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Braun M. — Differential Equations and Their Applications: An Introduction to Applied Mathematics
Braun M. — Differential Equations and Their Applications: An Introduction to Applied Mathematics



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Название: Differential Equations and Their Applications: An Introduction to Applied Mathematics

Автор: Braun M.

Аннотация:

Used in undergraduate classrooms across the country, this book is a clearly written, rigorous introduction to differential equations and their applications. Fully understandable to students who have had one year of calculus, this book differentiates itself from other differential equations texts through its engaging application of the subject matter to interesting scenarios. This fourth edition incorporates earlier introductory material on bifurcation theory and adds a new chapter on Sturm-Liouville boundary value problems. Computer programs in C, Pascal, and Fortran are presented throughout the text to show the read how to apply differential equations towards quantitative problems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd Edition

Год издания: 1991

Количество страниц: 546

Добавлена в каталог: 05.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint matrix      313
Analytic functions      187
APL programming      516
APL programming, addition      516
APL programming, division      518
APL programming, exponential      518
APL programming, functions      520
APL programming, functions, absolute value      520
APL programming, functions, arc cosine      520
APL programming, functions, arc sine      520
APL programming, functions, arc tangent      520
APL programming, functions, cosine      520
APL programming, functions, exponential      520
APL programming, functions, factorial      520
APL programming, functions, natural logarithm      520
APL programming, functions, signum      520
APL programming, functions, sine      520
APL programming, functions, tangent      520
APL programming, identifiers      519
APL programming, logical expressions      522
APL programming, multiplication      518
APL programming, programs      522
APL programming, subtraction      516
Asymptotic stability      379
Atomic waste problem      46
Autonomous systems      374
Bernoulli equation      67
Bessel equation      135
Bessel equation order $\nu$      216
Bessel equation order zero      218
Bessel function, $J_0(t)$      218
Bessel function, $J_\nu(t)$      216
Boundary conditions for elastic string      481
Boundary conditions for heat equation      480
Boundary conditions for Laplace equation      481
Boundary conditions for second order o.d.e.      474
Boundary-value problem      474 481
Boundary-value problem, heat equation      481
Boundary-value problem, Laplace equation      506
Boundary-value problem, wave equation      501
Carbon dating      19
Cauchy ratio test      187
Cayley — Hamilton theorem      349
Characteristic equation      136
Characteristic equation, complex roots      139
Characteristic equation, real and equal roots      143
Characteristic equation, real and unequal roots      136
Characteristic polynomial      332
Characteristic polynomial, complex roots      339
Characteristic polynomial, real distinct roots      332
Characteristic polynomial, repeated roots      343
Combat models      403
Complex exponentials      139
Compound interest      57
Convolution integral      250
Damping force      164
Detecting art forgeries      11
Detection of diabetes      176
Difference equations      91
Differential operators      127
Diffusion equation      479
Dirac delta function      242
Dirac delta function, Laplace transform of      244
Dirac, P.A.M.      242
Direction field      395
Dirichlet problem      481
Discontinuous forcing function      236
Eigenfunctions      476
Eigenvalues of boundary-value problem      476
Eigenvalues of matrix      331
Eigenvalues of matrix, multiplicity of      345
Eigenvectors of a matrix      331
Eigenvectors of a matrix, linear independence of      333
Elastic membrane, vibration of      480
Elastic string      480 501
Elastic string, boundary conditions for      481
Elastic string, fundamental frequencies of      503
Elastic string, initial conditions for      481
Elastic string, nonzero initial displacement      503
Elastic string, propagation of initial conditions      504
electrical circuits      173
Epidemic models      38
Epidemic models, gonorrhea      489
Epidemic models, plagues      39
Epidemic models, threshold theorem      458
Equilibrium points      371
Error effect of step size      102
Error for Euler’s method      100
Error for improved Euler’s method      109
Error for Runge — Kutta method      112
Error for three-term Taylor series      106
Error formula      101
Error, round-off      104
Escape velocity      52
Euler equation      143 147 196
Euler method      97
Euler method, formula error      101
Even functions      491
exact equations      58 60
Existence and uniqueness theorems for first-order equations      67
Existence and uniqueness theorems for orbits      312
Existence and uniqueness theorems for second-order equations      127
Existence and uniqueness theorems for systems of first-order equations      289 412
Extension of a function, even      493
Extension of a function, odd      494
Finding roots by iteration      81
First-order differential equations      1 2
First-order differential equations, exact      58 60
First-order differential equations, existence and uniqueness theorem for      67
First-order differential equations, general solutions of      4 21
First-order differential equations, homogeneous      3
First-order differential equations, initial-value problem      5 7 21
First-order differential equations, integrating factor for      8 64
First-order differential equations, linear      3
First-order differential equations, nonlinear      3
First-order differential equations, numerical solutions of      see "Numerical methods"
First-order differential equations, separable      21
First-order differential equations, several variables      262
First-order differential equations, systems of      263
Fourier series      485 486
Fourier series, convergence of      485 486
Fourier series, cosine series      492
Fourier series, Fourier coefficients      487
Fourier series, Parseval identity      490
Fourier series, sine series      492
Frobenius method      201
Fundamental matrix      353
Fundamental set of solutions      131
General solutions, first-order linear equations      4 21
General solutions, higher-order equations      257
General solutions, second-order equations      130 140 146
General solutions, systems of first-order equations      332
Generalized functions      247
Gompertzian relation      53
Gonorrhea model      489
Green’s Theorem      435
Heat equation      479 497
Heat equation, bar with insulated ends      498
Heat equation, boundary conditions      481
Heat equation, initial conditions      481
Heat equation, nonhomogeneous boundary conditions      501
Heat equation, smoothing of discontinuities in initial conditions      497
Hermite equation      195
Hermite polynomial      195
Higher-order equations      257
Higher-order equations, general solution      257
Higher-order equations, variation of parameters      260
Homogeneous equations      25
Hypergeometric equations      216
Identity matrix      309
Impedance      175
Improved Euler method      109
Indicial equation      207
Initial conditions      480
Initial conditions for elastic string      481
Initial conditions for heat equation      481
Initial conditions, propagation of initial conditions for wave equation      504
Initial conditions, smoothing of discontinuities for heat equation      497
Initial-value problem      5 7 21 126 257
Integral equation      70
Integrating factor      8 64
Inverse matrix      314
Judicious guessing of particular solutions      155
Jump discontinuities      225 236
Kirchoff's second law      174
Laguerre equation      216
Laplace equation      480 506
Laplace equation, boundary conditions      481
Laplace equation, Dirichlet problem      481
Laplace equation, Neumann problem      481
Laplace transform      223
Laplace transform of derivatives      227
Laplace transform of systems      366
Laplace transform of the convolution      250
Laplace transform of the Dirac delta function      244
Laplace transform, definition      224
Laplace transform, existence of      225
Laplace transform, inverse of      228
Legendre equation      195
Legendre polynomials      195
Limit cycles      434
Linear algebra      269 294
Linear differential equations      see "First-order differential equations" "Second-order "Systems
Linear independence      134 279
Linear independence of eigenvectors      333
Linear independence of vector functions      291
Linear independence of vectors      279
Linear operators      129
Linear transformations      322
Logistic curves      30 43
Logistic law of population growth      28
Malthusian law of population growth      27
Matrices      265
Matrices, addition of      274
Matrices, adjoint      313
Matrices, characteristic polynomial      332
Matrices, determinant of      297
Matrices, diagonal      299
Matrices, diagonal, lower      299
Matrices, diagonal, upper      299
Matrices, eigenvalues of      331
Matrices, eigenvectors of      331
Matrices, fundamental      353
Matrices, identity      309
Matrices, inverse      314
Matrices, product of      308
Mechanical vibrations      163
Mechanical vibrations, damped forced vibrations      167
Mechanical vibrations, damped free vibrations      165
Mechanical vibrations, forced free vibrations      168
Mechanical vibrations, free vibrations      164
Mechanical vibrations, resonant frequency      171
Method of elimination      255
Mixing problems      53
Natural frequency      169
Neumann problem      481
Newtonian mechanics      46 125 164
Newton’s method      88
Nonlinear differential equations autonomous system      374
Numerical methods      95
Numerical methods, effect of step size      102
Numerical methods, error      100 102 106 109 112
Numerical methods, Euler      97
Numerical methods, Euler, formula error      101
Numerical methods, improved Euler      109
Numerical methods, Runge — Kutta      112
Numerical methods, three-term Taylor series      106
Odd functions      491
Ohm’s Law      174
Orbits      392 395
Order of a differential equation      1
Ordinary differential equations definition      1
Parseval’s identity      490
Partial differential equations definition      479
Particular solution      149 362
Periodic solutions      414
Phase plane      392
Phase portrait      416 417
Picard iterates      70
Piecewise continuous functions      225
Poincare — Bendixson theorem      431
Population models      27
Population models, competitive exclusion      449
Population models, Logistic law of population growth      28
Population models, Malthusian law of population growth      27
Population models, sharks      441 442
Potential equation      480
Power series      186
Qualitative theory      370
Radioactive dating      12
Reduction of order      145
Reduction to systems of equations      263
Regular singular points      202
Resonance      168
resonant frequency      171
Reynolds number      50
Runge — Kutta method      112
Schwartz, Laurent      243 246
Second-order differential equations      125 136
Second-order differential equations, characteristic equation      136
Second-order differential equations, characteristic equation, complex roots      139
Second-order differential equations, characteristic equation, real and equal roots      143
Second-order differential equations, characteristic equation, real and unequal roots      136
Second-order differential equations, Euler equation      143 148 196
Second-order differential equations, existence and uniqueness theorem      127
Second-order differential equations, fundamental set of solutions      131
Second-order differential equations, general solutions      130 140 146
Second-order differential equations, homogeneous equation      126
Second-order differential equations, judicious guessing of particular solution      155
Second-order differential equations, nonhomogeneous equation      149
Second-order differential equations, nonhomogeneous equation, discontinuous function      236
Second-order differential equations, particular solution      149
Second-order differential equations, reduction of order      145
Second-order differential equations, series solution      183 186
Second-order differential equations, singular points      196 202
Second-order differential equations, variation of parameters      153
separable equations      20
Separation of variables      481 482
Separation of variables for heat equation      482 498
Separation of variables for Laplace equation      506 508
Separation of variables for wave equation      501
Sequence of eigenvalues      476
Series solution      183 186
Series solution, recurrence formula      185
Series solution, when roots of the indicial equation are equal      210 214
Series solution, when roots of the indicial equation differ by an integer      210 214
Singular points      196 202
Solutions, definition      1
Solutions, definition, first-order equations      4 21 60
Solutions, definition, higher-order equations      257
Solutions, definition, second-order equations      130 140 146
Solutions, definition, systems of first-order equations      332
Spread of technological innovations      39
Spring-mass dashpot system      163
Spring-mass dashpot system, damped vibrations      165 167
Spring-mass dashpot system, forced vibrations      168
Spring-mass dashpot system, free vibrations      164
Stability of a solution      371 376
Stability of equilibrium points      383 384
Stability, asymptotic      379
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