MAT 384

Özel Fonksiyonlar II

: 3 Saat/Hafta, Teori, 3 Kredi, 5 AKTS
Amaç/İçerik:: Gamma ve Beta Fonksiyonları. Bessel diferensiyel denklemi ve Bessel fonksiyonları. Bessel fonksiyonlarının diklik özelliği, normu, Bessel-Fourier serileri. Hankel fonksiyonları, Modifiye Bessel fonksiyonları. Legendre diferensiyel denklemi ve Legendre polinomları. Legendre polinomlarının dikliği ve normu, Legendre serileri, Adjoinr Formlar, Singüler Sturm-Liouville Sistemleri, Bazı önemli ortogonal polinomlar, Homojen olmayan Sturm-Liouville sistemi ve Green fonksiyonu.
Ön Koşul:: Yok
Değerlendirme Yöntemleri:: 1 Ara sınav, 1 Yarıyıl sonu sınavı
Önerilen Kaynak Listesi:: Tyn Myint-u, Partial Differential Equations of Mathematical Physics W. E.Boyce, R. C.Diprima, Elementary Differential Equations and Boundary Value Problems N. H.Asmar, Partial Differential Equations with Fourier Series and Boundary Value Problems Shepley L.Ross, Differential Equations Richard Haberman, Elementary Applied Partial Differential Equations.

: 3 hrs/week, Theory , 3 credits, ECTS 5
Objective:: Gamma and Beta Functions, Bessel's Equation and Bessel's Function Bessel-Fourier Series for Functions, Hankel Function, Modified Bessel Functions Legendre's Equation and Legender's Function, Legendre's Series, Adjoint forms:Lagrange Identitiy, Singular Sturm-Liouville Systems,Laguarre's Equation and Laguarre's Polynoms, Nonhomogen Sturm-Liouville System and Green Function.
Prerequisite:: None
Assessment Methods:: 1 Midterm, 1 Final exam
Recommended text:: Tyn Myint-u, Partial Differential Equations of Mathematical Physics W. E.Boyce, R. C.Diprima, Elementary Differential Equations and Boundary Value Problems N. H.Asmar, Partial Differential Equations with Fourier Series and Boundary Value Problems Shepley L.Ross, Differential Equations Richard Haberman, Elementary Applied Partial Differential Equations.