Foundations of Potential TheoryCourier Corporation, 1 janv. 1953 - 384 pages Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition. |
Table des matières
Chapter | 4 |
Newtons | 4 |
Interpretation of Newtons Law for Continuously Distributed Bodies | 4 |
Forces Due to Special Bodies | 4 |
Sets of Points | 5 |
The HeineBorel Theorem | 6 |
Functions of One Variable Regular Curves | 7 |
Material Curves or Wires | 8 |
The Potentials of Surface Distributions | 165 |
The Potentials of Double Distributions | 166 |
The Discontinuities of Logarithmic Potentials | 172 |
Chapter VII | 175 |
The Electrostatic Problem for a Spherical Conductor | 176 |
General Coördinates | 178 |
Ellipsoidal Coördinates | 184 |
The Conductor Problem for the Ellipsoid | 188 |
Material Surfaces or Laminas | 10 |
Curved Laminas | 12 |
Ordinary Bodies or Volume Distributions | 15 |
The Force at Points of the Attracting Masses | 17 |
Legitimacy of the Amplified Statement of Newtons Law Attraction between Bodies | 22 |
Presence of the Couple Centrobaric Bodies Specific Force | 26 |
Chapter II | 28 |
Expansion or Divergence of a Field | 35 |
The Divergence Theorem | 37 |
Flux of Force Solenoidal Fields | 40 |
Gauss Integral | 42 |
Sources and Sinks | 44 |
General Flows of Fluids Equation of Continuity 12348024 22 15 17 | 45 |
28 31 34 | 47 |
Chapter III | 48 |
Work and Potential Energy | 49 |
Equipotential Surfaces | 54 |
Potentials of Special Distributions 48 54 | 55 |
The Potential of a Homogeneous Circumference | 58 |
Two Dimensional Problems The Logarithmic Potential | 62 |
Magnetic Particles | 65 |
Magnetic Shells or Double Distributions | 66 |
Irrotational Flow | 69 |
Stokes Theorem | 72 |
Flow of Heat | 76 |
The Energy of Distributions | 79 |
Functions of Three Variables 100 113 10 Second Extension Principle The Divergence Theorem for Regular Re gions | 113 |
Lightening of the Requirements with Respect to the Field | 119 |
Chapter V | 121 |
Development of Potentials in Series | 124 |
Legendre Polynomials | 125 |
Analytic Character of Newtonian Potentials | 135 |
Spherical Harmonics | 139 |
Development in Series of Spherical Harmonics | 141 |
Development Valid at Great Distances | 143 |
Behavior of Newtonian Potentials at Great Distances | 144 |
Chapter VI | 146 |
The Potentials of Volume Distributions | 150 |
Lemmas on Surfaces | 157 |
The Potential of the Solid Homogeneous Ellipsoid | 192 |
Remarks on the Analytic Continuation of Potentials | 196 |
Further Examples Leading to Solutions of Laplaces Equation | 198 |
Electrostatics Nonhomogeneous Media | 206 |
Theorems of Uniqueness Chapter VIII | 215 |
Electric Images | 228 |
Greens Function | 238 |
Poissons Integral Existence Theorem for the Sphere | 244 |
Expansions in Spherical Harmonics | 251 |
58 | 255 |
62 | 256 |
The Continuation of Harmonic Functions | 259 |
Isolated Singularities of Harmonic Functions | 268 |
Equipotential Surfaces | 275 |
264 | 281 |
121 | 289 |
The Nonhomogeneous Integral Equation Summary of Results for Con | 297 |
The Integral Equation with Discontinuous Kernel | 307 |
Further Consideration of the Dirichlet Problem Superharmonic | 315 |
The Construction of a Sequence Defining the Solution of the Dirichlet | 322 |
Capacity | 330 |
The CauchyRiemann Differential Equations | 342 |
Geometric Significance of the Existence of the Derivative | 343 |
Cauchys Integral Theorem 6 Cauchys Integral | 348 |
125 | 351 |
Developments in Fourier Series | 353 |
The Convergence of Fourier Series | 355 |
Conformal Mapping | 359 |
Greens Function for Regions of the Plane | 363 |
Greens Function and Conformal Mapping | 365 |
65 | 370 |
| 377 | |
| 379 | |
| 380 | |
| 381 | |
| 382 | |
| 383 | |
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Expressions et termes fréquents
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