Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Book Endüstriyel Matematik(01. Izmir Institute of Technology, 2024) Tanoğlu, Gamze; Yurt, CanberkÜniversitelerin öğrencilere meslek kazandırma misyonu dijital yüzyılda yeni nesil üniversiteler tanımı ile birlikte değişerek farklı bir misyona doğru evrilmiştir. Değişen bu misyon üniversitenin ürettiği bilimi toplumun diğer paydaşları ile paylaşarak toplumu dönüştürmek biçimde ifade edilebilir. İzmir Yüksek Teknoloji Enstitüsü, çocukları ve gençleri toplumun en değerli paydaşları görerek onların dönüşümüne ve gelişimine katkı sunmayı üniversitenin eğitim modeli olarak benimsemiştir. Bu atölye çalışması ile lise öğrencilerinin matematik müfredatında gördüğü konuları pekiştirerek öğrenmesi benimsenmiştir. Ayrıca, öğrencilerin bilgisayar yardımı ile özellikle de algoritma mantığı kullanarak ele alınan konuları deneyimleyerek öğrenmesini hedeflemektedir. Böylece bu çalıma ile ezberden uzak kalıcı öğrenme modeli sunulmuş olup matematiğin soyut yapısından somut yapısına bir köprü oluşturulması amaçlanmaktadır. Umuyorum bu atölye çalışması öğrencilere matematiğin günlük hayatta nerelerde kullanıldığı konusunda fikir vererek eğlenceli bir bilim olduğu konusunda da bir vizyon sunar.Article Citation - WoS: 9Citation - Scopus: 8A Numerical Method Based on Legendre Wavelet and Quasilinearization Technique for Fractional Lane-Emden Type Equations(Springer, 2024) İdiz, F.; Tanoǧlu, G.; Aghazadeh, N.In this research, we study the numerical solution of fractional Lane-Emden type equations, which emerge mainly in astrophysics applications. We propose a numerical approach making use of Legendre wavelets and the quasilinearization technique. The nonlinear term in fractional Lane-Emden type equations is iteratively linearized using the quasilinearization technique. The linearized equations are then solved using the Legendre wavelet collocation method. The proposed method is quite effective to overcome the singularity in fractional Lane-Emden type equations. Convergence and error analysis of the proposed method are given. We solve some test problems to compare the effectiveness of the proposed method with some other numerical methods in the literature. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Article The Application of a Finite Difference Method To a Dynamical Interface Problem(Acad. Publications, 2003) Tanoğlu, Gamze; Ağıroğlu, İzzet OnurA multiple-order-parameter model for Cu-Au system on a face cubic centered lattice was recently developed in the presence of anisotropy. In that model, three order parameters (non-conserved) and one concentration order parameter (conserved), which has been taken as a constant, were considered. Later on, the model has been extended, so that, concentration has been taken as a variable. It has been seen that two models were in a good agreement near critical temperature since the non-conserved order parameter behaves like a constant near critical temperature in both models.Article Hirota Method for Solving Reaction-Diffusion Equations With Generalized Nonlinearity(World Academic Press, 2006) Tanoğlu, GamzeThe Hirota Method is applied to find an exact solitary wave solution to evolution equation with generalized nonlinearity. By introducing the power form of Hirota ansatz the bilinear representation for this equation is derived and the traveling wave solution is constructed by Hirota perturbation. We show that velocity of this solution is naturally fixed by truncating the Hirota’s perturbation expansion. So in our approach, this truncate on works similarly to the way Ablowitz and Zeppetella obtained an exact travelling wave solution of Fisher’s equation by finding the special wave speed for which the resulting ODE is of the Painleve type. In the special case the model admits N shock soliton solution and the reduction to Burgers’ equation.