Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
MATHEMATICAL MODELLING MAT 465 7 2 + 0 2 5
Ön Koşul Dersleri Functional Analysis, PDE.
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. YALÇIN YILMAZ Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı Mathematical modelling, solutions to IBV problem and eigenvalue problem, Dirac function, green functions, Stable phase methods, implicit function theorem, Perturbation of eigenvalues, nonlinear eigenvalue problems,Periodic functions and oscillation, IBV problems Dersin İçeriği IBV problems, green functions, eigenvalue problems, asymptotic expansions, modelling
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Mathematical modelling, solutions to IBV problem and eigenvalue problem, 1 - 4 - 15 - A - C - 2 - Dirac function, green functions, Stable phase methods, implicit function theorem, 1 - 4 - 15 - A - C - 3 - Perturbation of eigenvalues, nonlinear eigenvalue problems, 1 - 4 - 15 - A - C - 4 - Periodic functions and oscillation, IBV problems 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 Mathematical modelling
2 Derivation of heat equation
3 Derivation of wave equation
4 Derivation of laplace equation
5 Green functions
6 Dirac function
7 Solutions to IBV problems
8 Solutions to eigenvalue problems
9 Asymptotic expansions, partial integration
10 Laplace method, stable phase method
11 Midterm
12 Theory of regular perturbation; implicit function teorem
13 Perturbation of eigenvalues , nonlinear eigenvalue problems
14 Oscillation and periodical functions

#### Kaynaklar

Ders Notu [1]R.L.Street; Analysis and solutions of Partial Differential Equations (For Chapter 1 and 2) R. Dennemeyer; An Introduction to Partial Differential Equations and Boundary Value Problems. (For Chapter 2)
Ders Kaynakları [2]G. F. Carrier and Carl E. Pearson: Partial Differential Equations, Theory and Technique (For Chapter 2)
J.P. Keener: Principles of Applied Mathematics (For Chapter 3,4 and 5)

#### 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.
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. X
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics.
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.

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
Odev 1 10
KisaSinav 2 10
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
Assignment 1 15 15
Performance Task (Laboratory) 1 20 20
Toplam İş Yükü 109
Toplam İş Yükü /25(s) 4.36
Dersin AKTS Kredisi 4.36
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