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Tenenbaum M., Pollard H. — Ordinary differential equations: an elementary textbook for students of mathematics, engineering, and the sciences
 Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Ordinary differential equations: an elementary textbook for students of mathematics, engineering, and the sciences Авторы: 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. We do not wish to imply, however, that you will be able to read this text as if it were a novel. If you wish to derive any benefit from it, you must study each page slowly and carefully. You must have pencil and plenty of paper beside you so that you yourself can reproduce each step and equation in an argument. When we say "verify a statement," "make a substitution," "add two equations," "multiply two factors," etc., you yourself must actually perform these operations. If you carry out the explicit and detailed instructions we have given you, we can almost guarantee that you will, with relative ease, reach the conclusion. One final suggestion—as you come across formulas, record them and their equation numbers on a separate sheet of paper for easy reference. You may also find it advantageous to do the same for Definitions and Theorems. Язык: Рубрика: Математика/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1985 Количество страниц: 819 Добавлена в каталог: 05.11.2010 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
Предметный указатель
 , inverse operator      270 , expansion of      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 (, del)      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, , integral      620—622 Bessel functions, properties of Bessel functions of the first kind, , orthogonal, with respect to weight function x      622 Bessel functions, properties of Bessel functions of the first kind, , zeros      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 -function      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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