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

Stiffness constant, torsional      383
Straight line motion      138—166 314—316
Subnormal      112-1
Substitution, solving an equation by      101
Subtangent      112-1
Successive approximations      see "Picard's method of successive approximations"
Sum of two operators      256
Superposition principle      211 254
Surface, isothermal      185
Surface, neutral      384
Suspension cable      507—514
System of equations, meaning of a solution of a      393 see "System "System
System of first order equations, definition of a      394
System of first order equations, errors in numerical solution of      703
System of first order equations, existence and uniqueness theorem for      763—765
System of first order equations, linearization of      424—438
System of first order equations, Milne formula for a      703
System of first order equations, Picard's method of solution of a      723—726 726-9
System of first order equations, problems giving rise to a      see "Problems system
System of first order equations, Runge — Kutta formula for a      702—703
System of first order equations, series method of solution of a      555—562
System of first order equations, solution of a by numerical methods      702—706
System of first order equations, solution of a by Picard's method      723—726 726-9
System of first order equations, solution of a by series methods      555—562
System of first order equations, special types of second order equations giving rise to a      500—504
System of linear equations with constant coefficients of three equations      415—420
System of linear equations with constant coefficients, definition of a      398
System of linear equations with constant coefficients, degenerate      413—445
System of linear equations with constant coefficients, determinant of      399 400
System of linear equations with constant coefficients, equivalent triangular      405—413
System of linear equations with constant coefficients, general solution of a      398 399
System of linear equations with constant coefficients, problems giving rise to a      see "Problems system
System of linear equations with constant coefficients, solution of a by Laplace transforms      418—420
System of linear equations with constant coefficients, solution of a by operators      398—417
System of linear first order equations      396—397
System of linear first order equations, definition of a      396
System of linear first order equations, existence and uniqueness theorem for a      768—770
System of linear first order equations, problems leading to a      see "Problems system
System of linear first order equations, solution of a by numerical methods      702—706
System of linear first order equations, solution of a by Picard's method      723—726 726-9
System of linear first order equations, solution of a by series methods      555—562 see "System
Table, chain sliding from      190
Tables of differences      660 662 663 670
Tables of Laplace transforms      306 310
Tan x, expansion of      742
Tangent, hyperbolic      203
Taylor series      535
Taylor series with remainder      537
Taylor series, review of      531—537
Taylor series, solution by      645—652
Taylor series, solution by, comment on error in      649—652 653-4
Taylor series, solution by, creeping up process      646—647
Taylor series, solution by, direct substitution      646 see
Tchebycheff      see "Tschebyscheff's"
Temperature problems      129
terminal velocity      142
thermal conductivity      185
Third degree interpolating polynomial      676 678 679
Three-eighths rule      681
time constant      351
torque      381

Torsional, resistance constant      499
Torsional, stiffness constant      383 498
Total differential      72
Tractrix      176-6
Trajectories      115—120
Trajectories, isogonal      115—117
Trajectories, isogonal, definition of      115
Trajectories, orthogonal      117—120
Trajectories, orthogonal in polar coordinates      118
Trajectories, orthogonal in rectangular coordinates      117
Trajectories, orthogonal, definition of      117
Transient, current      372
Transient, motion      361
Transient, solution      361 372
Trapezoidal rule      675 678 679 682
Triangular system, equivalent      405 406 416
Trigonometric functions of complex numbers      201
Tschebyscheff's, equation      589
Tschebyscheff's, polynomials      589
Twice differentiable function, definition of      749
Twisting bodies      383
Undamped frequency      318—319
Undamped motion      313—342
Undamped motion, examples of      323—329
Undamped motion, forced      338—342
Undamped motion, free      see "Simple harmonic motion"
Undamped, resonance      341
Undamped, resonant frequency      341
Underdamped      351
Undetermined coefficients      221—230
Uniform convergence of a sequence of functions      729 732
Uniform convergence of a series of functions      732—733
Uniqueness theorems      see "Existence and uniqueness theorems"
Unit impulse function      344
Universal gravitation, Newton's law of      491
Unstable motion      340
Vanish identically, definition of      775
Variable mass      191—193
Variables, separable      52
Variables, separated      52
Variation of parameters      233—240
Varying amplitude, slowly      345
Vector, point-function      473
Vector, quantities      164 459
Velocity of escape      148
Velocity, formulas in polar coordinates      461
Velocity, terminal      142
Vertical motion      139—151
Vertical motion, body far from earth's surface      146—151
Vertical motion, body near earth's surface, air resistance      142—145
Vertical motion, body near earth's surface, no resistance      140—141
Volt      369
Voltage drop      369
Weddle's rule      677 678 679 691 703
Weight, specific      512
Wronskian, Abel's formula for      779
Wronskian, definition of      774
Wronskian, determinant of      774
Wronskian, determining linear dependence and independence by      775-Comment 63.56
Wronskian, determining linear dependence and independence of solutions by      781-Comment 64.15
Wronskian, theorems about      778—780
Young's modulus      385

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