Electromagnetic Theory, Volume 3

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American Mathematical Soc., 2003 - Science - 666 pages
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Oliver Heaviside is probably best known to the majority of mathematicians for the Heaviside function in the theory of distribution. However, his main research activity concerned the theory of electricity and magnetism, the area in which he worked for most of his life. Results of this work are presented in his fundamental three-volume ""Electromagnetic Theory"". The book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912. One of Heaviside's main achievements was the recasting of Maxwell's theory of electromagnetism into the form currently used by everyone. He is also known for the invention of operational calculus and for major contributions to solving theoretical and practical problems of cable and radio communication.All this is collected in three volumes of ""Electromagnetic Theory"". However, there is even more. For example, Chapter V in Volume II discusses the age of Earth, and several sections in Volume III talk about the teaching of mathematics in school. In addition to Heaviside's writings, two detailed surveys of Heaviside's work, by Sir Edmund Whittaker and by B. A. Behrend, are included in Volume I, and a long account of Heaviside's unpublished notes (which he presumably planned to publish as Volume IV of ""Electromagnetic Theory"") is included in Volume III.
 

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Contents

WAVES FROM MOVING SOURCE
ix
Simple Proof of Fundamental Property of a Plane Wave
3
The General Plane Wave
4
Generation of Waves by a Plane Source of Induction
6
Generation of Waves by a Plane Source of Displacement
8
Comparison of Electromagnetic with Aerial Waves
9
Waves ending perpendicularly upon a Conductor Conduction and Convection
10
Oblique Reflection at a Conducting Surface with H tangential Transformation to a Convection Problem
13
Connection Between the Compressed Electromagnetic Wave and Rankines Wave of Compression
152
Theory of the Rankinian Wave of Compression
154
Crossing of Two Waves Riemanns Solution
155
Modification of the Rankmian to make a Compressed Maxwellian Wave
156
The Waste of Energy from a Moving Electron
158
Sound Waves and Electromagnetics The Fanpotential
164
The Radiation from an Electron describing a Circular Orbit
169
The Radiation from an Electron moving in an Elliptic or any other Orbit
173

Generation of a Pair of Inclined Plane Waves by Motion of an Electrified Strip uv The applied force required
15
Generation of a Pair of Inclined Plane Waves by a Moving Source of Induction when uv
18
Slanting Plane Waves Generated by a Moving Magnet and by an Electrified Strip moving normally to its Plane
20
Generation of a Single Plane Wave by Motion of an Electrified Electret Also of Two Separated Plane Waves
23
Theory of the Steady Rectilinear Motion of a PointCharge or Electron through the Ether when uv and when uv
25
Construction of the Slanting Plane Waves generated by an Electrified Line by means of the Potential of an Electron
28
The steady Rectilinear Motion in its own line of a Terminated Electrified Live when uv and interpretation of the Impure Conical Wave Following an ...
30
The Wave from a Straight Line Source of Induction in a Nonconducting Dielectric
33
The Wave from a Straight Line Source of Induction In a Conductor
37
The Waves due to a Growing Plane Sheet ot Sources of Induction and to Travelling Filaments at any Speed
39
Reversion to Divergent Plane Waves Is the Ether Fixed?
43
Drag of Matter upon Ether Modified Circuital Equations and the Wavespeed resulting
44
Comparison of Wavespeeds in special Cases
46
Effect of Modified Circuital Equations on Electrical Distributions
50
Lorentzs Equations of a Moving Dielectric
52
The Wavespeed according to Lorentz
55
Possible Equations for a Moving Magnetised Substance
57
Larmors Equations for a Moving Body
59
Theory of Moving Electrified Cones uv The Moving Force upon them and upon an Electrified Line
61
Theory of Electrified Line of Finite Length Moving Transversely uv
65
Motion of Electrified Hyperboloids uv
69
Growing Plane Source of Induction Transition from uv to uv
72
The Waves from a Plane Strip Source of Induction suddenly started
76
Impressed Current along a Straight Axis The Operational Solution in General
78
Algebrisation of the Operational Solution in the case of Steady Motion of an Electron or of an Electrified Line uv
81
Application of Simply Periodic Analysis The Transition fromw to uc
84
Train of Simply Periodic Forced Waves along an Axis The Work done and Waste of Energy
86
Construction of the Simply Periodic Wave Train from the Two Electronic Steady Solutions
90
Connection between Moving Electrification and Moving Electrisation Transition from Cylindrical to Conical Wave
92
Spherical Impulsive Wave dne to sudden Displacement of an Electron
95
Spherical Impulse due to sudden change of Velocity of an Electron Rontgen Rays
98
Wave Train due to Damped Vibrations
100
Investigation of the Electromagnetic Field due to an Impressed Electric Current growing in a Straight Line The Solutions in Sphere and Cone
102
The electric field demands separate consideration to follow The Ellipsoidal and Conical Equipotential Surfaces
105
The Magnetic Force and Electric Current in the Cone and Sphere The Spherical Current Sheet
107
The Manner of Continuity of the Electric Current
110
The Electric Force and Time Integral of Magnetic Force
112
The Distribution of Displacement
114
Solutions for an Electron Jerked Away from a Stationary Compensating Charge The Spherical Pulse
117
Solutions for a Jerked Electron Without Compensating Charge
120
Comparison of two Cases of Motion of Electrification at the Speed of Light
122
Peculiarities at the Speed of Light
125
The Energy Wasted in the Spherical Pulse from a Jerked Electron and the Energy left behind
127
The Potential of a Charged Spheroid moving along its Axis
129
NOTE ON THE SIZE AND INEKTIA OF ELECTEONS
131
VECTOR ANALYSIS
135
WAVES IN THE ETHER Matter Electricity Ether and the Pressure of Radiation
144
The Moving Force Acting on a Deformable Ether
146
How to have Constant Speed through Space of Plane Radiation Traversing a Moving Compressible Ether
149
The Principle of Least Action Lagranges Equations
175
The Principle of Activity and Lagranges Equations Rotation of a Rigid Body
178
The Undistorted Cylindrical Wave
180
Extension of Kelvins Thermoelectric Theory
183
The Pressure of Radiation
186
Electromagnetics in a Moving Dielectric
190
The Charging of a Cable through a Condenser and Resistance
194
Other Critical Cases Mathematical Excursion
205
The Curbing Effect of an Inductance Shunt
209
The Transverse Momentum of an Electron
211
Extension to Helixal Motion
213
Deep Water Waves
214
The Solution of Definite Integrals by Differential Transformation
234
Given the Effect Find the Cause The Inversion of Operations
291
Theory of Electric Telegraphy
331
Some Plane and Cylindrical Waves
346
Plane Waves in a Dielectric Louded in a Certain Way
383
The Generation of Spherical Pulses in an Elastic Solid
388
Plane Waves in moving Mediums The Energy and Forces
401
The Electromagnetic Circuital Equations and Connected Matter
422
Theory of an Electric Charge in Variable Motion
432
Slanting Motion of Electrified Straight Line
498
The Magnetic Inertia of a Charged Conductor in a Field of Force
502
Vectors versus Quaternions
507
Quaternionic Innovations
510
The Teaching of Mathematics
513
The Teaching of Mathematics
515
The PanPotential as a SurfaceIntegral
517
Limitations on Scientific Prediction
518
SOME UNPUBLISHED NOTES OF OLIVER HEAVSIDE
521
INTRODUCTION
523
INFINITE INTEGRALS
526
PHYSICAL MATHEMATICS
561
ELECTRIC CIRCUIT THEORY
575
ELECTROMAGNETIC THEORY It will be recalled that at the turn of the century Heaviside regarded an electron as a very small charged particle Co...
604
UNIFIED FIELD THEORY
632
ACKNOWLEDGMENTS
639
APPENDIX
640
THE HEAVISIDE PAPERS FOUND AT PAIGNTON IN 1957
643
SUMMARY
645
HEAVISIDES DUPLEX EQUATIONS
646
HEAVISIDES UNIFIED FIELD THEORY
650
HEAVISIDES EXPANSION THEOREM
653
HEAMSIDES FRACTIONAL DIFFERENTIATION
655
HEAVISIDES INFINITE INTEGRAL
657
CONCLUSION
659
APPENDICES
660
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