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| Powers D.L. — Boundary Value Problems: And Partial Differential Equations |
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| Предметный указатель |
Periodic functions, extensions of 65—71
Periodic functions, extensions of, endpoints of 76—77
Periodic functions, extensions of, uniform convergence 82—83
Piecewise continuous functions 75—76
Piecewise smooth functions 76
Plate, flow past 289
Poiseuille flow 36
Poisson equation 268—269
Polar coordinates, potential equation in 256—257 275—279
Polynomial solution for potential equation 256
Potential equation 255—285
Potential equation in disk 275—279
Potential equation in rectangle 259—269
Potential equation in unbounded regions 270—272
Potential equation, limitations of product method 280—282
Potential equation, Poisson equation 268—269
Potential equation, polynomial solution for 256
Potential equation, soap films 283
Potential equation, solutions to (harmonic functions) 255
Principle of superposition 3 10 152
Principle of superposition, wave equation and standing waves 220
Probability density function 203
Product method (separation of variables) 150 166—167
Product method (separation of variables), limitations of 280—282
Product method (separation of variables), potential in rectangle 259—261 266
Radial heat flow 39—40
Radiation 142
Radical functions, integrals of 438
Rational functions, integrals of 438
Rayleigh method 239
Rayleigh quotient 239
Rectangle, potential equation in 259—269
Reduction or order 8—9
Regular singular points 7 38—40
Regular Sturm — Liouville problems 178—179
Regular Sturm — Liouville problems, convergence theorem 182
Regular Sturm — Liouville problems, one-dimensional wave equation 234
Removable discontinuities 74 79
Restoring term, forcing functions 117
Revision Rule 17
Right-hand limits 73—74
Robin conditions 139
Rod vibrations 253
Rods of heat-conducting material See heat conduction problems
Sampling theorem 121—124
Sawtooth function 81—82
Second-order equations, general form 205
Second-order equations, heat See heat conduction problems
Second-order equations, homogeneous 2—9
Second-order equations, nonhomogeneous 21—23
Second-order equations, potential See potential equation
Second-order equations, wave See wave equation
Sectionally continuous functions 75—76
Sectionally smooth functions 76
Semi-infinite intervals 40—41
Semi-infinite rods 188—191
Separation of variables (product method) 150 166—167
Separation of variables (product method), limitations of 280—282
Separation of variables (product method), potential in rectangle 259—261 266
Sine function 66—68
Sine function, Fourier sine integral representation 109—110
Sine function, hyperbolic 4
Sine function, integrals of 439
Singular boundary value problems 38—41
Singular eigenvalue problems 189
Singular points 7 38—40
Soap films 283
Soliton (solitary) waves 249
Solutions, general, boundary value problems 26
Solutions, general, homogeneous differential equations 158
| Solutions, general, nonhomogeneous linear equations 15
Solutions, general, one-dimensional wave equation 228
Solutions, general, second-order equations 3 205 280—281
Solutions, particular 15—23
Square-wave function 75—77 79—80
standing waves 220
Steady-state problems See also potential equation
Steady-state problems, temperature (heat conduction) 143—147
Steady-state problems, temperature (heat conduction), convection 170—174
Steady-state problems, temperature (heat conduction), different end conditions (example) 157—161
Steady-state problems, temperature (heat conduction), fixed end temperatures (example) 149—155
Steady-state problems, temperature (heat conduction), generalizations on 184—187
Steady-state problems, temperature (heat conduction), insulated ends (example) 157—161
Steady-state problems, temperature (heat conduction), semi-infinite rods 184—187 193—197
Steady-state problems, wave equation 218 232
Stefan — Boltzmann law of radiation 142
Stokes derivative 250
Stream function 284
Stresses due to thermal effects 214
String, vibrating 215—224. See also wave equation
String, vibrating, frequencies of vibration 223—224 234
String, vibrating, one-dimensional wave equation 233—235
Sturm — Liouville problems 178—179
Sturm — Liouville problems, expansions in series of eigenfunctions 181—182
Sturm — Liouville problems, generalizations on heat conduction problems 184—187
Sturm — Liouville problems, one-dimensional wave equation 234
Sulphur dioxide, diffusion of 55—56 192—193
Superposition, principle of 3 10 152
Superposition, wave equation and standing waves 220
Surfaces, insulated 157—161. See also heat conduction problems
Suspension bridge (hanging cable system) 26—29
Symmetry of sine and cosine functions 66—68
Table of integrals 438—440
Taylor series 114
Temperature (heat conduction), steady-state 143—147
Temperature (heat conduction), three-dimensional steady-state solution See potential equation
Temperature (heat conduction), two-dimensional steady-state equation 255
Term, forcing functions 117
thermal conductivity 137
Thermal diffusivity 137
Thermal stresses 214
Transient temperature distribution 146
Transient temperature distribution, fixed end temperatures 149—155
Transverse displacement See wave equation
Trapezoidal function 125
Traveling wave solution (d'Alembert's method) 227—231 252
Triangle function 123
Trigonometric functions 435
Trigonometric series, history of 124
Trivial solutions 150
Truncated Fourier series 92
Unbounded conditions, potential equation 270—272
Unbounded conditions, wave equation 239—244
Undetermined coefficients, nonhomogeneous linear equations 16—20
Uniform convergence 79—83
Variation of parameters 20—23
Velocity potential function 258 284
Vibrating string problem 215—224. See also wave equation
Vibrating string problem, frequencies of vibration 223—224 234
Vibrating string problem, one-dimensional wave equation 233—235
Water hammers 250
Wave equation 215—247 280
Wave equation, d'Alembert's method 227—231 252
Wave equation, estimating eigenvalues for 236—239
Wave equation, frequencies of vibration 223—224 234
Wave equation, one-dimensional, in general 233—235
Wave equation, vibrating string problem 215—224 234
Wave in unbounded regions 239—244
Whirling speeds 55
Windows 111
wronskian 3
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