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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
$u$-substitution      26 724
Air resistance      4
Alligood, Kathleen      347
Analytic methods      13 62
Analytic methods, systems      164 187
Angular frequency      299
Annihilation parameter      671
Apollo      13 666
Asymptotic stability      86
Attractor, Lorenz      710
Attractor, strange      710
Australia      15
Autonomous equations      24 40 76 96
Autonomous systems      181
Baby bottle      379
Beating      411
Bernoulli equation      729
Beth      16
Bifurcation      96—107
Bifurcation diagram      100
Bifurcation, creating equilibrium points      98 101
Bifurcation, definition      97
Bifurcation, discrete dynamical systems      692
Bifurcation, linear systems      348 375
Bifurcation, period-doubling      694
Bifurcation, pitchfork      693
Bifurcation, tangent      692
Bifurcation, value      100 103
Biography, Alligood, Kathleen      347
Biography, Curry, James H.      202
Biography, Kopell, Nancy      85
Biography, Lorenz, Edward N.      215
Biography, McKenna, Joseph      440
Biography, Smale, Stephen      63
Biography, Xia, Zhihong      495
Bob      see Boat
Boston      95
Braun      152 433
Bridges, Millennium      417
Bridges, Tacoma Narrows      433 448
Carbon dating      17
Carrying capacity      9—10
CD stores model      235
Cell phones      142
Center      299 301
Changing variables      455 724
Changing variables, $u$-substitution      724
Chaos      218 532 543 700 701
Chaos, sensitive dependence on initial conditions      703 706
Characteristic polynomial      265
Characteristic polynomial, three-dimensional matrix      358 361
Checking solutions      21 188
Chemical reactions      169 483
Chopping function      704
Circuit theory      see RC and RLC circuits
COBWEB      683
Coefficient matrix      238
Coefficient matrix, three-dimensional      354
Coefficient o:F damping      193
Competing species system      179 225 453 472
complex numbers      291 744
Compound interest      28 36 125
Computers      628 642 653
Conservation of energy      492
Conserved quantity      486 488
Constant-coefficient equations      325
Convolution      605 625
Cool picture      163
Cooling model      35 141
Cooperative species system      225 483
Critical loci      347
Critically damped harmonic oscillator      331
Curry, James H.      202
Cycles      674 679 683—690
Cycles, classification      689
Damping      193
Damping, adjustable      see MR fluids
Decoupled systems      189
Delayed logistic equation      718
Delta function      see Dirac delta function
Dempster, J. P.      18 152
Dense subset      705
dependent variables      3—4 20
Dependent variables, systems      173
Determinant      242 342
Determinant, three-dimensional matrix      357
Determinant, Wronskian      258
Dick      see Glen
Difference equation      see Discrete dynamical system
Dirac delta function      597
Direction field      173
Discontinuous forcing      572
Discrete dynamical system      634 670
Discrete dynamical system, bifurcation      692—696
Discrete dynamical system, bifurcation, logistic difference equation      696
Discrete dynamical system, bifurcation, period-doubling      694
Discrete dynamical system, bifurcation, pitchfork      693
Discrete dynamical system, bifurcation, tangent      692
Discrete dynamical system, cycles      674 679 683—690
Discrete dynamical system, cycles, attracting      689
Discrete dynamical system, cycles, classification      689
Discrete dynamical system, cycles, neutral      689
Discrete dynamical system, cycles, repelling      689
Discrete dynamical system, eventually fixed points      673
Discrete dynamical system, eventually periodic points      674
Discrete dynamical system, fixed points      673 683—690
Discrete dynamical system, fixed points, attracting      685
Discrete dynamical system, fixed points, classification      686
Discrete dynamical system, fixed points, finding      677
Discrete dynamical system, fixed points, neutral      685 689
Discrete dynamical system, fixed points, repelling      685
Discrete dynamical system, graphical iteration      683
Discrete dynamical system, histograms      676
Discrete dynamical system, Newton’s method      717
Discrete dynamical system, orbits      673
Discrete dynamical system, period-doubling route to chaos      698
Discrete dynamical system, periodic orbits      674
Discrete dynamical system, renormalization      699
Discrete dynamical system, seed      673
Discrete dynamical system, time series      676
Discrete dynamical system, web diagram      683
Discrete logistic equation      see Logistic difference equation
Dissipative systems      502—518
Dottie number      678
Duffing equation, periodically forced      532
Dynamical system, discrete time      670
D’Ancona, U.      13
Eigenvalue      263 264
Eigenvalue, complex      290
Eigenvalue, real distinct      268
Eigenvalue, repeated      309 310
Eigenvalue, three-dimensional matrix      357
Eigenvalue, zero      319
Eigenvector      263 266
Eigenvector, three-dimensional matrix      357
Electric circuit theory      see RC and RLC circuits
Energy      489 492
Energy, dissipation      505
Equilibrium points      5 70 78
Equilibrium points, bifurcation      102—104 348
Equilibrium points, center      299 301
Equilibrium points, classification      86 284 462
Equilibrium points, creation      101
Equilibrium points, Hamiltonian systems      496—497
Equilibrium points, linear systems      240—242
Equilibrium points, linearization      87 729
Equilibrium points, node      86
Equilibrium points, saddle      274 362 463
Equilibrium points, sink      86 279 362 463
Equilibrium points, source      86 283 362 463
Equilibrium points, spiral saddle      360
Equilibrium points, spiral sink      299 463
Equilibrium points, spiral source      299 463
Equilibrium points, stable      86 285
Equilibrium points, systems      156 177
Equilibrium points, unstable      285
Equilibrium solutions      5 10 70
Equilibrium solutions, systems      152 177
Eric      see Initial value
Euler’s formula      293 746
Euler’s method      53—60 641
Euler’s method, errors      62 72 628
Euler’s method, errors, first step      630
Euler’s method, errors, second step      633
Euler’s method, errors, total      635
Euler’s method, formula      56
Euler’s method, improved      641—647
Euler’s method, order      637
Euler’s method, step size      54 629
Euler’s method, systems      198—204
Eventually fixed points      673
Eventually periodic points      674
Existence and Uniqueness Theorem, applications      70—73
Existence and Uniqueness Theorem, first-order equations      68
Existence and Uniqueness Theorem, systems      205
Existence theorem      66
Explicit solutions      13 23
Exponential growth      562 670;
Extendability of solutions      66 82
Extended Linearity Principle      116 384
External forcing      383
Extinction      104
Extra firm mattress      168
Finite arithmetic      660—663
First-order differential equation      5 20
First-order differential equation, autonomous      24
First-order differential equation, Bernoulli equation      729
First-order differential equation, bifurcation      96
First-order differential equation, changing variables      724
First-order differential equation, Euler’s method      53
First-order differential equation, existence      68
First-order differential equation, linear      112
First-order differential equation, one-parameter family      97
First-order differential equation, power series      736
First-order differential equation, Riccati equation      731
First-order differential equation, separable      20
First-order differential equation, slope fields      36
First-order differential equation, uniqueness      68
First-order numerical method      637
Fixed points      673 683—690
Fixed points, attracting      685
Fixed points, classification      686
Fixed points, finding      677
Fixed points, neutral      685 689
Fixed points, Poincar$\acute{e}$ return map      536
Fixed points, repelling      685
Floating cube      441
Food chain model      525
Forced equation      383
Forced harmonic oscillator      382
Forced harmonic oscillator, beating      411
Forced harmonic oscillator, discontinuous forcing      586
Forced harmonic oscillator, glass harmonica      430
Forced harmonic oscillator, impulse forcing      595 598
Forced harmonic oscillator, phase angle      421
Forced harmonic oscillator, phase plane      401
Forced harmonic oscillator, resonance      415
Forced harmonic oscillator, sinusoidal forcing      397 413 421 589
Forced harmonic oscillator, undamped      409
Forced response      387
Fourier transform      560
Frequency, angular      299
Frequency, natural      299
Frequency, WEEI      299
General solution      7 23
General solution, systems      190
Gib      187 212
Gift      296 325
Glass armonica      see glass harmonica
Glass harmonica      430
Glen      see Dick
Glider      556
Gradient systems      513
Gradient systems, definition      516
Gradient systems, lobster motion      513
Gradient systems, Lyapunov functions      513
Graphical iteration      683
Gravitational force      489
Growth-rate coefficient      4
Guess-and-test method      118 194 388
Guess-and-test method, ultimate guess      736
Half-life      17
Hamilton, William R.      488
Hamiltonian function      488
Hamiltonian function, construction      493
Hamiltonian systems      484—497
Hamiltonian systems, conserved quantity      486
Hamiltonian systems, definition      488
Hamiltonian systems, energy      489
Hamiltonian systems, equilibrium points      496
Hamiltonian systems, Hamiltonian function      488
Hamiltonian systems, ideal pendulum      490
Hamiltonian systems, phase portraits      488
Hamiltonian systems, undamped harmonic oscillator      488
Hammer strike      421 595
harmonic oscillator      159 160 193 234 250 269 315 377 379
Harmonic oscillator, as Hamiltonian system      488
Harmonic oscillator, classification      330
Harmonic oscillator, clock      340
Harmonic oscillator, coefficient of damping      193
Harmonic oscillator, critically damped      331 334—335
Harmonic oscillator, damped      507
Harmonic oscillator, forced      see Forced harmonic oscillator
Harmonic oscillator, hard spring      552
Harmonic oscillator, modified damping      227
Harmonic oscillator, natural frequency      207 330
Harmonic oscillator, overdamped      331 333—334
Harmonic oscillator, resonance      415
Harmonic oscillator, sinusoidal forcing      397 421
Harmonic oscillator, soft spring      552
Harmonic oscillator, spring constant      160
Harmonic oscillator, trace-determinant plane      346
Harmonic oscillator, undamped      301 330
Harmonic oscillator, underdamped      331—332
Harry      187 212
Harvesting      146
Heaviside function      573
Heaviside function, derivative of      602
Heaviside, Oliver      573
Hedgpath, J.W.      15
Hermite equation      739
Hermite polynomials      739
Hey, Jude      420
Histograms      676
Homogeneous equations      114 325 383 734
Hooke’s law of springs      160
Ideal pendulum      490
Identity matrix      264
Implicit solutions      28
Improved Euler’s method      641—647
Improved Euler’s method,cost      646
Improved Euler’s method,definition      644
Improved Euler’s method,errors      644
Improved Euler’s method,order      646
Impulse forcing      595
Independent variable      3 4 20
INDEX      827
Initial condition      5 22 154
Initial condition, discrete dynamical system      see seed
Initial point      155
1 2 3
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