Araştırma Makalesi
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Diferansiyel Denklemlerin Geometrik Yaklaşımı Üzerine

Yıl 2022, Sayı: 39, 1 - 5, 31.07.2022
https://doi.org/10.31590/ejosat.1142206

Öz

Çevremizdeki fiziksel gerçekleri ifade etmek, matematiksel modelleri hem teoride hem de uygulamada kullanmayı gerektirir. Bu modeller genellikle diferansiyel denklemleri içerdiğinden, açılabilir regle yüzeyler ve doğru kongrüanslarını kullanarak bu modellere yeni bir geometrik yaklaşım sunuyoruz.

Bu makalede, birinci mertebeden diferansiyel denkleme göre teğet açılabilir bir regle yüzey ve çözüm fonksiyonu sunulmaktadır. Ayrıca, tam diferansiyel denklemin çözümüne ve çözüm fonksiyonuna dayalı bir doğru kongrüansı ifade edilmektedir. Ayrıca, teğet açılabilir regle yüzeyler ve doğru kongrüanslar ile ilgili bazı örnekler verilmektedir.

Kaynakça

  • Bottema, O. and Roth, B. (1979) Theoretical Kinematics, North- Holland Press, New York.
  • Chen, M. and Tang, K. (2010) A fully geometric approach for developable cloth deformation simulation. Vis. Computer 26 (2010), 853–863.
  • Frey, W. and Bindschadler, D. (1993) Computer aided design of a class of developable Bézier surfaces, vol. 8057, General Motors R & D Publication.
  • Nagle, K. R., Saff, E. B. and Snider, A. D. (2012) Fundamentals of Differential Equations. Boston: Addison-Wesley.
  • Kreyszig, E. (1991) Differential geometry, Dover Publications.
  • Odehnal, B. and Pottmann, H. (2001) Computing with discrete models of ruled surfaces and line congruences, Proceedings of the 2nd workshop on computational kinematics, Seoul.
  • P´erez, F. and Su´arez, J. A. (2007) Quasi-developable Bspline surfaces in ship hull design. Comp. Aided Geom. Design 39(2007), 853–862.
  • Pottman, H. and Wallner, J. (2001) Computational Line Geometry, Springer-Verlag, Berlin, Heidelberg.
  • Zill, D. G. (2001) A first course in differential equations with modeling applications. Pacific Grove, CA: Brooks/Cole Thomson Learning.

On The Geometric Approach of Differential Equations

Yıl 2022, Sayı: 39, 1 - 5, 31.07.2022
https://doi.org/10.31590/ejosat.1142206

Öz

Expressing physical facts around us possesses to use mathematical models in both theory and application. Since these models usually involves differential equations, we present a novel geometric approach to these models using developable ruled surfaces and line congruences.

In this paper, a tangent developable ruled surface according to first order differential equation and its solution function is presented. Moreover, we expressed a line congrunce based on the solution of exact differential equation and its solution function. Also, some examples of tangent developable ruled surfaces and line congruences are given.

Kaynakça

  • Bottema, O. and Roth, B. (1979) Theoretical Kinematics, North- Holland Press, New York.
  • Chen, M. and Tang, K. (2010) A fully geometric approach for developable cloth deformation simulation. Vis. Computer 26 (2010), 853–863.
  • Frey, W. and Bindschadler, D. (1993) Computer aided design of a class of developable Bézier surfaces, vol. 8057, General Motors R & D Publication.
  • Nagle, K. R., Saff, E. B. and Snider, A. D. (2012) Fundamentals of Differential Equations. Boston: Addison-Wesley.
  • Kreyszig, E. (1991) Differential geometry, Dover Publications.
  • Odehnal, B. and Pottmann, H. (2001) Computing with discrete models of ruled surfaces and line congruences, Proceedings of the 2nd workshop on computational kinematics, Seoul.
  • P´erez, F. and Su´arez, J. A. (2007) Quasi-developable Bspline surfaces in ship hull design. Comp. Aided Geom. Design 39(2007), 853–862.
  • Pottman, H. and Wallner, J. (2001) Computational Line Geometry, Springer-Verlag, Berlin, Heidelberg.
  • Zill, D. G. (2001) A first course in differential equations with modeling applications. Pacific Grove, CA: Brooks/Cole Thomson Learning.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Vahide Bulut 0000-0002-0786-8860

Erken Görünüm Tarihi 26 Temmuz 2022
Yayımlanma Tarihi 31 Temmuz 2022
Yayımlandığı Sayı Yıl 2022 Sayı: 39

Kaynak Göster

APA Bulut, V. (2022). On The Geometric Approach of Differential Equations. Avrupa Bilim Ve Teknoloji Dergisi(39), 1-5. https://doi.org/10.31590/ejosat.1142206