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MATH 208 | Ders Tanıtım Bilgileri

Dersin Adı

Introduction to Differential Equations II

Kodu	Yarıyıl	Teori (saat/hafta)	Uygulama/Lab (saat/hafta)	Yerel Kredi	AKTS
MATH 208	SPRING	2	2	3	5

Ön-Koşul(lar)	MATH 207 To get a grade of at least FD
Dersin Dili	English
Dersin Türü	Zorunlu
Dersin Düzeyi	Lisans
Dersin Veriliş Şekli	face to face
Dersin Öğretim Yöntem ve Teknikleri	Problem Solving Case Study Q&A Simulation
Ulusal Meslek Sınıflandırma Kodu	-
Dersin Koordinatörü	Doç. Dr. Sevin Gümgüm
Öğretim Eleman(lar)ı	Doç. Dr. Sevin Gümgüm
Yardımcı(ları)	-

Dersin Amacı

This course includes classification, applications and solution methods of partial differential equations. Fourier series for periodic functions, solution of heat and wave equation by separation method, solution methods of Laplace equation in rectangular and polar coordinates are aimed.

Öğrenme Çıktıları

Bu dersi başarıyla tamamlayabilen öğrenciler;

Ad	Açıklama	PC Alt	* Katkı Düzeyi
Ad	Açıklama	PC Alt	1	2	3	4	5
LO1	Classify partial differential equations. model first and second order partial differential equations.						X
LO2	Find solutions of the first order partial differential equations by analytic methods.						X
LO3	Use Laplace transform to obtain solutions of first and second order partial differential equations.						X
LO4	Analytically solve heat, diffusion and wave model.						X
LO5	Get numerical solutions of second order partial differential equations.						X

Ders Tanımı

In this course basic concepts and classification of partial differential equations will be discussed. The heat, wave and Laplace equation will be given and the solution methods will be taught.

Dersin İlişkili Olduğu Sürdürülebilir Kalkınma Amaçları

Dersin Kategorisi	Temel Ders
	Uzmanlık/Alan Dersleri	X
	Destek Dersleri
	İletişim ve Yönetim Becerileri Dersleri
	Aktarılabilir Beceri Dersleri

HAFTALIK KONULAR VE İLGİLİ ÖN HAZIRLIK ÇALIŞMALARI

Hafta	Konular	Ön Hazırlık	Öğrenme Çıktısı
1	Mathematical background for the study of partial differential equations	Erwin Kreyszig, “Advanced Engineering Mathematics”,10Th Edition, (John Wiley and Sons), Sections 9.5, 9.7, 9.8	-
2	Description of partial differential equations. Classification and model definitions. First order partial differential equations	Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 1.1. to 1.7	-
3	Modelling first order partial differential equations. Solving by the method of characteristics	Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 2.1. to 2.4	-
4	Modelling continuity equation, wave equation and traffics flow and applications	Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 2.1. to 2.4	-
5	Partial Laplace transform. Solving first order partial differential equations by partial Laplace transform.	“http://www.math.ttu.edu/~gilliam /ttu/s10/m3351_s10/c15_laplace_trans_pdes.pdf” Chapter 15	-
6	Heat Equation. Solution by separation of variables. Existence and Uniqueness of Solutions.	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.5.	-
7	Heat and diffusion equations examples and interpretation of the solution results	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.5-10.7	-
8	The wave equation. Solution by seperation of variables. Existence and Uniqueness of Solutions.	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.6.	-
9	Midterm Exam		-
10	The Laplace's equation in rectangular coordinates. Solution by separation of variables. Existence and Uniqueness of Solutions.	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.7.	-
11	Laplace's equation in polar coordinates and its solution by the method of separation of variables.	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.7.	-
12	Solving second order partial differential equations by partial Laplace transform.	“http://www.math.ttu.edu/~gilliam/ttu/s10/m3351_s10/c15_laplace_trans_pdes.pdf” Chapter 15	-
13	Numerical solutions of heat equation	David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), Sections: 9.1,9.2	-
14	Numerical solutions of wave equation	David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), Sections: 9.1,9.2	-
15	Semester review		-
16	Final exam		-

Ders Kitabı	Kent Nagle Edward B. Saff and Arthur David Snider “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition (Pearson 2011) ISBN-13: 978-0321747747.
Önerilen Okumalar/Materyaller	Readings/Materials Yehuda Pinchover and Jacob Rubistein “An Introduction to Partial Differential Equations” (Cambridge University Press 2005) ISBN-13:978-0-521-84886-2 Erwin Kreyszig “Advanced Engineering Mathematics” 10Th Edition (John Wiley and Sons) ISBN: 978-0-470-45836-5 David R. Kincaid and E. Ward Cheney “Numerical Analysis” (Brooks/Cole 1991) ISBN-10: 0-534-13014-3

DEĞERLENDİRME ÖLÇÜTLERİ

Yarıyıl Aktiviteleri	Sayı	Katkı Payı %	LO1	LO2	LO3	LO4	LO5
Ödev	1	20	X	X	X	X	X
Ara Sınav	1	30	X	X	X	X	X
Final Sınavı	1	50	X	X	X	X	X
Toplam	3	100

AKTS / İŞ YÜKÜ TABLOSU

Yarıyıl Aktiviteleri	Sayı	Süre (Saat)	İş Yükü
Katılım	-	-	-
Teorik Ders Saati	16	4	64
Laboratuvar / Uygulama Ders Saati	-	-	-
Sınıf Dışı Ders Çalışması	14	3	42
Arazi Çalışması	-	-	-
Küçük Sınav / Stüdyo Kritiği	-	-	-
Portfolyo	-	-	-
Ödev	1	10	10
Sunum / Jüri Önünde Sunum	-	-	-
Proje	-	-	-
Seminer/Çalıştay	-	-	-
Sözlü Sınav	-	-	-
Ara Sınavlar	1	14	14
Final Sınavı	1	20	20
		Toplam	150