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.
Stiffness constant, torsional383 Straight line motion138—166314—316 Subnormal112-1 Substitution, solving an equation by101 Subtangent112-1 Successive approximationssee "Picard's method of successive approximations" Sum of two operators256 Superposition principle211254 Surface, isothermal185 Surface, neutral384 Suspension cable507—514 System of equations, meaning of a solution of a393see"System"System System of first order equations, definition of a394 System of first order equations, errors in numerical solution of703 System of first order equations, existence and uniqueness theorem for763—765 System of first order equations, linearization of424—438 System of first order equations, Milne formula for a703 System of first order equations, Picard's method of solution of a723—726726-9 System of first order equations, problems giving rise to asee "Problemssystem System of first order equations, Runge — Kutta formula for a702—703 System of first order equations, series method of solution of a555—562 System of first order equations, solution of a by numerical methods702—706 System of first order equations, solution of a by Picard's method723—726726-9 System of first order equations, solution of a by series methods555—562 System of first order equations, special types of second order equations giving rise to a500—504 System of linear equations with constant coefficients of three equations415—420 System of linear equations with constant coefficients, definition of a398 System of linear equations with constant coefficients, degenerate413—445 System of linear equations with constant coefficients, determinant of399400 System of linear equations with constant coefficients, equivalent triangular405—413 System of linear equations with constant coefficients, general solution of a398399 System of linear equations with constant coefficients, problems giving rise to asee "Problemssystem System of linear equations with constant coefficients, solution of a by Laplace transforms418—420 System of linear equations with constant coefficients, solution of a by operators398—417 System of linear first order equations396—397 System of linear first order equations, definition of a396 System of linear first order equations, existence and uniqueness theorem for a768—770 System of linear first order equations, problems leading to asee "Problemssystem System of linear first order equations, solution of a by numerical methods702—706 System of linear first order equations, solution of a by Picard's method723—726726-9 System of linear first order equations, solution of a by series methods555—562see"System Table, chain sliding from190 Tables of differences660662663670 Tables of Laplace transforms306310 Tan x, expansion of742 Tangent, hyperbolic203 Taylor series535 Taylor series with remainder537 Taylor series, review of531—537 Taylor series, solution by645—652 Taylor series, solution by, comment on error in649—652653-4 Taylor series, solution by, creeping up process646—647 Taylor series, solution by, direct substitution646see Tchebycheffsee "Tschebyscheff's" Temperature problems129 terminal velocity142 thermal conductivity185 Third degree interpolating polynomial676678679 Three-eighths rule681 time constant351 torque381
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