Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
ANALYTİC METHODS II MEK 602 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. ERGÜN NART Dersi Verenler 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 It contains analytical solution methods in engineering mathematics. It starts with variational calculus, continue with complex functions, and finishes with Hilbert transformations.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Students know the main idea of variational calculus 1 - 2 - 3 - 4 - 15 - A - C - 2 - They apply variational calculus in mechanical problems 1 - 2 - 3 - 4 - 15 - A - C - 3 - Student know definitions, introduction, multivalued functions of complex variables 1 - 2 - 3 - 4 - 15 - A - C - 4 - They take derivatives of complex variable functions and test Cauchy-Riemann conditions 1 - 2 - 3 - 4 - 15 - A - C - 5 - Students find Laurent series for functions 1 - 2 - 3 - 4 - 15 - A - C - 6 - They calculate infinite integrals 1 - 2 - 3 - 4 - 15 - A - C - 7 - Students know partial differential equations and the solution techniques, and apply boundary conditions 1 - 2 - 3 - 4 - 15 - A - C - 8 - They know integral transformations 1 - 2 - 3 - 4 - 15 - A - C - 9 - Students apply Laplace transformation to engineering problems 1 - 2 - 3 - 4 - 15 - A - C - 10 - They apply Mellin transformation to engineering problems 1 - 2 - 3 - 4 - 15 - A - C - 11 - Students apply Henkel transformation to engineering problems 1 - 2 - 3 - 4 - 15 - A - C - 12 - They apply Hilbert transformation to engineering problems 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 Variational Calculus
2 Complex Variables : Definitions, introduction, multivalued functions
3 Derivatives, Analytic Functions, Cauchy-Riemann Conditions
4 Laurent series, Residues, simple and multiple poles, examples : contour integrals, evaluation of some real definite integrals
5 Infinite integrals, examples : Fourier integrals, branch cuts
6 Partial Differential Equations ( unbounded domain )
7 Characteristic equation, example : the wave equations, continuous eigenvalues : Fourier series to Fourier integrals
8 Integral Transforms
9 Initial Value Problems Laplace Transform
10 Midterm exam
11 Boundary Value Problems in Polar Coord. Mellin Transforms
12 Integral Equations
13 Boundary Value Problems in cylindrical coord. Hankel Transform
14 Hibert Transforms

#### 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

#### 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
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 &quot;limited or incomplete data&quot; by using the scientific methods.
6 Ability to consolidate engineering problems, develop proper method(s) to solve and apply the innovative solutions to them
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
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 45
KisaSinav 1 15
Odev 1 2
ProjeTasarim 1 10
KisaSinav 2 15
Odev 2 2
Odev 3 2
Odev 4 2
Odev 5 2
Odev 6 2
Odev 7 3
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 4 4
Quiz 2 5 10
Assignment 7 5 35
Project / Design 1 5 5
Final examination 1 10 10
Toplam İş Yükü 160
Toplam İş Yükü /25(s) 6.4
Dersin AKTS Kredisi 6.4
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