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Diferansiyel Formlar ile Diferansiyel Operatörlerin Genelleştirilmesi

Year 2018, Volume: 8 Issue: 1, 383 - 390, 01.01.2018

Emre Dil

Abstract

Bu çalışmada, diferansiyel formları kullanarak farklı koordinat sistemlerinde; Kartezyen, silindirik ve küresel koordinat sistemlerinde, gradyan, diverjans, rotasyonel ve Laplasyen gibi fizikte en çok kullanılan diferansiyel operatörleri türeteceğiz. Son olarak bu diferansiyel operatörleri genelleştirilmiş koordinatlar için türeceğiz

Keywords

Diferansiyel formlar Diferansiyel operatörler Vektör kalkülüs

References

  • Bachman, D. 2006. A geometric approach to differential forms. Birkhäuser, Boston, USA, 45 p.
  • Edwards, HM. 1994. Advanced calculus: A differential forms approach. Birkhäuser, Boston, USA, 1-21 pp.
  • Kreyszig, E. 2006. Advanced engineering mathematics. 9th Edition, Wiley, Singapore A71, A84, pp.
  • Morita, S. 2001. Geometry of differential forms. Am. Math. Soc., 201: 1-150.

Generalization of differential operators by using differential forms

Year 2018, Volume: 8 Issue: 1, 383 - 390, 01.01.2018

Emre Dil

Abstract

In this study, we derive the mostly used differential operators in physics, such as gradient, divergence, curl and Laplacian in different coordinate systems; Cartesian, cylindrical and spherical coordinate systems by using the differential forms. Also, we finally derive these differential operators for the generalized coordinates.

Keywords

Differential forms Differential operators Vector calculus

References

  • Bachman, D. 2006. A geometric approach to differential forms. Birkhäuser, Boston, USA, 45 p.
  • Edwards, HM. 1994. Advanced calculus: A differential forms approach. Birkhäuser, Boston, USA, 1-21 pp.
  • Kreyszig, E. 2006. Advanced engineering mathematics. 9th Edition, Wiley, Singapore A71, A84, pp.
  • Morita, S. 2001. Geometry of differential forms. Am. Math. Soc., 201: 1-150.
There are 4 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Emre Dil

Publication Date January 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 1

Cite

APA Dil, E. (2018). Generalization of differential operators by using differential forms. Karaelmas Fen Ve Mühendislik Dergisi, 8(1), 383-390.
AMA Dil E. Generalization of differential operators by using differential forms. Karaelmas Fen ve Mühendislik Dergisi. January 2018;8(1):383-390.
Chicago Dil, Emre. “Generalization of Differential Operators by Using Differential Forms”. Karaelmas Fen Ve Mühendislik Dergisi 8, no. 1 (January 2018): 383-90.
EndNote Dil E (January 1, 2018) Generalization of differential operators by using differential forms. Karaelmas Fen ve Mühendislik Dergisi 8 1 383–390.
IEEE E. Dil, “Generalization of differential operators by using differential forms”, Karaelmas Fen ve Mühendislik Dergisi, vol. 8, no. 1, pp. 383–390, 2018.
ISNAD Dil, Emre. “Generalization of Differential Operators by Using Differential Forms”. Karaelmas Fen ve Mühendislik Dergisi 8/1 (January 2018), 383-390.
JAMA Dil E. Generalization of differential operators by using differential forms. Karaelmas Fen ve Mühendislik Dergisi. 2018;8:383–390.
MLA Dil, Emre. “Generalization of Differential Operators by Using Differential Forms”. Karaelmas Fen Ve Mühendislik Dergisi, vol. 8, no. 1, 2018, pp. 383-90.
Vancouver Dil E. Generalization of differential operators by using differential forms. Karaelmas Fen ve Mühendislik Dergisi. 2018;8(1):383-90.