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Remarks on Standard Textbook Defınıtıons of Vector Operators

Year 2014, Volume: 7 Issue: 2, 83 - 104, 01.08.2014
https://doi.org/10.20854/befmbd.00710

Abstract

The common definitions of gradient, curl and divergence operators in standard textbooks on vector analysis and electromagnetic theory in the space of continuous functions are reviewed, critisized and suggestions are done for their clear and precise comprehension with quotations from literature

References

  • G.E. Hay, Vector and Tensor Analysis, Dover Pub. 1953.
  • A.P. Wills, Vector Analysis with an Introduction to Tensor Analysis, Dover Pub. 1958.
  • R.E. Collin, Principles and Applications of Electromagnetic Fields, McGraw-Hill Book Company, Inc. 1961.
  • N. Tralli, Classical Electromagnetic Theory, McGraw-Hill Book Company, Inc. 1963.
  • R. Becker, Electromagnetic Fields and Interactions, Dover Publ. 1964.
  • E.C. Jordan, Electromagnetic Waves and Radiating Systems, Prentice Hall, Inc. 1964.
  • E.M. Purcell, Electricity and Magnetism, Berkeley Physics Course. Vol.2, McGraw-Hill Book Company, Inc. 1965.
  • W.T. Scott, The Physics of Electricity and Magnetism, John Wiley & Sons, Inc. 1966.
  • E.V. Bohn, Introduction to Electromagnetic Fields and Waves, Addison-Wesley Pub. 1968.
  • A. Shadowitz, The Electromagnetic Field, Dover Publ. 1975.
  • M. Schwartz, Principles of Electrodynamics, Dover Publ. 1987.
  • D.J. Griffiths, Introduction to Electrodynamics, Prentice Hall, Inc. 1989.
  • D.V. Widder, Advanced Calculus, 2nd Ed. Dover Pub. 1989.
  • R.S. Elliot, Electromagnetics. History, Theory, and Applications, IEEE Press, 1993.
  • R.E.DuBroff, S.V. Marshall and G.G. Skitek, Electromagnetic Concepts and Applications, 4th Ed. Prentice Hall, Inc. 1996.
  • K.R. Demarest, Engineering Electromagnetics, Prentice Hall, Inc. 1998.
  • B. Di Bartolo, Classical Theory of Electromagnetism, World Scientific Publ. 2004
  • F.T. Ulaby, Fundamentals of Applied Electromagnetics, 6th Ed. Prentice Hall, Inc. 2010.
  • C.E. Weatherburn, Advanced Vector Analysis, Bell’s Mathematical Series, 1949.
  • S.A. Schelkunoff, Electromagnetic Waves, D. Van Nostrad Company, Inc. 1956.
  • R.M. Fano, L.J.Chu and R.B. Adler, Electromagnetic Fields, Energy, and Forces, John Wiley & Sons, Inc. 1960.
  • J.D. Kraus, Electromagnetics, McGraw-Hill, Inc. 1968.
  • P. Hammond, Applied Electromagnetism, Pergamon Press, 1971.
  • L.M. Magid, Electromagnetic Fields, Energy and Waves, John Wiley and Sons, Inc., 1972.
  • N.N. Rao, Elements of Engineering Electromagnetics, Prentice Hall, Inc. 1991.
  • W.H. Hayt, Engineering Electromagnetics, McGraw-Hill, Inc. 1989.
  • D.K. Cheng, Field and Wave Electromagnetics, Addison-Wesley Publ. Company, Inc. 1983
  • M.R. Spiegel, Theory and Problems of Vector Analysis, Schaum’s Outline Series, McGraw-Hill Book Company, Inc. 1974.
  • A.I. Borisenko and I.E. Tarapov, Vector and Tensor Analysis with Applications, (Translated and edited by R.A. Silverman), Prectice Hall Inc., 1968.
  • C.E. Weatherburn, Differential Geometry of Three Dimensions, Cambridge University Press, 1927.
  • R.W.P. King, The Theory of Electromagnetism, Pergamon Press, 1964.
  • L. Eyges, The Classical Electromagnetic Field, Dover Publ. 1980.
  • R.W.P. King, Electromagnetic Engineering, McGraw-Hill Book Company, Inc. 1945.
  • J.W. Gibbs, The Scientific Papers of J. Willard Gibbs, Vol. II, Ox Bow Pr Publ. 1994.
  • E.B. Wilson, Vector Analysis, N.Y., Charles Scribner’s Sons, 1901.
  • C.T. Tai, "Another Matter of History", IEEE Antennas and Propagation Magazine, 21-26, Feb. 1991
  • P. Moon and D.E. Spencer, Vectors, Princeton, N.J., D. Van Nostrand, 1965.
  • C.T. Tai, “Unified Definition of Divergence, Curl, and Gradient”, Appl. Math. Mech. Vol.7, No.1, 1986.
  • C.T. Tai, “A Systematic Treatment of Vector Analysis”, IEEE Trans. On Education, Vol.34, No.2 167-174, 1991.
  • J.W. Gibbs, Vector Analysis, New Haven, CT: Yale University Press, 1948.
  • H.B. Philips, Vector Analysis, New York: Wiley, 1933.
  • H.E. Newell, Vector Analysis, New York McGraw Hill, 1955
  • M. Javid and P.M. Brown, Field Analysis and Electromagnetics, New York: McGraw Hill, 1963.
  • N.H. Fang and T.Y. Zhu, “Unified Represenation of Vector Functions and Dyadic Functions in Field Theory in Orthogonal Systems”, Acta Antennie Sinica, Vol.3, No.1, 1987 (in Chinese)
  • C.T. Tai, Generalized Vector and Dyadic Analysis, IEEE Press 1992.
  • B. Polat, "A Distributional Investigation of Point Sources in Classical Electromagnetism", Revue Roumaine des Sciences Techniques - Série Électrotechnique et Énergétique, Vol.57 No.2, 123-133 (2012)
  • B. Polat, "Space Curve Types of Distributions and Sources", IEEE Antennas and Propagation Magazine, Vol.54 No.3, 68-85, (2012).
  • B. Polat, "Distributional Derivatives on a Regular Open Surface with Physical Applications", TWMS Journal of Applied and Engineering Mathematics Vol.1 No.2 pp.203-222 (2011).
  • H. Grassmann and L. Kannenberg, A New Branch of Mathematics: The “Ausdehnungslehre" of 1844 and Other Works, Open Court Publishing, Chicago, 1995.
  • Cartan, E., Les Systemes Différentielles Extérieurs, Hermann, Paris, 1945.
  • H. Flanders, Differential Forms with Applications to the Physical Sciences, Dover, New York, 1963.
  • Warnick, K.F., R.H. Selfridge, and D.V. Arnold, “Teaching Electromagnetic Field Theory Using Differential Forms”, IEEE Trans. Educ., Vol. 40, No. 1, 53{68, 1997.
  • K.F. Warnick and P. Russer, “Differential Forms and Electromagnetic Field Theory”, Progress in Electromagnetics Research, Vol.148, 83- 112, 2014.
  • F. Cajori, A History of Mathematical Notations, Dover Publ. 1993.
  • M.J. Crowe, A History of Vector Analysis, Dover Publ. 1994.

VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR

Year 2014, Volume: 7 Issue: 2, 83 - 104, 01.08.2014
https://doi.org/10.20854/befmbd.00710

Abstract

Bu çalışmada tüm dünyada yaygın şekilde kullanılan temel vektörel
analiz ve elektromanyetizma kitaplarında karşımıza çıkan vektör
operatörlerin (gradyan, diverjans ve rotasyonel) sürekli
fonksiyonlar uzayındaki geleneksel tanımları incelenmiş, bu
operatörlerin daha net ve doğru şekilde açıklanmaları amacıyla
literatürden atıflarla beraber eleştiriler ve öneriler sunulmuştur

References

  • G.E. Hay, Vector and Tensor Analysis, Dover Pub. 1953.
  • A.P. Wills, Vector Analysis with an Introduction to Tensor Analysis, Dover Pub. 1958.
  • R.E. Collin, Principles and Applications of Electromagnetic Fields, McGraw-Hill Book Company, Inc. 1961.
  • N. Tralli, Classical Electromagnetic Theory, McGraw-Hill Book Company, Inc. 1963.
  • R. Becker, Electromagnetic Fields and Interactions, Dover Publ. 1964.
  • E.C. Jordan, Electromagnetic Waves and Radiating Systems, Prentice Hall, Inc. 1964.
  • E.M. Purcell, Electricity and Magnetism, Berkeley Physics Course. Vol.2, McGraw-Hill Book Company, Inc. 1965.
  • W.T. Scott, The Physics of Electricity and Magnetism, John Wiley & Sons, Inc. 1966.
  • E.V. Bohn, Introduction to Electromagnetic Fields and Waves, Addison-Wesley Pub. 1968.
  • A. Shadowitz, The Electromagnetic Field, Dover Publ. 1975.
  • M. Schwartz, Principles of Electrodynamics, Dover Publ. 1987.
  • D.J. Griffiths, Introduction to Electrodynamics, Prentice Hall, Inc. 1989.
  • D.V. Widder, Advanced Calculus, 2nd Ed. Dover Pub. 1989.
  • R.S. Elliot, Electromagnetics. History, Theory, and Applications, IEEE Press, 1993.
  • R.E.DuBroff, S.V. Marshall and G.G. Skitek, Electromagnetic Concepts and Applications, 4th Ed. Prentice Hall, Inc. 1996.
  • K.R. Demarest, Engineering Electromagnetics, Prentice Hall, Inc. 1998.
  • B. Di Bartolo, Classical Theory of Electromagnetism, World Scientific Publ. 2004
  • F.T. Ulaby, Fundamentals of Applied Electromagnetics, 6th Ed. Prentice Hall, Inc. 2010.
  • C.E. Weatherburn, Advanced Vector Analysis, Bell’s Mathematical Series, 1949.
  • S.A. Schelkunoff, Electromagnetic Waves, D. Van Nostrad Company, Inc. 1956.
  • R.M. Fano, L.J.Chu and R.B. Adler, Electromagnetic Fields, Energy, and Forces, John Wiley & Sons, Inc. 1960.
  • J.D. Kraus, Electromagnetics, McGraw-Hill, Inc. 1968.
  • P. Hammond, Applied Electromagnetism, Pergamon Press, 1971.
  • L.M. Magid, Electromagnetic Fields, Energy and Waves, John Wiley and Sons, Inc., 1972.
  • N.N. Rao, Elements of Engineering Electromagnetics, Prentice Hall, Inc. 1991.
  • W.H. Hayt, Engineering Electromagnetics, McGraw-Hill, Inc. 1989.
  • D.K. Cheng, Field and Wave Electromagnetics, Addison-Wesley Publ. Company, Inc. 1983
  • M.R. Spiegel, Theory and Problems of Vector Analysis, Schaum’s Outline Series, McGraw-Hill Book Company, Inc. 1974.
  • A.I. Borisenko and I.E. Tarapov, Vector and Tensor Analysis with Applications, (Translated and edited by R.A. Silverman), Prectice Hall Inc., 1968.
  • C.E. Weatherburn, Differential Geometry of Three Dimensions, Cambridge University Press, 1927.
  • R.W.P. King, The Theory of Electromagnetism, Pergamon Press, 1964.
  • L. Eyges, The Classical Electromagnetic Field, Dover Publ. 1980.
  • R.W.P. King, Electromagnetic Engineering, McGraw-Hill Book Company, Inc. 1945.
  • J.W. Gibbs, The Scientific Papers of J. Willard Gibbs, Vol. II, Ox Bow Pr Publ. 1994.
  • E.B. Wilson, Vector Analysis, N.Y., Charles Scribner’s Sons, 1901.
  • C.T. Tai, "Another Matter of History", IEEE Antennas and Propagation Magazine, 21-26, Feb. 1991
  • P. Moon and D.E. Spencer, Vectors, Princeton, N.J., D. Van Nostrand, 1965.
  • C.T. Tai, “Unified Definition of Divergence, Curl, and Gradient”, Appl. Math. Mech. Vol.7, No.1, 1986.
  • C.T. Tai, “A Systematic Treatment of Vector Analysis”, IEEE Trans. On Education, Vol.34, No.2 167-174, 1991.
  • J.W. Gibbs, Vector Analysis, New Haven, CT: Yale University Press, 1948.
  • H.B. Philips, Vector Analysis, New York: Wiley, 1933.
  • H.E. Newell, Vector Analysis, New York McGraw Hill, 1955
  • M. Javid and P.M. Brown, Field Analysis and Electromagnetics, New York: McGraw Hill, 1963.
  • N.H. Fang and T.Y. Zhu, “Unified Represenation of Vector Functions and Dyadic Functions in Field Theory in Orthogonal Systems”, Acta Antennie Sinica, Vol.3, No.1, 1987 (in Chinese)
  • C.T. Tai, Generalized Vector and Dyadic Analysis, IEEE Press 1992.
  • B. Polat, "A Distributional Investigation of Point Sources in Classical Electromagnetism", Revue Roumaine des Sciences Techniques - Série Électrotechnique et Énergétique, Vol.57 No.2, 123-133 (2012)
  • B. Polat, "Space Curve Types of Distributions and Sources", IEEE Antennas and Propagation Magazine, Vol.54 No.3, 68-85, (2012).
  • B. Polat, "Distributional Derivatives on a Regular Open Surface with Physical Applications", TWMS Journal of Applied and Engineering Mathematics Vol.1 No.2 pp.203-222 (2011).
  • H. Grassmann and L. Kannenberg, A New Branch of Mathematics: The “Ausdehnungslehre" of 1844 and Other Works, Open Court Publishing, Chicago, 1995.
  • Cartan, E., Les Systemes Différentielles Extérieurs, Hermann, Paris, 1945.
  • H. Flanders, Differential Forms with Applications to the Physical Sciences, Dover, New York, 1963.
  • Warnick, K.F., R.H. Selfridge, and D.V. Arnold, “Teaching Electromagnetic Field Theory Using Differential Forms”, IEEE Trans. Educ., Vol. 40, No. 1, 53{68, 1997.
  • K.F. Warnick and P. Russer, “Differential Forms and Electromagnetic Field Theory”, Progress in Electromagnetics Research, Vol.148, 83- 112, 2014.
  • F. Cajori, A History of Mathematical Notations, Dover Publ. 1993.
  • M.J. Crowe, A History of Vector Analysis, Dover Publ. 1994.
There are 55 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Burak Polat This is me

Publication Date August 1, 2014
Published in Issue Year 2014 Volume: 7 Issue: 2

Cite

APA Polat, B. (2014). VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 7(2), 83-104. https://doi.org/10.20854/befmbd.00710
AMA Polat B. VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR. BUJSE. August 2014;7(2):83-104. doi:10.20854/befmbd.00710
Chicago Polat, Burak. “VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 7, no. 2 (August 2014): 83-104. https://doi.org/10.20854/befmbd.00710.
EndNote Polat B (August 1, 2014) VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 7 2 83–104.
IEEE B. Polat, “VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR”, BUJSE, vol. 7, no. 2, pp. 83–104, 2014, doi: 10.20854/befmbd.00710.
ISNAD Polat, Burak. “VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR”. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 7/2 (August 2014), 83-104. https://doi.org/10.20854/befmbd.00710.
JAMA Polat B. VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR. BUJSE. 2014;7:83–104.
MLA Polat, Burak. “VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 7, no. 2, 2014, pp. 83-104, doi:10.20854/befmbd.00710.
Vancouver Polat B. VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR. BUJSE. 2014;7(2):83-104.