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Stavroulakis I.P., Tersian S.A. — Partial Differential Equations: An Introduction with Mathematica and Maple
Stavroulakis I.P., Tersian S.A. — Partial Differential Equations: An Introduction with Mathematica and Maple

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Название: Partial Differential Equations: An Introduction with Mathematica and Maple

Авторы: Stavroulakis I.P., Tersian S.A.

Аннотация:

This introductory text for undergraduate and first year graduate courses explains the basic equations of mathematical physics and the properties of their solutions based on classical calculus and ordinary differential equations, including using the newest software. Stavroulakis (U. of Ioannina, Greece) and Tersian (U. of Rousse, Bulgaria) break the work down into first-order partial differential equations (PDEs), second-order PDEs, one-dimensional wave equation, one-dimensional diffusion equation, weak solutions, shock waves, conservation laws, the Laplace equation, Fourier series and Fourier methods for PDEs and diffusion and wave equations in higher dimensions. They include exercises and answers or hints for solving them.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2004

Количество страниц: 306

Добавлена в каталог: 10.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolutely integrable function      203
Almost-linear equation      2 46
Autonomous system      12
Bernoulli D. I      228
Bernoulli number      228
Bernoulli polynomial      228
Bernstein S.N.      257
Bernstein’s polynomial      257
Bessel equation      218
Bessel F.W.      218
Bessel function first kind      219
Bessel function second kind      220
Bessel inequality      218
Blow up      21
Boundary conditions, Dirichet      3 78
Boundary conditions, Neumann      4 80
Boundary conditions, Robin      4
Boundary value problem      3
Burgers J.M.      140
Canonical form      7 62
Cauchy A.      12
Cauchy Problem, Diffusion Equation      103
Cauchy problem, first order equation      13
Cauchy problem, wave equation      68
Characteristic curves      7 11
Characteristic form      60
Characteristic strip      33
Characteristic system      11
Characteristic triangle      70
Chladny E.      280
Chladny’s figures      280
Classification      46
Classification, second-order equations n var      59
Classification, second-order equations two var      46
Compatibility condition      84
Complex form Fourier Series      215
Conservation law      130
Conservation of energy      92 131
Conservation of mass      131
Conservation of momentum      131
Convergence, absolute      202
Convergence, mean-square      202
Convergence, pointwise      201
Convergence, uniform      201
Dirac kernel      124
Dirac P.      124
Dirichlet boundary condition      78
Dirichlet kernel      213
Dirichlet L.P.G.      78
Dirichlet principle      178
Discriminant      47
Domain      1
Domain of dependence      70
Domain of influence      70
D’Alembert formula      68
D’Alembert J.      68
Eigenfunction      231
Eigenvalue      231
Eigenvalue problem      230
Energy, kinetic      92
Energy, potential      92
Energy, thermal      101
Energy, total      92
Equation, almost-linear      2
Equation, biharmonic      2
Equation, Born — Infeld      2 58
Equation, Burgers      2 140
Equation, diffusion one-dim      97
Equation, diffusion or heat      2
Equation, eikonal      2 34
Equation, elliptic      48
Equation, Euler      247
Equation, fully-nonlinear      3
Equation, homogeneous      3 39
Equation, hyperbolic      48
Equation, inhomogeneous      3 40
Equation, Korteweg-de Vries      2
Equation, Laplace      2 169
Equation, linear      2 39
Equation, Liouville      151
Equation, Monge — Amp$\grave{e}$re      2
Equation, nonlinear      2
Equation, parabolic      48
Equation, Poisson      169
Equation, quasi-linear      3 11
Equation, shock waves      2
Equation, transport      2
Equation, Tricomi      57
Equation, ultrahyperbolic      63
Equation, wave      2 67
Error function      73 110
Euler L.      131
First integral      23
First-order PDEs      3
Fourier cosine series      200
Fourier J.B.J.      199
Fourier method, diffusion equation      229
Fourier method, Laplace equation      243
Fourier method, wave equation      238
Fourier series      199
Fourier sine series      199
Fully-nonlinear equation      28
Function, biharmonic      181
Function, even      207
Function, Gamma      220
Function, harmonic      169
Function, odd      208
Function, piecewise continuous      204
Function, Robin      4 170
Function, subharmonic      181
Functionally independent functions      10
Fundamental solution      180
Gamma function      220
Gauss formula      174
Gauss K.      173
Gauss — Ostrogradskii formula      173
General solution      4 40
Gibbs J.W.      213
Gibbs phenomenon      213
Gradient catastrophe      21 144
Green G.      91
Green’s first identity      174
Green’s function      7 182
Green’s identity      173
Green’s second identity      174
Hadamard J.      70
Harmonic function      169
Harnack A.      193
Harnack’s first theorem      195
Harnack’s inequality      193
Harnack’s second theorem      195
Heaviside function      145
Hopf — Cole transformation      141
Huygens C.      274
Huygens’ principle      274
Hyperbolic system      131
Ill-posed problem      71
Improper integrals      104
Index, negative      62
Index, positive      62
Inhomogeneous      3
Inhomogeneous diffusion equation      118
Inhomogeneous wave equation      87
Initial value problem      3
Integral surface      12
Inverse mapping theorem      13
Irreducible equation      43
Jump discontinuity      204
kinetic energy      92
Kirchoff G.R.      269
Kirchoff’s formula      269
Laplace P.S.      169
Legendre A.      37 224
Legendre differential equation      224
Legendre polynomial      224
Legendre transformation      37
Linear equation      4 46
Linear operator      2 40
Liouville J.      151
Liouville’s equation      151
Liouville’s theorem      194
Maximum-minimum principle, diffusion equation      98
Maximum-minimum principle, Laplace equation      171
Mean value property      175
Method of shifting the data      235
Method of steepest descent      142
Mixed problem wave equation      84
Mollifiers      124
Mollifying kernels      124
Monge cone      29
Monge G.      29
Negative index      62
Neumann boundary condition      4 80
Neumann K.G.      80
Nodal set      280
Non-factorable equation      40
Nonlinear operator      2
Operator, linear      2
Operator, nonlinear      2
Order      1
Orthogonal system      200
Orthonormal system      217
Parseval M — A.Ch      205
Parseval’s equality      205
Periodic function      203
Point, elliptic      48 63
Point, hyperbolic      48 63
Point, parabolic      48 63
Point, ultrahyperbolic      63
Poisson formula, diffusion equation      103
Poisson formula, Laplace equation      189 190
Poisson S.D.      103
potential energy      92
Principal part      47
Quasi-linear equation      3 11
Rank      10
Rankine — Hugoniot condition      164
Reducible equation      40
Reflection method      78
Region      1
Regularizations      125
Riemann G.F.      154
Riemann problem      154
Schwarz H.A.      125
Second-order PDEs      39
Shock speed      155
Shock wave      123 155
Sobolev S.L.      124
Sobolev space      124
Solution      1
Spherical means      269
Spherical wave equation      76
Steepest descent      142
Strictly hyperbolic system      136
Strip condition      33
Sturm — Liouville problem      230
Superposition      231
Swimmer effect      83
Symmetry of Green’s function      183
Taylor B.      142
thermal conductivity      97
Thermal energy      101
Transpose matrix      61
Ultrahyperbolic equation      63
Variation of constants (param.)      234
Wave equation      67
Weak derivative      123
Weak solution      123 135
Weierstrass criterion      105 202
Weierstrass K.W.      105
Well-posedness      70 170
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