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Tenenbaum M., Pollard H. — Ordinary differential equations: an elementary textbook for students of mathematics, engineering, and the sciences
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 sciences

Авторы: Tenenbaum M., Pollard H.


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: en

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

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Предметный указатель
$D^{-n}$, inverse operator      270
$e^x,e^z$, 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($\pi$)      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 ($\nabla$, 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, $J_k(x)$      611—615
Bessel functions of the second kind, $—N_k(x)$      612
Bessel functions, $J_0(x), J_1(x)$      614
Bessel functions, $J_{-k}(x)$      613
Bessel functions, modified Bessel functions of the first kind      619
Bessel functions, properties of Bessel functions of the first kind, $J_k(x)$      619—622
Bessel functions, properties of Bessel functions of the first kind, $J_k(x)$, integral      620—622
Bessel functions, properties of Bessel functions of the first kind, $J_k(x)$, orthogonal, with respect to weight function x      622
Bessel functions, properties of Bessel functions of the first kind, $J_k(x)$, 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 $\delta$-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
1 2 3 4 5
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