TÜRKÇE
ENGLISH
Information
| Code | MDZ202 |
| Name | Differential Equations |
| Semester | 4. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ZERRİN GÜL ESMERLİGİL |
Course Goal
Objectives of this course is, to solve many problems in engineering, first, formulate these problems with mathematical statements and find solutions of problems by using initial and bounded condition.
Course Content
First order differential equations; separable equations, linear equations, Exact equations and integrating factor, Higher order differential equations; the method of variation of parameters, Constant coefficient equations, the method of undetermined coefficients/ Laplace transformation; basic definition and theorems.
Course Precondition
None
Resources
Differential Equations L.Shipley ROSS
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Has the knowledge on initial problems |
| LO02 | Can make definition and classification of differential equations |
| LO03 | Can obtain a differential equation eliminating arbitrary constants from a given function. |
| LO04 | Can remember general type of differential equations of first order and can find general solutions of them |
| LO05 | Can know about main theory of higher order linear differential equations. |
| LO06 | Can find the general solutions of homogeneous linear differential equations with constant coefficients. |
| LO07 | Can find general solutions of with constant coefficients using undetermined coefficients. |
| LO08 | Can find general solutions of Cauchy Euler equations |
| LO09 | Has the knowledge on bounded value problems |
| LO10 | Can find the general solutions of nonhomogeneous linear differential equations with constant coefficients. |
| LO11 | Can find general solutions of Linear equations with constant coefficients. |
| LO12 | Has the knowledge on the seperable Differential Equations |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Students has sufficient knowledge on theoretical and applied subjects in the light of contemporary knowledge and scientific approaches in the field of mining. | |
| PLO02 | Beceriler - Bilişsel, Uygulamalı | Applies the knowledge she has received in the field of mining in multidisciplinary studies to produce solutions to the problems she has encountered. | |
| PLO03 | Beceriler - Bilişsel, Uygulamalı | Analyzes problems with the help of up-to-date information and makes inferences for solutions. | 4 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | It applies physical, chemical, mechanical and mineralogical analyzes in accordance with TSE standards in field studies or laboratory conditions. | 4 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Has the ability to analyze the engineering plans. | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | It dominates the machinery park in mining enterprises and can use them for the execution of mining activities. | 4 |
| PLO07 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Students has the ability to solve the problems she encounters by working individually or in a team with other disciplines. | 5 |
| PLO08 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | It constantly follows the developments in the mining field, as it knows that the information is not static. | 4 |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | It can use printed publications or databases to obtain the necessary information in mining processes. | 5 |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | He/she carries out all his/her work in a planned way in order to constantly improve himself/herself and increase her knowledge level. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Uses computers and other electronic resources in mining. | 5 |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | Uses at least one foreign language at B1 General Level in order to communicate and access information. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Performs technical drawings by thinking in three dimensions in the studies she has done in her field. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | It has the awareness of adhering to moral and ethical values while carrying out its mining activities. | 5 |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | It is aware of the need to prioritize the environment and the health of employees, as it has an infrastructure on Occupational Health and Safety awareness in mining and their legal obligations. | |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | Knows that the solutions to the problems in the mining field affect societies and communities, so they have information about the innovative applications and models developed. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition of Differential Equations and Classification | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Iitial and Bounded Value Problems | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Obtained Differential Equations | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Exact Differential Equations and Integrating Factor | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Seperable Differential Equations | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Homogenous Differential Equations | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Linear and Bernouilli Differential Equations | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Midterm Exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | Main theory of High order Linear Differential Equations | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Homogenous Differential Equations with Costant Coefficient I | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Homogenous Differential Equations with Costant Coefficient II | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Uncertain Coefficient Method | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Method of the variation of Parameters | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Cauchy-Euler Equation | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | General Review | Literature research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Final exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Final exam | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 2 | 28 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 88 | ||
| Total Workload / 25 (h) | 3,52 | ||
| ECTS | 4 ECTS | ||