Freiling G., Yurko V. Lectures on Differential Equations of Mathematical Physics: A First Course
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Index
302
E
eigenvalue, 23, 30, 31, 33, 44, 78, 103, 104, 133, 134
eigenvalues, 23, 24, 30, 31, 32, 33, 34, 36, 44, 45,
77, 78, 82, 102, 103, 104, 108, 132, 133, 134, 137,
143, 153, 159, 236, 237, 238, 239, 241, 242, 243,
244, 252, 254, 255
elasticity, vii, 2, 4, 15, 231
electromagnetic, vii, 15, 231
energy, 27, 168, 217, 261
engineering, vii, viii, 4, 65
English, 301, 302, 303
equality, 23, 29, 38, 41, 79, 80, 89, 121, 147, 151
equilibrium, 2
Euler, 216, 266
Euler equations, 266
evolution, viii, 77, 151, 154, 303
exercise, 21
exponential, 121
F
flow, 5
Fourier, 25, 26, 28, 38, 120, 132, 143, 160, 163, 186,
246, 256, 302
functional analysis, 210
Fur, 122
G
gas, 5
gene, 84, 103
generalization, 30
generalizations, 84, 103
gravitational field, 196, 275
H
H1, 29, 41, 42, 98, 236
Hamiltonian, 303
heat, viii, 4, 5, 9, 11, 157, 162, 225, 251, 252, 256
Hilbert, 217
Hilbert space, 217
homogeneous, 2, 4, 19, 49, 71, 76, 85, 88, 116, 146,
162, 210, 213, 219, 232, 234, 239, 240, 241, 245,
246, 247, 248, 253, 256
hydrodynamics, vii, 15, 231
hyperbolic, vii, viii, 6, 8, 9, 11, 15, 46, 50, 51, 228,
231, 232
hypothesis, 74, 81, 114
I
identity, 84, 113, 170, 174, 179
images, 177
independent variable, 11, 15, 23, 29, 46, 55, 62, 223
induction, 48, 49, 67, 91, 93, 95, 97, 98, 189, 223
inequality, 25, 94, 144, 162, 171, 176, 188, 191, 201
infinite, 12, 15, 21, 64, 136, 162, 214, 215, 232
integration, 32, 40, 66, 92, 97, 106, 124, 133, 160,
163, 164, 168, 170, 205, 262, 263, 298
interval, 22, 65, 77, 78, 84, 118, 157, 287
inversion, 122
isotropy, 168, 261
K
kernel, 38, 79, 84, 87, 119, 210
Kirchhoff, viii, 56, 59, 62, 63
Korteweg-de Vries, viii
L
L2, 25, 26, 29, 30, 32, 33, 38, 39, 41, 44, 77, 79, 80,
86, 88, 89, 91, 102, 103, 109, 121, 124, 127, 132,
133, 134, 136, 139, 145, 146, 148, 162, 218, 219,
220, 237
lead, 1, 4, 5, 13
linear, 1, 10, 11, 46, 51, 84, 85, 87, 90, 112, 118,
119, 120, 121, 142, 149, 152, 168, 210, 222, 261,
291
linear systems, 222
literature, 16
location, 191
lying, 189, 203
M
M1, 49
manifold, 121
mapping, 124, 273
mathematical, vii, viii, 1, 4, 5, 12, 13, 15, 22, 29, 38,
77, 151, 220, 227, 231, 301
mathematics, 77
matrix, 82, 108, 301
mechanics, 1, 5, 77
models, 13
modulus, 140
monotone, 188
Moscow, 301, 302, 303
multidimensional, 4, 12
multiplication, 121, 225
N
natural, vii, viii, 65, 77, 84, 103
natural science, vii, viii, 65, 77
natural sciences, vii, viii, 65, 77
Nd, 48
New York, 301, 302, 303
Index
303
nonlinear, viii, 77, 151, 225, 303
nonlinear systems, 225
normal, 24, 57, 167, 168, 169, 170, 173, 180, 199,
208, 212, 225, 239, 264, 268, 274, 277, 279, 296
O
operator, 3, 38, 55, 62, 77, 78, 79, 80, 82, 84, 85, 90,
102, 103, 113, 119, 125, 132, 146, 151, 152, 167,
185, 217, 251, 260, 296
Operators, 302
ordinary differential equations, vii, 11, 163
orientation, 52
oscillation, vii, 2, 4, 12, 15, 22, 78, 231
oscillations, 2, 3, 4, 64, 232, 239, 240, 241, 245, 246,
247, 248
P
parabolic, viii, 6, 9, 11, 12, 157, 228, 251
parameter, 23, 30, 38, 77, 87, 102, 132, 152, 159,
236, 241, 254
partial differential equations, vii, viii, 1, 4, 5, 6, 11,
12, 15, 22, 157, 167, 231, 251, 260, 301
perturbations, 13, 64
Philadelphia, 303
physical properties, 4
physics, vii, viii, 1, 4, 5, 12, 13, 15, 22, 29, 38, 77,
151, 220, 227, 231, 301
plane waves, 64
play, viii, 77, 151
Poisson, viii, 5, 63, 162, 164, 167, 183, 185, 188,
195, 196, 251, 260, 265, 267, 274, 275, 278
Poisson equation, viii, 5, 167, 195, 196, 260, 265,
267, 275
polar coordinates, 185, 260, 264, 265, 266, 268, 272,
278, 296, 297, 298
polynomial, 261
power, 221
propagation, 4, 5, 157, 162
property, 91, 127, 224, 263
proposition, 26
prototype, vii, 15, 231
Q
quantum, vii, 15, 231
quantum theory, vii, 15, 231
quasi-linear, 1, 6
R
radiation, 256
radius, 56, 62, 169, 170, 171, 173, 175, 179, 181,
196, 201, 221, 265, 266, 267, 269, 270, 272, 274
range, 298
reading, vii, viii, 22, 29, 65
real numbers, 88, 236
recall, 102
rectilinear, 263
reduction, 9, 151, 152, 230
reflection, 20, 131, 233, 268, 270, 273, 287
regular, 121, 194, 195
research, vii
resistance, 3, 248
Russian, 301, 302
S
scalar, 181, 217
scattering, 125, 137, 142, 147, 148, 149, 150, 151,
152, 154, 303
science, 4
separation, 22, 29, 159, 163, 185, 236, 238, 243, 245,
248, 252, 255, 256, 257, 288, 290, 296, 297, 298
series, 24, 25, 26, 28, 38, 41, 45, 46, 49, 68, 85, 86,
92, 95, 98, 99, 160, 186, 221, 222, 223, 224, 225,
237, 245, 256
sign, 7, 11, 37, 164, 183, 203, 205
signals, 3
signs, 11
singular, 302
singularities, 102, 104, 206, 207, 208, 209
smoothness, 59, 68, 85, 89
soliton, 154
solitons, 154, 155, 303
solutions, vii, viii, 5, 6, 11, 13, 15, 16, 18, 22, 23, 24,
27, 29, 30, 39, 45, 49, 51, 80, 90, 91, 100, 102,
103, 104, 126, 127, 128, 129, 132, 138, 151, 152,
153, 154, 157, 159, 162, 163, 167, 174, 175, 178,
180, 186, 194, 199, 210, 211, 212, 214, 215, 217,
231, 236, 238, 239, 240, 241, 242, 243, 244, 245,
247, 249, 252, 254, 258, 259, 266, 289, 293
spatial, viii, 2, 3, 4, 5, 13, 15, 157, 167, 260
spectra, 83, 84
spectral analysis, 77
spectrum, 23, 30, 37, 78, 101, 102, 103, 104, 132,
148, 150
speed, 3, 12, 15, 18, 20, 22
stability, 4, 13, 17, 49, 61, 159
students, vii
substitution, 8, 9, 10, 32, 41, 44, 46, 89, 177, 289
successive approximations, viii, 48, 67, 68, 91, 100
superposition, 18, 24, 45, 159, 239, 295
symbols, 33
symmetry, 65, 201, 296, 298
systems, viii, 84, 127, 129, 222, 225, 302
T
temperature, viii, 4, 5, 13, 157, 162, 167, 253, 256,
260
Index
304
textbooks, 220
theory, vii, viii, 1, 11, 13, 15, 25, 38, 78, 79, 84, 90,
102, 151, 210, 219, 227, 231, 262
three-dimensional, 4, 64
time, 4, 5, 12, 15, 64, 234
transformation, 6, 79, 84, 90, 125
transformations, 11
translation, 301
transmission, 3, 132
two-dimensional, 3, 9, 62
U
undergraduate, vii
uniform, 4, 188, 192
V
values, 13, 23, 30, 102, 132, 236, 263, 264
variable, viii, 4, 15, 157, 170, 261, 296, 298
variables, viii, 1, 2, 3, 4, 5, 6, 9, 10, 13, 22, 23, 29,
51, 56, 69, 98, 159, 163, 167, 185, 228, 229, 230,
232, 236, 238, 243, 245, 248, 252, 255, 256, 257,
260, 262, 284, 285, 288, 290, 296, 297, 298
vector, 181, 261, 277
velocity, 2, 15, 18, 234, 247, 248
viscosity, 16
W
wave equations, 3, 64
wave propagation, vii, 3, 15, 64, 231
Y
yield, 23, 29, 73, 74, 82, 144