TÜRKÇE
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Information
| Code | MDZ208 |
| Name | Maths 4 |
| Term | 2024-2025 Academic Year |
| Semester | 4. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 5 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 Instructor |
1 |
Course Goal / Objective
In order to solve a large number of problems in engineering, we first formulate these problems with mathematical expressions and use some initial and boundary conditions to reveal the functions that form the solutions of the problems.
Course Content
First order differential equations; Separable equations, Linear Equations, Exact diff. equations and integral factor, Higher order diff. Equations, Equations with constant coefficients, Undetermined coefficients method. method of variation of parameters, Laplace transforms, basic definitions and theorems
Course Precondition
NONE
Resources
Differential Equations L.Shipley ROSS
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Gains information about startup problems. |
| LO02 | Can define and classify differential equation. |
| LO03 | A differential equation can be obtained by eliminating arbitrary constants from a given relation. |
| LO04 | Can recognize general types of first order differential equations and find their general solutions. |
| LO05 | Knows the basic theory of higher order Linear Differential equations. |
| LO06 | Can find general solutions of homogeneous linear differential equations with constant coefficients. |
| LO07 | Can use Uncertain coefficients Method to find specific solution. |
| LO08 | Finds the general solution of the Cauchy Euler Equation. |
| LO09 | Gains information about boundary value problems. |
| LO10 | Can find general solutions of non-homogeneous Linear Differential equations with Constant Coefficients. |
| LO11 | Can use Variation of Parameters Method to find specific solution. |
| LO12 | Gain information about separable 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. | |
| 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. | 5 |
| 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 and classification of Differential Equations | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Initial and boundary value problems | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Obtaining differential equations | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Exact Differential Equations and Integral Factor | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Separable Differential equations | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Homogeneous Differential equations | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Linear and Bernouilli Differential Equations | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Lecture Notes | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Basic theory of Linear Equations | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Homogeneous equations with constant coefficients I | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Homogeneous equations with constant coefficients II | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Uncertain Coefficients Method | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Method of change of parameters | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Cauchy Euler Equation | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | An overview | Literature Research | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Lecture Notes | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Lecture Notes | 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 | 4 | 56 |
| 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) | 116 | ||
| Total Workload / 25 (h) | 4,64 | ||
| ECTS | 5 ECTS | ||