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Blanchard P., Devaney R.L. — Differential Equations
Blanchard P., Devaney R.L. — Differential Equations



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Название: Differential Equations

Авторы: Blanchard P., Devaney R.L.

Аннотация:

Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of readily available technology, the authors eliminate most of the specialized techniques for deriving formulas for solutions found in traditional texts and replace them with topics that focus on the formulation of differential equations and the interpretations of their solutions. Students will generally attack a given equation from three different points of view to obtain an understanding of the solutions: qualitative, numeric, and analytic. Since many of the most important differential equations are nonlinear, students learn that numerical and qualitative techniques are more effective than analytic techniques in this setting. Overall, students discover how to identify and work effectively with the mathematics in everyday life, and they learn how to express the fundamental principles that govern many phenomena in the language of differential equations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third edition

Год издания: 2006

Количество страниц: 828

Добавлена в каталог: 12.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Predator-prey system, modified      157
Predator-prey system, pesticides      167
Predator-prey system, Runge — Kutta method      658
Predator-prey system, three species      525
Qualitative Methods      6 13 62
Qualitative methods, systems      164 181
Radioactive decay      16
Ramp function      579
RC circuit      44 61 568 577
RC circuit, constant input voltage      45
RC circuit, on-off input voltage      46
RC circuit, periodic input voltage      47
RC circuit, zero input voltage      45
Red Sox      299 1919—2003
Renormalization      699
Resonance      415
Resonance, Millennium Bridge      417
Restoring force      159
Return map      731; see Poincar$\acute{e}$ return map
Riemann Sums      642
RLC circuit      375 391 447
Robo-lobster      513
Rock and Roll      see Paul
ROPE      77
Round-off error      see Finite arithmetic
Rubber band      229 448
Runge — Kutta method      649—658
Runge — Kutta method, definition      650
Runge — Kutta method, error      653
Runge — Kutta method, finite arithmetic      660
Runge — Kutta method, Mathematica program      655
Runge — Kutta method, order      653
Runge — Kutta method, step size      653
Runge — Kutta method, systems      657
Runge — Kutta method, TI calculator program      654
Runge — Kutta method, С program      656
Saddle      274 277 362
Saddle node bifurcation      see Tangent
Saddle, connection      487
Saddle, nonlinear      463
Saddle, separatrix      287 463
Salvadori, Mario      208 433
Saving model      28
Sawtooth function      581
Second-order differential equation      161
Second-order differential equation, forced      383
Second-order differential equation, Hermite equation      739
Second-order differential equation, homogeneous      383
Second-order differential equation, Legendre equation      743
Second-order differential equation, linear      325
Second-order differential equation, nonhomogeneous      383
Second-order differential equation, power series      739
Second-order numerical methods      646
See Harmonic oscillator, Springs, hard      552
Seed      673
Sensitive dependence on initial conditions      703 706
separable equations      23—28
Separable equations, missing solutions      27
Separation of variables      20—32
Separatrix      287 463
Separatrix, stable      463
Separatrix, unstable      463
Shock absorbers      339
Shock absorbers, active      231 426
Shock absorbers, truck seats      231
Shock absorbers, washing machines      426
simple harmonic motion      331
Simpson’s rule      650
Singular matrix      242
Sink, first-order equation      86
Sink, linear systems      279 362
Sink, nonlinear      463
Sink, spiral      299 463
Sinusoidal forcing      397 413 421 589
Skyscraper, P — Delta effect      207
Skyscraper, swaying      206
Skyscraper, tuned-mass damper      509
Slope fields      36—43
Slope fields, sketching      37
Slope fields, special cases, $dy/dt = f(t)$      39— 40
Slope fields, special cases, autonomous equations      40
Smale, Stephen      63
Sock absorbers      see washing machines
Solution      6—7 20
Solution curve      155
Solution, asymptotic      82
Solution, checking      21 188
Solution, domain of definition      66 82
Solution, existence and uniqueness      65
Solution, general      7 23 190
Solution, implicit      28
Solution, initial-value problem      7 22—23 162 188
Solution, linearly independent      355
Solution, missing      27
Solution, periodic      154 299
Solution, separatrix      287
Solution, system      13 154
Source, first-order equation      86
Source, linear systems      283 362
Source, nonlinear      463
Source, spiral      299 463
speed bumps      421
Spiral saddle      360
Spiral sink      299 463
Spiral source      299 463
Spring constant      160
springs      160
Springs, soft      552
Square wave      581
Stable equilibrium point      86 285
Stable separatrix      463
Steady-state response      387
Steady-state solution      120
Step function      see Heaviside function
Step size      54
Straight-line solutions      267
Superposition, principle of      see Linearity Principle
Suspension bridge      417 433 448
Suspension bridge, Lazer — McKenna light flexible long span      441
Suspension system model      339
systems      152
Systems, autonomous      181
Systems, checking solutions      188
Systems, coupled      12
Systems, decoupled      189
Systems, dimension      240
Systems, direction field      173
Systems, Euler’s method      198
Systems, Existence and Uniqueness Theorem      205
Systems, first-order      12
Systems, general solution      190
Systems, linear      237
Systems, Metaphor of the parking lot      175
Systems, nullcline      472
Systems, phase plane      156
Systems, phase portrait      156
Systems, Runge — Kutta method      657
Systems, three-dimensional      354—365
Systems, vector field      171
Tacoma Narrows bridge      433—440 448
Tangent bifurcation      692
Taylor polynomial      459
Taylor polynomial, power series methods      736
Taylor’s Theorem      457 631 641
Template, Lorenz      711
Tent function      716
Time-series      676
Trace      342
Trace-determinant plane      342
Trace-determinant plane, critical loci      347
Trapezoid Rule      642 650
Trolley cars      95
Truck seats      231
Tuned-mass damper      509
Undamped harmonic oscillator      330
Underdamped harmonic oscillator      331
Undetermined coefficients, method of      118 388
Unforced equation      383
Uniqueness Theorem, first-order equations, applications      70—73
Uniqueness Theorem, systems      205
Unstable equilibrium point      285 299
Unstable separatrix      463
van der Pol equation      201 452
Vector field      171 173
Volterra — Lotka system      482
Volterra, V.      13
Washing machines      426
Weather      214 539
Web diagram      683
WEEI      299
World Series      2004
wronskian      258
Wytham Woods      18
Xia, Zhihong      495
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