MK575 Analytical Methods in Engineering

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MK575
Name Analytical Methods in Engineering
Term 2024-2025 Academic Year
Semester . Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 3 National Credit
Teaching Language İngilizce
Level Yüksek Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator


Course Goal / Objective

Demonstrate analytical and series solutions of differential equations.

Course Content

Review of ordinary differential equations (first order ordinary differential equations, second order equations, Euler equation, higher order linear equations; series solution of second order linear equations; solving linear ordinary differential equations by Laplace transform technique). Partial differential equations (Separation of variables technique. Fourier series and the Fourier theorem. Diffusion equation, Wave equation and Laplace's equations). Complex variable theory. Analytic function of a complex variable. Line integrals of complex functions. The calculation of residues. Evaluation of contour integrals by residue theory. Conformal mapping.

Course Precondition

Yok

Resources

Elementary Differential Equations and Boundary Value Problems, 11th Ed., BOYCE, DIPRIMA & MEADE, Wiley

Notes

Elementary Differential Equations and Boundary Value Problems, 11th Ed., BOYCE, DIPRIMA & MEADE, Wiley


Course Learning Outcomes

Order Course Learning Outcomes
LO01 The student can perform the solution of the ordinary differential equations.
LO02 The student can perform the solution of the partial differential equations.
LO03 The student can perform the solution of the nonlinear differential equations.
LO04 The student can perform the series solution of the differential equations.
LO05 The student can perform the solution of the linear differential equations by the Laplace transformation.
LO06 The student can perform the Fourier series expansion of the differential equations.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Understands and applies basic sciences, mathematics and engineering sciences at a high level. 5
PLO02 Bilgi - Kuramsal, Olgusal He/she has extensive and in-depth knowledge, including the latest developments in his/her field. 4
PLO03 Beceriler - Bilişsel, Uygulamalı They reach the latest information in a field and have a high level of proficiency in the methods and skills necessary to comprehend and research them. 3
PLO04 Beceriler - Bilişsel, Uygulamalı They carry out a comprehensive study that brings innovation to science and technology, develops a new scientific method or technological product/process, or applies a known method to a new field. 2
PLO05 Beceriler - Bilişsel, Uygulamalı Independently perceives, designs, implements and concludes an original research process; manages this process. 2
PLO06 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Contributes to the science and technology literature by publishing the outputs of its academic studies in respected academic environments.
PLO07 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Evaluates scientific, technological, social and cultural developments and conveys them to the society with the awareness of scientific impartiality and ethical responsibility.
PLO08 Yetkinlikler - İletişim ve Sosyal Yetkinlik Performs critical analysis, synthesis and evaluation of ideas and developments in the field of expertise. 3
PLO09 Yetkinlikler - İletişim ve Sosyal Yetkinlik Communicates effectively, both verbally and in writing, with those working in the field of specialization and the wider scientific and social community, communicating and discussing at an advanced level of written, oral and visual communication using a foreign language at least at the C1 General Level of the European Language Portfolio.
PLO10 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Carring out literature survey


Week Plan

Week Topic Preparation Methods
1 Introduction to Differantial Equations Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
2 Review of ordinary differential equations, first order ordinary differential equations Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
3 second order equations Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
4 Euler equation Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
5 higher order linear equations Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
6 series solution of second order linear equations Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
7 solving linear ordinary differential equations by Laplace transform technique Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
8 Mid-Term Exam Study the relevant chapter of the textbook. Ölçme Yöntemleri:
Yazılı Sınav
9 Partial differential equations Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
10 Separation of variables technique. Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
11 Fourier series and the Fourier theorem. Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
12 Diffusion equation, Wave equation and Laplace's equations. Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
13 Complex variable theory. Analytic function of a complex variable. Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
14 The calculation of residues. Evaluation of contour integrals by residue theory. Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
15 Conformal mapping. Study the relevant chapter of the textbook. Öğretim Yöntemleri:
Anlatım
16 Term Exams Study the relevant chapter of the textbook. Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Study the relevant chapter of the textbook. Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 3 42
Out of Class Study (Preliminary Work, Practice) 14 6 84
Assesment Related Works
Homeworks, Projects, Others 3 5 15
Mid-term Exams (Written, Oral, etc.) 1 5 5
Final Exam 1 8 8
Total Workload (Hour) 154
Total Workload / 25 (h) 6,16
ECTS 6 ECTS

Update Time: 07.10.2024 11:30