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Information
| Code | OMZ201 |
| Name | Applied Engineering Mathematics |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ALİ KESKİN |
| Course Instructor |
Doç. Dr. DİLEK KAHYALAR
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To equip students with knowledge of the basic mathematical concepts used in engineering and to demonstrate analytical solution methods for differential equations that they will encounter in automotive engineering practice.
Course Content
Series. Power Series. Taylor and MacLaurin Series. Complex Numbers. Vector Functions. Gradient, Divergence, Laplacian Operators. Directional Derivatives. Linear Integrals. Area Integrals. Definition and Types of Differential Equations. First Order Equations. Linear Equations. First Order Partial Differential Equations. Second Order Constant Coefficient Equations. Laplace Transform.
Course Precondition
There are no prerequisites for the course.
Resources
Sherman Stein and Anthony Barcellos, Calculus and Analytic Geometry, Mcgraw-Hill, 5th Edition, 1232pp,1992.
Notes
Course presentations and notes of the instructor responsible for the course
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understands sequences, series and complex numbers. |
| LO02 | Defines the concept of vector and the relationship between vectors, lines and planes in 3-dimensional space, and the operations of limit, continuity, derivative and integration in vector-valued functions. |
| LO03 | Explains partial derivatives and the chain rule in functions of several variables. |
| LO04 | Understand the importance of differential equations from an engineering perspective. |
| LO05 | Define differential equations and list the solution methods. |
| LO06 | List the first order differential equations. |
| LO07 | List the second and higher order differential equations. |
| LO08 | List the differential equations with boundary conditions. |
| LO09 | List differential equations with the help of Laplace transform. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Applies sufficient knowledge of mathematics, science, and discipline-specific topics in automotive engineering, utilizing theoretical and practical knowledge in solving complex engineering problems. | 3 |
| PLO02 | Beceriler - Bilişsel, Uygulamalı | Identifies, defines, and solves complex engineering problems in automotive engineering applications using scientific methods. | |
| PLO03 | Beceriler - Bilişsel, Uygulamalı | Designs a complex system, process, device, or product in automotive engineering under realistic constraints and conditions to meet specific requirements and effectively applies modern design methods in this process. | |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Uses information technologies to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in automotive engineering applications. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Designs and conducts experiments, collects data, analyzes, and interprets the results to examine complex engineering problems or discipline-specific research topics in the field of automotive engineering. | |
| PLO06 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Effectively takes responsibility individually and as a team member in intradisciplinary (automotive engineering) and multidisciplinary teams. | |
| PLO07 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Gains knowledge of the legislation related to automotive engineering and awareness of professional ethical responsibility. | |
| PLO08 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning and constantly improving and renewing itself in the field of automotive engineering. | |
| PLO09 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Gains the ability to communicate verbally and in writing in Turkish/English regarding the field of automotive engineering, write reports, prepare design and production reports, make effective presentations and use communication technologies. | |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | Using project design and management knowledge, he/she attempts to develop and realize new ideas regarding automotive engineering applications. | |
| PLO11 | Yetkinlikler - Alana Özgü Yetkinlik | Have awareness of the effects of Automotive Engineering applications on health, environment and safety at universal and social dimensions, and the legal consequences of the problems and solutions of the age reflected in the field of automotive engineering. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Sequences. Series. Convergence-Divergence | Reviewing course notes | Öğretim Yöntemleri: Anlatım |
| 2 | Power Series. Taylor and MAclaurin Series | Conducting research on the subject | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 3 | Complex Numbers | Gathering preliminary information about the subject | Öğretim Yöntemleri: Anlatım |
| 4 | Partial Differentiation. Chain Rule | Review of course notes | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Vector Calculus. Gradient and Directional Derivative | Examining the questions in the lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Multiple Integrals: Double Integrals | Examining the lecture notes of the relevant section | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 7 | Integrals with polar coordinates. Applications | Gathering preliminary information about the subject from lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Midterm Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Divergence, Curl and Laplacian. Line Integrals | Review of related book | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Differential Equations, First-order Differential Equations | Conducting research on the subject | Öğretim Yöntemleri: Anlatım |
| 11 | Linear First-order Partial Differential Equations | Gathering preliminary information about the subject from literature | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Nonhomogeneous Differantial Equations | Examining the questions in the lecture notes | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Laplace transformation | Examining the lecture notes of the relevant section | Öğretim Yöntemleri: Anlatım |
| 14 | Second-order Linear Partial Diffrantial Equations | Gathering preliminary information about the subject from lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 15 | Applications of Differential Equations | Examining the questions in the book | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Writing Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Writing Exam | 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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 7 | 7 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 109 | ||
| Total Workload / 25 (h) | 4,36 | ||
| ECTS | 4 ECTS | ||