Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
SPECIAL FUNCTIONS MAT 362 6 2 + 0 2 4
Ön Koşul Dersleri Analysis I, Analysis II, Differential Equations I, Differential Equations II.
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. ŞEVKET GÜR Dersi Verenler Dersin Yardımcıları Research Assistants in Applied Mathematics Dersin Kategorisi Alanına Uygun Öğretim Dersin Amacı Certain mathematical functions occur often enough in fields like physics and engineering to warrant special consideration. They form a class of well studied functions with an extensive literature and appropriately enough are collectively called special functions. These functions carry such names as Bessel functions, Legendre functions and the like. This course seeks to provide information about these functions. Dersin İçeriği The Gamma and Beta Functions, The Sturm-Liouville systems, The Bessel Differential Equations and the Bessel Functions, The Gauss differential equations and the Hypergeometric functions, The Legendre Differential Equations and the Legendre Functions.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She Recognizes gamma and beta functions. 1 - 4 - 15 - A - C - 2 - He/She Recognizes Sturm-Liouville system. 1 - 4 - 15 - A - C - 3 - He/She Recognizes and solves Bessel equation. 1 - 4 - 15 - A - C - 4 - He/She Recognizes and solves Gauss equation 1 - 4 - 15 - A - C - 5 - He/She Recognizes and solves Legendre equation. 1 - 4 - 15 - A - C - 6 - He/She has knowledge about solutions without solving the equation. 1 - 4 - 15 - A - C - 7 - He/She Establishes a connection between special functions. 1 - 4 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 The gamma and Beta functions.
2 The Sturm Liouville system.
3 The Sturm Liouville system.
4 The Sturm Liouville system.
5 The Bessel Differential Equations and the Bessel functions
6 The Bessel Differential Equations and the Bessel functions
7 The Bessel Differential Equations and the Bessel functions
8 The Gauss differential equations and the Hypergeometric functions
9 The Gauss differential equations and the Hypergeometric functions
10 Midterm
11 The Gauss differential equations and the Hypergeometric functions
12 The Legendre Differential Equations and the Legendre functions.
13 The Legendre Differential Equations and the Legendre functions.
14 The Legendre Differential Equations and the Legendre functions.

#### Kaynaklar

Ders Notu [1] Uygulamalı Matematik, Prof.Dr.Abdullah Altın,Gazi Kitabevi, 2011.
Ders Kaynakları [2] Special Functions, Earl. D. Rainville
[3] Special Functions, George E. Andrews, Richard Askey, Ranjan Roy
[4] Hypergeometric Functions and Their Applications, James B. Seaborn

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language.
5 He/ she has the knowledge of computer software information as a mathematician needs.
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them. X
8 He/ she uses the ability of abstract thinking. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 75
KisaSinav 1 10
KisaSinav 2 10
Odev 1 5
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 2 32
Hours for off-the-classroom study (Pre-study, practice) 16 2 32
Mid-terms 1 10 10
Quiz 2 10 20
Assignment 1 5 5
Final examination 1 10 10
Toplam İş Yükü 109
Toplam İş Yükü /25(s) 4.36
Dersin AKTS Kredisi 4.36
; ;