Faculty Of Engıneerıng
Computer And Software Engıneerıng
Course Information
| DIFFERENTIAL EQUATIONS | |||||
|---|---|---|---|---|---|
| Code | Semester | Theoretical | Practice | National Credit | ECTS Credit |
| Hour / Week | |||||
| MAT203 | Fall | 4 | 0 | 4 | 5 |
| Prerequisites and co-requisites | MAT 104 Mathematics II |
|---|---|
| Language of instruction | English |
| Type | Required |
| Level of Course | Bachelor's |
| Lecturer | Asst. Prof. Çağdaş ALLAHVERDİ |
| Mode of Delivery | Face to Face |
| Suggested Subject | None |
| Professional practise ( internship ) | None |
| Objectives of the Course | The objectives of this course are to introduce the student with the concept of a differential equation, basic techniques for solving certain classes of differential equations, especially those which are linear, and making connections between the qualitative features of the equation and the solutions. Connections to problems from the physical world are emphasized. As well as ordinary differential equations, the course aims to introduce the students to certain partial differential equations. |
| Contents of the Course | First order equations and various applications. Higher order linear differential equations. Power series solutions. The Laplace transform. Solutions of initial value problems. Systems of linear differential equations. Introduction to partial differential equations. |
Learning Outcomes of Course
| # | Learning Outcomes |
|---|---|
| 1 | Apply mathematics, science and engineering knowledge and experience to real world problems. |
| 2 | Design and execute experiments and analyze the results. |
| 3 | Identify engineering problems and suggest solutions. |
| 4 | Express himself freely and develop new ideas through communication. |
| 5 | Have the ability of time management and plan his professional development. |
| 6 | Perform his job willingly and in service of community. |
| 7 | Work with professional and ethical responsibility for the benefit of humanity. |
Course Syllabus
| # | Subjects | Teaching Methods and Technics |
|---|---|---|
| 1 | Definitions, terminology and initial value problems | Lecturing |
| 2 | First order differential equations: separable and linear equations | Lecturing |
| 3 | First order differential equations: exact equations | Lecturing |
| 4 | Modeling with first order differential equations: linear equations | Lecturing |
| 5 | Modeling with first order differential equations: nonlinear equations | Lecturing |
| 6 | Higher order differential equations: reduction of order, homogeneous linear equations, superposition and annihilator appr. | Lecturing |
| 7 | Modeling with higher order differential equations: spring-mass systems, series circuit analogue etc. | Lecturing |
| 8 | Midterm Exam | Exam |
| 9 | Series solutions of linear equations | Lecturing |
| 10 | Matrix notation of differential equations | Lecturing |
| 11 | Laplace transform | Lecturing |
| 12 | Homogeneous linear systems | Lecturing |
| 13 | Nonhomogeneous linear systems | Lecturing |
| 14 | Numerial solutions of ordinary differential equations: Euler methods | Lecturing |
| 15 | Numerial solutions of ordinary differential equations: Runge-Kutta method | Lecturing |
| 16 | Final Exam | Exam |
Course Syllabus
| # | Material / Resources | Information About Resources | Reference / Recommended Resources |
|---|---|---|---|
| 1 | Dennis G. Zill, A First Course in Differential Equations with Modeling Applications, 10th Edition, ISBN-13: 978-1-111-82705-2 ISBN-10: 1-111-82705-2, 2012. |
Method of Assessment
| # | Weight | Work Type | Work Title |
|---|---|---|---|
| 1 | 40% | Mid-Term Exam | Mid-Term Exam |
| 2 | 60% | Final Exam | Final Exam |
Relationship between Learning Outcomes of Course and Program Outcomes
| # | Learning Outcomes | Program Outcomes | Method of Assessment |
|---|---|---|---|
| 1 | Apply mathematics, science and engineering knowledge and experience to real world problems. | 1 | 1͵2 |
| 2 | Design and execute experiments and analyze the results. | 1 | 1͵2 |
| 3 | Identify engineering problems and suggest solutions. | 1 | 1͵2 |
| 4 | Express himself freely and develop new ideas through communication. | 1 | 1͵2 |
| 5 | Have the ability of time management and plan his professional development. | 1 | 1͵2 |
| 6 | Perform his job willingly and in service of community. | 1 | 1͵2 |
| 7 | Work with professional and ethical responsibility for the benefit of humanity. | 1 | 1͵2 |
Work Load Details
| # | Type of Work | Quantity | Time (Hour) | Work Load |
|---|---|---|---|---|
| 1 | Course Duration | 14 | 4 | 56 |
| 2 | Course Duration Except Class (Preliminary Study, Enhancement) | 14 | 4 | 56 |
| 3 | Presentation and Seminar Preparation | 0 | 0 | 0 |
| 4 | Web Research, Library and Archival Work | 0 | 0 | 0 |
| 5 | Document/Information Listing | 0 | 0 | 0 |
| 6 | Workshop | 0 | 0 | 0 |
| 7 | Preparation for Midterm Exam | 0 | 0 | 0 |
| 8 | Midterm Exam | 1 | 3 | 3 |
| 9 | Quiz | 0 | 0 | 0 |
| 10 | Homework | 4 | 8 | 32 |
| 11 | Midterm Project | 0 | 0 | 0 |
| 12 | Midterm Exercise | 0 | 0 | 0 |
| 13 | Final Project | 0 | 0 | 0 |
| 14 | Final Exercise | 0 | 0 | 0 |
| 15 | Preparation for Final Exam | 0 | 0 | 0 |
| 16 | Final Exam | 1 | 3 | 3 |
| 150 | ||||