Tenenbaum M., Pollard H. — Ordinary differential equations: an elementary textbook for students of mathematics, engineering, and the sciences
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Íàçâàíèå: Ordinary differential equations: an elementary textbook for students of mathematics, engineering, and the sciences
Àâòîðû: Tenenbaum M., Pollard H.
Àííîòàöèÿ:
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.
Principal value of 199 Principle of superposition211254 Problem involving a centrifugal force380 Problems, first order equations107—195377-7377-10 Problems, first order equations, accretion122—124 Problems, first order equations, atmospheric pressure186—188 Problems, first order equations, body falling in water144 Problems, first order equations, chain around a cylinder188—189 Problems, first order equations, decomposition131—132 Problems, first order equations, dilution122—124 Problems, first order equations, electric circuit184—185377-7377-10 Problems, first order equations, first order processes137 Problems, first order equations, flow of heat, steady state185—186 Problems, first order equations, flow through an orifice183—184 Problems, first order equations, geometric107—111 Problems, first order equations, growth131—132 Problems, first order equations, horizontal motion160—162 Problems, first order equations, inclined motion164—166 Problems, first order equations, interest126—127 Problems, first order equations, isogonal trajectory115—117 Problems, first order equations, moon151-6151-7151-8156-38156-39 Problems, first order equations, motion of a complex system189—191 Problems, first order equations, oceanic pressure186187 Problems, first order equations, orthogonal trajectories117—120 Problems, first order equations, pursuit curves168—175 Problems, first order equations, raindrop143 Problems, first order equations, relative pursuit curves177—182 Problems, first order equations, rocket motion191—193 Problems, first order equations, rope around a cylinder188—189 Problems, first order equations, rotation of a liquid in a cylinder193—194 Problems, first order equations, second order processes134—137 Problems, first order equations, steady state flow of heat185—186 Problems, first order equations, straight line motion138—166 Problems, first order equations, temperature129—130 Problems, first order equations, variable mass191—193 Problems, first order equations, vertical motion139—151 Problems, linear second order equations313—389 Problems, linear second order equations, bending of beams383—389 Problems, linear second order equations, circle, particle moving on circumference of316—317 Problems, linear second order equations, damped harmonic motion347—353 Problems, linear second order equations, damped harmonic motion, definition of347 Problems, linear second order equations, damped motion, forced359—364 Problems, linear second order equations, damped motion, free347—353 Problems, linear second order equations, elastic helical spring324—326 Problems, linear second order equations, elastic helical spring in parallel330-13 Problems, linear second order equations, elastic helical spring in series330-14 Problems, linear second order equations, electric circuit, simple369—375 Problems, linear second order equations, forced motion with damping359—364 Problems, linear second order equations, forced undamped motion338—342 Problems, linear second order equations, free damped motion347—353 Problems, linear second order equations, free undamped motion313—329see Problems, linear second order equations, particle moving on a straight line314—316 Problems, linear second order equations, particle moving on circumference of a circle316—317 Problems, linear second order equations, pendulum, simplesee "Pendulum" Problems, linear second order equations, problem involving a centrifugal force380 Problems, linear second order equations, rolling bodies381—383 Problems, linear second order equations, simple electric circuit369—375 Problems, linear second order equations, simple harmonic motion313—329see Problems, linear second order equations, straight line, particle moving on314—316 Problems, linear second order equations, twisting bodies383 Problems, linear second order equations, undamped motion313—342 Problems, linear second order equations, undamped motion, examples of323—329 Problems, linear second order equations, undamped motion, forced338—342 Problems, linear second order equations, undamped motion, free313—321 Problems, special types of second order nonlinear equations506—530 Problems, special types of second order nonlinear equations, central force521—522 Problems, special types of second order nonlinear equations, geometric528—530 Problems, special types of second order nonlinear equations, pursuit523—525 Problems, special types of second order nonlinear equations, special central force521—522 Problems, special types of second order nonlinear equations, suspension cable507—514 Problems, system of equations440—492 Problems, system of equations, biological447—451 Problems, system of equations, central forcesee "Particle in motion in space subject to a central force" Problems, system of equations, electrical451—455 Problems, system of equations, mechanical440—443 Problems, system of equations, particle in motion in spacesee "Particle in motion in space subject to a central force" Problems, system of equations, plane motion of a particlesee "Particle in motion in space subject to a central force" Problems, system of equations, plane motion of a projectile463—465 Problems, system of equations, planetary motion491—492 Problems, system of equations, projectile in plane463—465 Product of two operators257 Projectile, motion of a463—465 Proof by mathematical induction250 Properties of Bessel function of first kind619—622 Properties of Laguerre polynomials627—630 Properties of Laplace transforms295—296 Properties of Legendre polynomials598—605 Properties of polynomial operatorssee "Polynomial operators" pure imaginary number197 Pursuit curves168—175523—525 Pursuit curves, relative177—182 Radioactive material2 Radius of curvature528 Raindrop problem143 Range of a function911 Ratio test for convergence532 Real number system197 Real part of a complex number197 Rectangular form of a complex number199 Recursion formula577 Recursion formula for Bessel equation610 Recursion formula for Hermite polynomial607-18 Recursion formula for Laguerre equation625 Recursion formula for Legendre polynomial601 Reduction of order method241—246 Region, bounded14 Region, F-2 of atmosphere155 Region, simply connected71 Regular singularity571 Regular singularity at 586 Relative pursuit curve177—182 Remainder function670 Resistance, coefficient of348 Resistance, electric370 resistors369 Resistors in series454-2 Resonance373443 Resonance, undamped341 Resonant frequency, undamped341 Response of a system, impulsive344 Riccati equation97247 Riemann integral70 Riemann-integrable70731 Rocket motion191—193 Rodrigue's formula602 Rolling bodies381—383 Roots in conjugate pairs204-9 Roots of indicial equation574—584 Roots, imaginary217—220 Roots, real and distinct213—214 Roots, real but some multiple214—217 Rope around a cylinder188—189 Rotating tube, particle in a380 Rotation of a liquid193—194 Rotational inertia381 Rounding off errors636690 Runge — Kutta formulas for second order equation709 Runge — Kutta formulas for system of two first order equations702—703 Runge — Kutta formulas for y'=f(x,y)653—658 Runge — Kutta formulas, comment on error in657—658 Satellites488—491496 Second order equations500—504707—711712-1712-3 Second order equations, numerical solution of707—711 Second order equations, numerical solution of, by Adams' method712-3 Second order equations, numerical solution of, by Milne's method710—711 Second order equations, numerical solution of, by Runge — Kutta method709 Second order equations, numerical solution of, error in712-1 Second order equations, special types of nonlinear500—504 Second order processes, problems134—137 Separable variables52
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