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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
ANALYTİCAL METHODS I MEK 503 0 3 + 0 3 6
Ön Koşul Dersleri
Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi Yüksek Lisans
Dersin Türü ZORUNLU
Dersin Koordinatörü Doç. Dr. ERGÜN NART
Dersi Verenler Dr.Öğr.Üyesi MUSTAFA ÇAĞRI KUTLU
Dersin Yardımcıları
Dersin Kategorisi
Dersin Amacı
The main aim is to teach students the theory of Advanced Analytical Methods and have them solve various examples from Mechanical engineering
Dersin İçeriği
The solution methods in mathematical modeling of continuous and discrete systems in engineering are given. The solution of Bessel differential equation and Sturm-Liouville problems in continuous systems are lectured.
Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - Students can classify physical systems and problems 3 - 4 - 15 - 2 - 1 - A - C -
2 - They know generalized mathematical models 3 - 4 - 15 - 2 - 1 - A - C -
3 - Students turn discrete systems into discrete eigenvalue problems and solve 3 - 4 - 15 - 2 - 1 - A - C -
4 - They solve differential equation and differential equation systems 3 - 4 - 2 - 1 - A - C -
5 - Students select suitable series and solve differential equations 3 - 4 - 15 - 2 - 1 - A - C -
Öğretim Yöntemleri: 3:Discussion 4:Drilland Practice 15:Problem Solving 2:Question-Answer 1:Lecture
Ölçme Yöntemleri: A:Testing C:Homework

Ders Akışı

Hafta Konular ÖnHazırlık
1 Classification of physical systems and problems
2 Generalized mathematical models
3 Discrete eigenvalue problems, properties of eigenvalues & eigenvectors, zero and repeated eigenvalues, iterative methods
4 Linear System of ODEs, characteristic eq. , variation of parameters, non-homog. eqs., nonlinear eqs. examples
5 Method of Frobenius, Fuchs theorem: series expansion around singular points
6 Laplaces eq. in cylindrical coordinates: Solution of Bessels eq., properties of Gamma function, Bessel function of 1st and 2nd kind, modified Bessel functions, applications
7 Eigenvalue problems for continuous systems, eigenvalues, eigenfunctions & the solution of initial-boundary problems
8 Sturm-Liouville problem for second order systems, general self-adjoint systems, self-adjoint B.C.
9 Properties of eigenvalues and eigenfunction, orthogonalization of eigenfunctions
10 Midterm exam
11 Applications : nonsymetric vibration of circular membrane
12 Non-selfadjoint boundary conditions: self-adjoint systems in generalized sense, orthogonality condition, example: vibrating elastic bar with a concentrated mass
13 Sturm-Liouville problem for 4th order systems
14 Approximate solution of self-adjoint and nonself-adjoint eigenvalue problems, weighted residual techniques.

Kaynaklar

Ders Notu F.B. Hildebrand, Advanced Calculus for Applications 2nd Edition, Prentice-Hall, Inc.
F.B. Hildebrand, Methods of Applied Mathematics, Dover Publications, Inc.
Ders Kaynakları C.R. Wylie, L.C. Barrett, Advanced Engineering Mathematics, McGraw-Hill Book Company

Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
Odev 1 100
Toplam 100
Yıliçinin Başarıya Oranı 30
Finalin Başarıya Oranı 70
Toplam 100

AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 3 3
Quiz 2 3 6
Assignment 7 5 35
Final examination 1 10 10
Toplam İş Yükü 150
Toplam İş Yükü /25(s) 6
Dersin AKTS Kredisi 6
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