BibTex RIS Kaynak Göster

Diferansiyel Formlar ile Diferansiyel Operatörlerin Genelleştirilmesi

Yıl 2018, Cilt: 8 Sayı: 1, 383 - 390, 01.01.2018

Emre Dil

Öz

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

Anahtar Kelimeler

Diferansiyel formlar Diferansiyel operatörler Vektör kalkülüs

Kaynakça

  • 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

Yıl 2018, Cilt: 8 Sayı: 1, 383 - 390, 01.01.2018

Emre Dil

Öz

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.

Anahtar Kelimeler

Differential forms Differential operators Vector calculus

Kaynakça

  • 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.
Toplam 4 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Emre Dil

Yayımlanma Tarihi 1 Ocak 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 1

Kaynak Göster

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. Ocak 2018;8(1):383-390.
Chicago Dil, Emre. “Generalization of Differential Operators by Using Differential Forms”. Karaelmas Fen Ve Mühendislik Dergisi 8, sy. 1 (Ocak 2018): 383-90.
EndNote Dil E (01 Ocak 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, c. 8, sy. 1, ss. 383–390, 2018.
ISNAD Dil, Emre. “Generalization of Differential Operators by Using Differential Forms”. Karaelmas Fen ve Mühendislik Dergisi 8/1 (Ocak 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, c. 8, sy. 1, 2018, ss. 383-90.
Vancouver Dil E. Generalization of differential operators by using differential forms. Karaelmas Fen ve Mühendislik Dergisi. 2018;8(1):383-90.