gauss's limit      144
Gauss, C.F.      19 144 145
Generalized coordinates      458
Generalized Riccati equation      76Ч79 186 218Ч221
Geppert, H.      144
Gerber, P.      180 549
Glaisher, J.W.L.      58 549
Goldstein, S.      400 549
Golomb, M.      549
Gomory, R.E.      549
Gompertz curve      98
Gompertz, B.      98
Goursat, E.J.B.      20 54 89Ч90 443 550
Graffi, D.      550
Green, G.      451
Greenhill, A.G.      58 160 168 203 550
Gregory formula      474
Gregory Ч Newton formula      469
Gregory, J.      469 474 478
Greig, J.      547
Gronwall, T.H.      550
Groups, associated with linear fractional transformation      222
Growth, hereditary factor in      112Ч113 413 417Ч423
Growth, problem of      99Ч112
Gudermann, C.      152 550
Guigue, R.      550
Haag, J.      368 550
Haar, A.      454
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