Tenenbaum M., Pollard H. — Ordinary differential equations: an elementary textbook for students of mathematics, engineering, and the sciences :: Электронная библиотека попечительского совета мехмата МГУ

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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 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

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Предметный указатель

Principal value of $\theta$       199
Principle of superposition      211 254
Problem involving a centrifugal force      380
Problems, first order equations      107—195 377-7 377-10
Problems, first order equations, accretion      122—124
Problems, first order equations, atmospheric pressure      186—188
Problems, first order equations, body falling in water      144
Problems, first order equations, chain around a cylinder      188—189
Problems, first order equations, decomposition      131—132
Problems, first order equations, dilution      122—124
Problems, first order equations, electric circuit      184—185 377-7 377-10
Problems, first order equations, first order processes      137
Problems, first order equations, flow of heat, steady state      185—186
Problems, first order equations, flow through an orifice      183—184
Problems, first order equations, geometric      107—111
Problems, first order equations, growth      131—132
Problems, first order equations, horizontal motion      160—162
Problems, first order equations, inclined motion      164—166
Problems, first order equations, interest      126—127
Problems, first order equations, isogonal trajectory      115—117
Problems, first order equations, moon      151-6 151-7 151-8 156-38 156-39
Problems, first order equations, motion of a complex system      189—191
Problems, first order equations, oceanic pressure      186 187
Problems, first order equations, orthogonal trajectories      117—120
Problems, first order equations, pursuit curves      168—175
Problems, first order equations, raindrop      143
Problems, first order equations, relative pursuit curves      177—182
Problems, first order equations, rocket motion      191—193
Problems, first order equations, rope around a cylinder      188—189
Problems, first order equations, rotation of a liquid in a cylinder      193—194
Problems, first order equations, second order processes      134—137
Problems, first order equations, steady state flow of heat      185—186
Problems, first order equations, straight line motion      138—166
Problems, first order equations, temperature      129—130
Problems, first order equations, variable mass      191—193
Problems, first order equations, vertical motion      139—151
Problems, linear second order equations      313—389
Problems, linear second order equations, bending of beams      383—389
Problems, linear second order equations, circle, particle moving on circumference of      316—317
Problems, linear second order equations, damped harmonic motion      347—353
Problems, linear second order equations, damped harmonic motion, definition of      347
Problems, linear second order equations, damped motion, forced      359—364
Problems, linear second order equations, damped motion, free      347—353
Problems, linear second order equations, elastic helical spring      324—326
Problems, linear second order equations, elastic helical spring in parallel      330-13
Problems, linear second order equations, elastic helical spring in series      330-14
Problems, linear second order equations, electric circuit, simple      369—375
Problems, linear second order equations, forced motion with damping      359—364
Problems, linear second order equations, forced undamped motion      338—342
Problems, linear second order equations, free damped motion      347—353
Problems, linear second order equations, free undamped motion      313—329 see
Problems, linear second order equations, particle moving on a straight line      314—316
Problems, linear second order equations, particle moving on circumference of a circle      316—317
Problems, linear second order equations, pendulum, simple      see "Pendulum"
Problems, linear second order equations, problem involving a centrifugal force      380
Problems, linear second order equations, rolling bodies      381—383
Problems, linear second order equations, simple electric circuit      369—375
Problems, linear second order equations, simple harmonic motion      313—329 see
Problems, linear second order equations, straight line, particle moving on      314—316
Problems, linear second order equations, twisting bodies      383
Problems, linear second order equations, undamped motion      313—342
Problems, linear second order equations, undamped motion, examples of      323—329
Problems, linear second order equations, undamped motion, forced      338—342
Problems, linear second order equations, undamped motion, free      313—321
Problems, special types of second order nonlinear equations      506—530
Problems, special types of second order nonlinear equations, central force      521—522
Problems, special types of second order nonlinear equations, geometric      528—530
Problems, special types of second order nonlinear equations, pursuit      523—525
Problems, special types of second order nonlinear equations, special central force      521—522
Problems, special types of second order nonlinear equations, suspension cable      507—514
Problems, system of equations      440—492
Problems, system of equations, biological      447—451
Problems, system of equations, central force      see "Particle in motion in space subject to a central force"
Problems, system of equations, electrical      451—455
Problems, system of equations, mechanical      440—443
Problems, system of equations, particle in motion in space      see "Particle in motion in space subject to a central force"
Problems, system of equations, plane motion of a particle      see "Particle in motion in space subject to a central force"
Problems, system of equations, plane motion of a projectile      463—465
Problems, system of equations, planetary motion      491—492
Problems, system of equations, projectile in plane      463—465
Product of two operators      257
Projectile, motion of a      463—465
Proof by mathematical induction      250
Properties of Bessel function of first kind      619—622
Properties of Laguerre polynomials      627—630
Properties of Laplace transforms      295—296
Properties of Legendre polynomials      598—605
Properties of polynomial operators      see "Polynomial operators"
pure imaginary number      197
Pursuit curves      168—175 523—525
Pursuit curves, relative      177—182
Radioactive material      2
Radius of curvature      528
Raindrop problem      143
Range of a function      9 11
Ratio test for convergence      532
Real number system      197
Real part of a complex number      197
Rectangular form of a complex number      199
Recursion formula      577
Recursion formula for Bessel equation      610
Recursion formula for Hermite polynomial      607-18
Recursion formula for Laguerre equation      625
Recursion formula for Legendre polynomial      601
Reduction of order method      241—246
Region, bounded      14
Region, F-2 of atmosphere      155
Region, simply connected      71
Regular singularity      571
Regular singularity at $\infty$       586
Relative pursuit curve      177—182
Remainder function      670
Resistance, coefficient of      348
Resistance, electric      370
resistors      369
Resistors in series      454-2
Resonance      373 443
Resonance, undamped      341
Resonant frequency, undamped      341
Response of a system, impulsive      344
Riccati equation      97 247
Riemann integral      70
Riemann-integrable      70 731
Rocket motion      191—193
Rodrigue's formula      602
Rolling bodies      381—383
Roots in conjugate pairs      204-9
Roots of indicial equation      574—584
Roots, imaginary      217—220
Roots, real and distinct      213—214
Roots, real but some multiple      214—217
Rope around a cylinder      188—189
Rotating tube, particle in a      380
Rotation of a liquid      193—194
Rotational inertia      381
Rounding off errors      636 690
Runge — Kutta formulas for second order equation      709
Runge — Kutta formulas for system of two first order equations      702—703
Runge — Kutta formulas for y'=f(x,y)      653—658
Runge — Kutta formulas, comment on error in      657—658
Satellites      488—491 496
Second order equations      500—504 707—711 712-1 712-3
Second order equations, numerical solution of      707—711
Second order equations, numerical solution of, by Adams' method      712-3
Second order equations, numerical solution of, by Milne's method      710—711
Second order equations, numerical solution of, by Runge — Kutta method      709
Second order equations, numerical solution of, error in      712-1
Second order equations, special types of nonlinear      500—504
Second order processes, problems      134—137
Separable variables      52

Separated variables      52
Sequence of functions, convergence of a      728 732
Sequence of functions, uniform convergence of a      729 732
Series for and       201
Series for cos x and cos z      201
Series for sin x and sin z      201
Series for tan x      742
Series of functions      732—733
Series of functions, converges uniformly      732 733
Series, binomial      599
Series, convergence of      531 532
Series, defines a function      533
Series, determination of coefficients of a      534
Series, differentiation of a      534
Series, equality of      534
Series, expansion of inverse operators by      272—277
Series, Frobenius      572
Series, Frobenius, solution of homogeneous linear equation by      572—584
Series, Frobenius, solution of nonhomogeneous linear equation      585-18
Series, hypergeometers      587
Series, interval of convergence of      532
Series, Maclaurin      535
Series, partial sums of      732
Series, power      531
Series, ratio test for convergence of      532
Series, solutions by      see "Solution by series methods"
Series, Taylor      535
Series, Taylor, with remainder      537
Set, elements of a      6
Set, meaning of a      5—6
Simple beam      384
Simple electric circuit      369—375
simple harmonic motion      313—329
Simple harmonic motion, amplitude      317
Simple harmonic motion, definition of      314
Simple harmonic motion, description of the motion      315 317
Simple harmonic motion, elastic helical spring      324—326
Simple harmonic motion, equilibrium position      317
Simple harmonic motion, examples of bodies moving in      323—329
Simple harmonic motion, frequency, natural (undamped)      318 319
Simple harmonic motion, harmonic oscillators      323—329
Simple harmonic motion, natural (undamped) frequency      318 319
Simple harmonic motion, particle moving on a straight line      314—316
Simple harmonic motion, particle moving on circumference of a circle      316—317
Simple harmonic motion, pendulum      327—329
Simple harmonic motion, period      318
Simple harmonic motion, phase and phase angle      318
Simple harmonic motion, simple pendulum      327—329
Simple harmonic motion, spring, helical      324—326
Simply, connected region      71
Simply, supported beam      384
Simpson's rule      675 678 679 684
Simultaneous equations      see "Entries under System"
Sine x, sin z, expansions of      201
Sine, hyperbolic      203
Singular point of y'=f(x,y)      43 744—747
Singular solution      34
Singularity of a linear equation      570
Singularity of a linear equation, irregular      572
Singularity of a linear equation, regular      571
Singularity of a linear equation, regular at $\infty$       586
Sixth degree interpolating polynomial      677
Sliding friction      160
Slope field      39
Slowly varying amplitude      345
Solution about a regular singularity      572—584 585 586
Solution about a regular singularity at $\infty$       586
Solution about a regular singularity of a homogeneous linear equation, where roots of indicial equation, differ by an integer      578—582
Solution about a regular singularity of a homogeneous linear equation, where roots of indicial equation, do not differ by an integer      574—578
Solution about a regular singularity of a homogeneous linear equation, where roots of indicial equation, equal      583—584
Solution about a regular singularity of a nonhomogeneous linear equation      585-18
Solution by series methods      537—584
Solution by series methods by Frobenius series      see "Solution about a regular singularity"
Solution by series methods by Taylor series of a linear equation      537—546
Solution by series methods by Taylor series of a nonlinear equation of order n      562—567
Solution by series methods by Taylor series of a system of first order equations      555—559
Solution by series methods by Taylor series of a system of linear first order equations      559—562
Solution by series methods by Taylor series of y'=f(x,y)      548—553
Solution of a system of equations      394—420
Solution of a system of equations by numerical methods      702—706
Solution of a system of equations by Picard's method      723—726 726-9
Solution of a system of equations by series method      555—562 see
Solution of a system of equations of a first order linear system      396—397
Solution of a system of equations of a first order system      394—396
Solution of a system of equations of a linear system with constant coefficients      398—420
Solution of a system of equations of a linear system with constant coefficients by Laplace transforms      418—420
Solution of a system of equations of a linear system with constant coefficients by polynomial operators      398—417
Solutions of differential equations by integrating factors      82—90 94
Solutions of differential equations by inverse operators      272—282 288—291
Solutions of differential equations by Laplace transforms      296—302
Solutions of differential equations by lineal element diagram      39
Solutions of differential equations by method of Frobenius      572—584
Solutions of differential equations by numerical methods      631—718
Solutions of differential equations by operators      262—265 272—282 288—291
Solutions of differential equations by partial fraction expansion of inverse operators      288—291
Solutions of differential equations by Picard's method of successive approximations      720—726
Solutions of differential equations by polynomial operators      262—265
Solutions of differential equations by power series      537—553 562—567
Solutions of differential equations by reduction of order      242—246
Solutions of differential equations by separation of variables      51—55
Solutions of differential equations by series      537—553 562—567
Solutions of differential equations by substitution and other means      101
Solutions of differential equations by successive approximations      720—726
Solutions of differential equations by undetermined coefficients      221—230
Solutions of differential equations by variation of parameters      233—240
Solutions of differential equations, by choice of method      99
Solutions of differential equations, by complex variables      230—231
Solutions of differential equations, definition of      22
Solutions of differential equations, existence of      see "Existence and uniqueness theorems"
Solutions of differential equations, explicit      21—23
Solutions of differential equations, general      28—37
Solutions of differential equations, general, definition of      35
Solutions of differential equations, implicit      24—27
Solutions of differential equations, linear combination of      208
Solutions of differential equations, multiplicity of      28—31
Solutions of differential equations, n-parameter family of      30 31—33
Solutions of differential equations, number of independent      208 786
Solutions of differential equations, particular      35
Solutions of differential equations, singular      34
Solutions of differential equations, steady state      361 372
Solutions of differential equations, transient      361 372
Solutions of differential equations, uniqueness of      see "Existence and uniqueness theorems"
Solutions of differential equations, Wronskian of      781-Comment 64.15
Solve a differential equation, meaning of      22 81
Special central force problem      521—522
Special types of second order equations      500—504
Special types of second order equations, x absent      503—504
Special types of second order equations, x and y' absent      500—501
Special types of second order equations, y absent      502—503
Specific, gravity      153
Specific, heat      130
Specific, weight      512
Speed of escape      148
Speed, terminal      142
Spring constant      324
Spring, helical      see "Elastic helical springs"
Sputnik      491-7
Stable motion      339
Starting formula      680
Starting methods      632
Starting methods, polygonal method      see "Polygonal method"
Starting methods, polygonal method, an improvement of      641—643
Starting methods, Runge — Kutta      see "Runge — Kutta formulas"
Starting methods, Taylor series      645—652
Static friction      160
Steady state, current      372
Steady state, flow of heat      185—186
Steady state, motion      361
Steady State, Solution      361 372
Stiffness coefficient of a spring      324

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