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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
Dersin Yardımcıları
Dersin Kategorisi Alanına Uygun Temel Öğretim
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 1 - 2 - 3 - 4 - 15 - A - C -
2 - They know generalized mathematical models 1 - 2 - 3 - 4 - 15 - A - C -
3 - Students turn discrete systems into discrete eigenvalue problems and solve 1 - 2 - 3 - 4 - 15 - A - C -
4 - They solve differential equation and differential equation systems 1 - 2 - 3 - 4 - A - C -
5 - Students select suitable series and solve differential equations 1 - 2 - 3 - 4 - 15 - A - C -
Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 15:Problem Solving
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
1 Ability to access wide and deep information with scientific researches in the field of Engineering, evaluate, interpret and implement the knowledge gained in his/her field of study X
2 Develop new strategic approach and produce solutions by taking responsibility in unexpected and complicated situations in mechatronic engineering
3 Aware of social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation, and announcement
4 Develop and use data processing and communication technologies together with the machine, electronic and computer software-hardware knowledge required by the field of mechatronic engineering expertise
5 Ability to complete and implement "limited or incomplete data" by using the scientific methods. X
6 Ability to consolidate engineering problems, develop proper method(s) to solve and apply the innovative solutions to them X
7 Ability to develop new and original ideas and method(s), to develop new innovative solutions at design of system, component or process
8 Ability to design and apply analytical, modeling and experimental based research, analyze and interpret the faced complex issues during the design and apply process X
9 Gain high level ability to define the required information and data
10 Aware of new and developing application of profession and ability to analyze and study on those applications
11 Ability to interpret engineering applications social and environmental dimensions and it´s compliance with the social environment
12 At least be capable of oral and written communication in a foreign language
13 Ability to work in multi-disciplinary teams and to take responsibility to define approaches for complex situations
14 Systematic and clear verbal or written transfer of the process and results of studies at national and international environments
15 Gain comprehensive information on modern techniques, methods and their borders which are being applied to engineering

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 40
KisaSinav 2 15
KisaSinav 3 15
Odev 4 30
Toplam 100
Yıliçinin Başarıya Oranı 40
Finalin Başarıya Oranı 60
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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