Remarks on Standard Textbook Defınıtıons of Vector Operators

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

Keywords

• Vector calculus, vector operators, electromagnetic fields, electromagnetics education

VEKTÖR OPERATÖRLERİN STANDART DERS KİTABI TANIMLAMALARI ÜZERİNE YORUMLAR

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

Keywords

• Vektörel Analiz, Vektör Operatörler, Elektromanyetik Alanlar, Elektromanyetizma Eğitimi.

References

1. G.E. Hay, Vector and Tensor Analysis, Dover Pub. 1953.
2. A.P. Wills, Vector Analysis with an Introduction to Tensor Analysis, Dover Pub. 1958.
3. R.E. Collin, Principles and Applications of Electromagnetic Fields, McGraw-Hill Book Company, Inc. 1961.
4. N. Tralli, Classical Electromagnetic Theory, McGraw-Hill Book Company, Inc. 1963.
5. R. Becker, Electromagnetic Fields and Interactions, Dover Publ. 1964.
6. E.C. Jordan, Electromagnetic Waves and Radiating Systems, Prentice Hall, Inc. 1964.
7. E.M. Purcell, Electricity and Magnetism, Berkeley Physics Course. Vol.2, McGraw-Hill Book Company, Inc. 1965.
8. W.T. Scott, The Physics of Electricity and Magnetism, John Wiley & Sons, Inc. 1966.

9. E.V. Bohn, Introduction to Electromagnetic Fields and Waves, Addison-Wesley Pub. 1968.
10. A. Shadowitz, The Electromagnetic Field, Dover Publ. 1975.
11. M. Schwartz, Principles of Electrodynamics, Dover Publ. 1987.
12. D.J. Griffiths, Introduction to Electrodynamics, Prentice Hall, Inc. 1989.
13. D.V. Widder, Advanced Calculus, 2nd Ed. Dover Pub. 1989.
14. R.S. Elliot, Electromagnetics. History, Theory, and Applications, IEEE Press, 1993.
15. R.E.DuBroff, S.V. Marshall and G.G. Skitek, Electromagnetic Concepts and Applications, 4th Ed. Prentice Hall, Inc. 1996.
16. K.R. Demarest, Engineering Electromagnetics, Prentice Hall, Inc. 1998.
17. B. Di Bartolo, Classical Theory of Electromagnetism, World Scientific Publ. 2004
18. F.T. Ulaby, Fundamentals of Applied Electromagnetics, 6th Ed. Prentice Hall, Inc. 2010.
19. C.E. Weatherburn, Advanced Vector Analysis, Bell’s Mathematical Series, 1949.
20. S.A. Schelkunoff, Electromagnetic Waves, D. Van Nostrad Company, Inc. 1956.
21. R.M. Fano, L.J.Chu and R.B. Adler, Electromagnetic Fields, Energy, and Forces, John Wiley & Sons, Inc. 1960.
22. J.D. Kraus, Electromagnetics, McGraw-Hill, Inc. 1968.
23. P. Hammond, Applied Electromagnetism, Pergamon Press, 1971.
24. L.M. Magid, Electromagnetic Fields, Energy and Waves, John Wiley and Sons, Inc., 1972.
25. N.N. Rao, Elements of Engineering Electromagnetics, Prentice Hall, Inc. 1991.
26. W.H. Hayt, Engineering Electromagnetics, McGraw-Hill, Inc. 1989.
27. D.K. Cheng, Field and Wave Electromagnetics, Addison-Wesley Publ. Company, Inc. 1983
28. M.R. Spiegel, Theory and Problems of Vector Analysis, Schaum’s Outline Series, McGraw-Hill Book Company, Inc. 1974.
29. A.I. Borisenko and I.E. Tarapov, Vector and Tensor Analysis with Applications, (Translated and edited by R.A. Silverman), Prectice Hall Inc., 1968.
30. C.E. Weatherburn, Differential Geometry of Three Dimensions, Cambridge University Press, 1927.
31. R.W.P. King, The Theory of Electromagnetism, Pergamon Press, 1964.
32. L. Eyges, The Classical Electromagnetic Field, Dover Publ. 1980.
33. R.W.P. King, Electromagnetic Engineering, McGraw-Hill Book Company, Inc. 1945.
34. J.W. Gibbs, The Scientific Papers of J. Willard Gibbs, Vol. II, Ox Bow Pr Publ. 1994.
35. E.B. Wilson, Vector Analysis, N.Y., Charles Scribner’s Sons, 1901.
36. C.T. Tai, "Another Matter of History", IEEE Antennas and Propagation Magazine, 21-26, Feb. 1991
37. P. Moon and D.E. Spencer, Vectors, Princeton, N.J., D. Van Nostrand, 1965.
38. C.T. Tai, “Unified Definition of Divergence, Curl, and Gradient”, Appl. Math. Mech. Vol.7, No.1, 1986.
39. C.T. Tai, “A Systematic Treatment of Vector Analysis”, IEEE Trans. On Education, Vol.34, No.2 167-174, 1991.
40. J.W. Gibbs, Vector Analysis, New Haven, CT: Yale University Press, 1948.
41. H.B. Philips, Vector Analysis, New York: Wiley, 1933.
42. H.E. Newell, Vector Analysis, New York McGraw Hill, 1955
43. M. Javid and P.M. Brown, Field Analysis and Electromagnetics, New York: McGraw Hill, 1963.
44. 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)
45. C.T. Tai, Generalized Vector and Dyadic Analysis, IEEE Press 1992.
46. 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)
47. B. Polat, "Space Curve Types of Distributions and Sources", IEEE Antennas and Propagation Magazine, Vol.54 No.3, 68-85, (2012).
48. 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).
49. H. Grassmann and L. Kannenberg, A New Branch of Mathematics: The “Ausdehnungslehre" of 1844 and Other Works, Open Court Publishing, Chicago, 1995.
50. Cartan, E., Les Systemes Différentielles Extérieurs, Hermann, Paris, 1945.
51. H. Flanders, Differential Forms with Applications to the Physical Sciences, Dover, New York, 1963.
52. 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.
53. K.F. Warnick and P. Russer, “Differential Forms and Electromagnetic Field Theory”, Progress in Electromagnetics Research, Vol.148, 83- 112, 2014.
54. F. Cajori, A History of Mathematical Notations, Dover Publ. 1993.
55. M.J. Crowe, A History of Vector Analysis, Dover Publ. 1994.