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Articles

On Helmholtz's Theorem and its Interpretations

Pages 471-483 | Published online: 03 Apr 2012

References

  • O’Rahilly , A. 1938 . Electromagnetics, A Discussion of Fundamentals , London : Cork University Press .
  • Sommerfeld , A. 1950 . Mechanics of Deformable Bodies , Edited by: Kuerti , G. Vol. 2 , New York : Academic Press . Translated from the 2d German
  • King , R. W. P. 1963 . Fundamental Electromagnetic Fields , New York : Dover Publications .
  • Miller , B. P. 1984 . Interpretations from Helmholtz’ theorem in classical electromagnetism . American Journal of Physics , 52 ( No. 10 ) Oct. : 948 – 950 .
  • Kobe , D. H. 1984 . Helmholtz’s theorem for antisymmetric second-rank tensor fields and electromagnetism with magnetic monopoles . American Journal of Physics , 52 ( No. 4 ) April : 354 – 358 .
  • Kobe , D. H. 1986 . Helmholtz’s theorem revisited . American Journal of Physics , 54 ( No. 6 ) June : 552 – 554 .
  • Korn , G. A. and Korn , T. M. 1968 . Mathematical Handbook for Scientists and Engineering (Definition, formulas, references and reviews) , New York : McGraw-Hill .
  • Hauser , W. 1970 . On the fundamental equations of electromagnetics . American Journl of Physics , 38 ( No. 1 ) Jan. : 80 – 85 .
  • Plonsey , R. and Collin , R. E. 1961 . Principles and Applications of Electromagnetic Fields , New York : McGraw-Hill .
  • Arfken , G. B. and Weber , H. J. 1995 . Mathematical Methods for Physicists , San Diego : Academic Press .
  • Cheng , D. K. 1989 . Field and Wave Electromagnetics , New York : Addison-Wesley Pub. Co. .
  • Collin , R. E. 1991 . Field Theory of Guided Waves , New York : IEEE Press .
  • Morse , P. M. and Feshbach , H. 1953 . Methods of Theoretical Physics , Vol. 1 , New York : McGraw-Hill Book Company, Inc. .
  • Weisstein , E. W. 1999 . CRC Concise Encyclopedia of Mathematics , Boca Raton , Fla : CRC Press .
  • Woodside , D. A. 1999 . Uniqueness theorems for classical fourvector fields in Euclidean and Minkowski spaces . Journal of Mathematical Physics , 40 ( No. 10 ) Oct. : 4911 – 4943 .
  • Courant , R. 1962 . Methods of Mathematical Physics , Vol. 2 , New York : Interscience Publisher .
  • Courant , R. 1953 . Methods of Mathematical Physics , Vol. 1 , New York : Interscience Publisher .
  • Stratton , J. A. 1941 . Electromagnetic Theory , New York : John Wiley & Sons .
  • Lamb , H. 1993 . Hydrodynamics , 6th edition , New York : Cambridge University Press .
  • Schwartz , M. , Green , S. and Rutledge , W. A. 1960 . Vector Analysis, with Applications to Geometry and Physics , New York : Harper .
  • Shadowitz , A. 1975 . The Electromagnetic Field , New York : McGraw-Hill .
  • Landau , L. D. and Lifshitz , E. M. 1970 . Theory of Elasticity , New York : Pergamon Press . Translated from Russian by J. B. Sykes and W. H. Reid
  • Muskhelishvili , N. I. 1953 . Some Basic Problems of the Mathematical Theory of Elasticity: Fundamental Equations, Plane Theory of Elasticity, Torsion, and Bending , Edited by: Radok , J. R. M. Groningen : P. Noordhoff . Translated from Russian
  • Marsden , J. E. and Hughes , T. J. R. 1983 . Mathematical Foundations of Elasticity , Englewood Cliffs , N. J : Prentice-Hall .
  • Schwarz , G. 1995 . Hodge Decomposition — A Method for Solving Boundary Value Problems , Berlin : Springer .
  • Zhou X. L. , “ On uniqueness theorem of a vector function ,” Accepted for publication in Progress In Electromagnetics Research PIER 65 , 93 – 102 , 2006 .

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