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Tenenbaum M., Pollard H. — Ordinary differential equations: an elementary textbook for students of mathematics, engineering, and the sciences
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Название: Ordinary differential equations: an elementary textbook for students of mathematics, engineering, and the sciencesАвторы: Tenenbaum M., Pollard H. Аннотация: This book has been written primarily for you, the student. We have tried to make it easy to read and easy to follow.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1985Количество страниц: 819Добавлена в каталог: 05.11.2010Операции: Положить на полку |
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270 201 Abel's formula 779 Absolute value of a complex number 198 Acceleration in polar coordinates 461 Acceleration in rectangular coordinates 460 Acceleration, Definition of 138 Acceleration, due to gravity 140 Accretion problems 122—124 Adams' method, second order equation 712-3 Adams' method, y'=f(x,y) 681 Air resistance 141 Airplane problems see "Pursuit curves" Algebra of complex numbers 200—201 Algebra of operators 255—259 Algebra, fundamental theorem of 197 198 Amplification ratio 363 Amplitude 317 Amplitude, damped 351 Amplitude, modulated 345 Amplitude, slowly varying 345 Analog computation 375—376 Analytic function 537 548 Analytic function on an interval 537 Analytic geometry, review of 62 Apogee 490 Approximations by Picard method see "Picard's method of successive approximations" Approximations by polynomial interpolation see "Polynomial interpolation" Approximations to e 639-9 644-8 Approximations to integrals see "Numerical methods" Approximations to log 2 639-10 644-9 Approximations to pi( 639-8 644-7 Arbitrary constants 129 130 Arc length of a curve 111 Arc tan x, expansion of 533 537 Archimedes' principle 335 Argument (Arg) of a complex number 199 Arithmetical errors 636 Associative law for operators of addition 256 Associative law for operators of multiplication 257 Atmospheric pressure 186—188 Axis of a beam 383 Backward differences ( 668—670 Beams, axis of 383 Beams, bending moment of 384 Beams, bending of 383—389 Beams, cantilever 384 Beams, condition of continuity of curve of 387 Beams, condition of continuity of slope of 387 388 Beams, elastic curve of 384 Beams, modulus of elasticity of 385 Beams, neutral surface of 384 Beams, simple 384 Beams, simply supported 384 Beams, Young's modulus of 385 Beats 346 Bending moment 384 Bending of beams see "Beams" Bernoulli equation 95—96 Bessel equation 579 583 609—622 Bessel equation of index 1/2 579 Bessel equation of index zero 583 Bessel equation, equations leading to a 615—619 Bessel functions 611—622 Bessel functions of the first kind, 611—615 Bessel functions of the second kind, 612 Bessel functions, 614 Bessel functions, 613 Bessel functions, modified Bessel functions of the first kind 619 Bessel functions, properties of Bessel functions of the first kind, 619—622 Bessel functions, properties of Bessel functions of the first kind, 620—622 Bessel functions, properties of Bessel functions of the first kind, 622 Bessel functions, properties of Bessel functions of the first kind, 619—620 beta function 306 Binomial series 599 Biological problem 447—451 Body falling in water 144 Bounded region 14 Bridge, over gorge 362 Bridge, troops crossing a 362 Buoyancy 335 Cable, hanging 507—512 Cable, suspension 507—514 Calorie 185 Cantilever beam 384 Capacitance 370 Capacitor 369 Capacitor in series 455-3 Carbon-14 test 5 Catenary 510 Cave, prehistoric 2 Center of attraction 470 Central force 380 470 see Centrifugal force 380 Centripetal force 380 Chain around a cylinder 188—189 Chain sliding from a table 190 Characteristic equation 212—220 444 Characteristic equation, definition of 212 Characteristic equation, roots of imaginary 217—220 Characteristic equation, roots of real and distinct 213—214 Characteristic equation, roots of real but some multiple 214—217 Charcoal problem 2 Charge, electric 370 Circuit, closed electric 369 see Clairaut equation 757—760 Clairaut equation, geometric problems giving rise to 761 Clairaut equation, parabolic reflector 759—760 Closed electric circuit 369 Coefficient of friction 160 Coefficient of inductance 370 Coefficient of resistance 348 Coefficient of sliding friction 160 Coefficient of static friction 160 Combination, linear 205 Commutative law for operators of addition 256 Commutative law for operators of multiplication 258 Complementary function 210 Complete elliptic integral of the first kind 333 Complex electric circuits 451—455 Complex functions 201—203 Complex functions, exponential 201 Complex functions, hyperbolic 203 Complex functions, trigonometric 201 complex numbers 197—201 Complex numbers, absolute value of 198 Complex numbers, algebra of 200—201 Complex numbers, argument (Arg) of 199 Complex numbers, conjugate of 198 Complex numbers, definition of 197 Complex numbers, imaginary part of 197 Complex numbers, polar form of 199 Complex numbers, real part of 197 Complex numbers, rectangular form of 199 Complex variables 201—203 Complex variables, solution by use of 230 Compound interest 128-5 128-6 Computation, analog 375—376 Condition of continuity of a curve 387 Condition of continuity of a slope 387 388 Conductivity, thermal 185 Conic, equation in polar coordinates 483 Conjugate of a complex number 198 Conservation of angular momentum 472 Conservation of energy 329 475 Conservative field 473 Construction of a table of Laplace transforms 302—306 309—311 Continuing formulas, Adams 681 712-3 Continuing formulas, improvement of polygonal method 641—643 Continuing formulas, polygonal see "Polygonal method" Continuing formulas, Runge — Kutta see "Runge — Kutta method" Continuing formulas, Taylor series 645—652 Continuing formulas, third degree interpolating polynomial 676 Continuing methods 632 Continuous function 732 Continuous function at a point 730 Continuous function in a region 731 Continuous function on an interval 730 Convergence of a sequence of functions 728 732 Convergence of improper integral 292 294 Convergence of power series 531—532 Convergence, interval of 532 Convergence, ratio test for 532 Convergence, uniform of a sequence of functions 729 732 Convergence, uniform of a series of functions 732—733 Coordinates of a point 6 Corrector formulas 680 Corrector formulas, fifth degree polynomial 676 Corrector formulas, Simpson 675 Corrector formulas, sixth degree polynomial 677 Corrector formulas, three-eights rule 681 Corrector formulas, trapezoidal 675 Corrector formulas, Weddle's rule 677 Corrector methods 632 Cosine x, cosine z, expansions of 201 Cosine, hyperbolic 203 Coupled springs 440—443 Critically damped 350 Cumulative errors 636 690 Current, electric 369 370 Current, induced 185 Current, steady state 372 Current, transient 372 Curvature, radius of 528 Curve, elastic 384 Curves of pursuit 168—175 523—525 Curves, envelopes of a family of 748—754 Cycloid 335 D, differential operator 251 Damped, amplitude 351 Damped, critically 350 Damped, frequency 351 Damped, harmonic motion 348—353 Damped, motion 347—353 359—364 Damped, motion, definition 347 Damped, motion, forced 359—364 Damped, motion, free (damped harmonic) 348—353 Damped, period 351 Damped, periodic 351 Damping factor 351 Decomposition problems 131—132 Decrement, logarithmic 356 Degenerate systems 413—415 Dependence see "Linear dependence of functions" Determinant of a system of equations 400 Determinant, definition of 399 770 771 Determinant, Grammian 777 Determinant, theory of 770—774 Determinant, Wronskian 774 Diagram, lineal element 39 Differences, backward 668—670 Differences, finite 659—661 Differences, forward 659—668 Differences, tables of 660 662 663 670 Differential equations of first order see "First order equations" Differential equations with homogeneous coefficients 57—60 Differential equations with linear coefficients 63—68 Differential equations with separable variables 51—55 Differential equations, Bernoulli 95—96 Differential equations, Bessel 579 583 609—622 Differential equations, Clairaut 757—760 Differential equations, definition of ordinary 20 Differential equations, Euler 247 Differential equations, exact 70—78 248—26 Differential equations, exact, definition of 73 Differential equations, exact, recognizable 80—82 Differential equations, existence of solutions of see "Existence and uniqueness theorems" Differential equations, explicit solution of a 22 Differential equations, finding a, from its n-parameter family 31—33 Differential equations, finding an integrating factor 84—90 94—95 248 Differential equations, finding an integrating factor for first order 84—90 Differential equations, finding an integrating factor for linear first order 94—95 Differential equations, finding an integrating factor for linear second order 248 Differential equations, Gauss's 587 Differential equations, general solution of 28—37 Differential equations, general solution of, definition 35 Differential equations, Hermite 607 Differential equations, homogeneous in x 505 Differential equations, hypergeometric 589 Differential equations, implicit solution of 24 Differential equations, initial conditions 36 Differential equations, integral curve of, definition 39 Differential equations, integrating factor of see "Integrating factors" Differential equations, Laguerre 624—630 Differential equations, Legendre 586 591—605 606-13 Differential equations, linear of first order 91—95 Differential equations, linear of higher order see "Linear differential equations" Differential equations, miscellaneous first order 101—103 Differential equations, multiplicity of solutions of 28 Differential equations, n-parameter family of solutions of 30 Differential equations, nonlinear see "Nonlinear equations" Differential equations, numerical solutions of see "Numerical methods" Differential equations, order of 21 Differential equations, ordinary 20 Differential equations, partial 20 Differential equations, particular solution of 35 Differential equations, recognizable exact 80—82 Differential equations, Riccati 97 247-22 23 24 Differential equations, singular, point of 43 Differential equations, singular, solution of 34 Differential equations, solution of a, definition 22 Differential equations, systems of see "System of equations" Differential equations, Tschebyscheff 589 Differential equations, variables separable 51—55 Differential of a function 47—51 Differential of one independent variable 48 Differential of two independent variables 50 Differential, exact 72 Differential, operator 251 Differential, total 72 Dilution problems 122—124 Dirac 344 Direction field 39 Direction field, construction of a 38—41 Direction field, isoclines of a 40—41 Distributive law of multiplication for operators 258 Divergence of improper integrals 292 Domain of independent variable 9 11 e, an approximation to 639-9 644-8 Elastic curve 384 Elastic helical spring in series 330-14 Elastic helical springs 324—326 Elastic helical springs, parallel 330-13 Elasticity, modulus of 385 Electric circuits, complex 451—455 Electric circuits, first order 184—185 377-7 10 Electric circuits, simple 369—375 Electromotive force 369 Electromotive force, induced 185 Element of a set 6 Element, line 39 Element, lineal 39 Elementary functions 17 Eliminant 750 Ellipse, equation in polar coordinates 483 Elliptic integral of the first kind, complete 333 Elliptic integral of the first kind, incomplete 334 Energy, inverse square law 487—488 Energy, kinetic 329 475 Energy, law of conservation of 329 475
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