| Course Name | Introduction to Differential Equations I |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| MATH 207 | Fall/Spring | 2 | 2 | 3 | 5 |
| Prerequisites |
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| Course Language | English | |||||||||||
| Course Type | Elective | |||||||||||
| Course Level | First Cycle | |||||||||||
| Mode of Delivery | - | |||||||||||
| Teaching Methods and Techniques of the Course | Problem SolvingCase StudyQ&A | |||||||||||
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| Assistant(s) | ||||||||||||
| Course Objectives | This course is an introduction to the basic concepts, theory, methods and applications of ordinary differential equations. The aim of this course is to solve differential equations and to develop the basics of modeling of real life problems. |
| Learning Outcomes | The students who succeeded in this course;
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| Course Description | In this course basic concepts of differential equations will be discussed.The types of first order ordinary differential equations will be given and the solution methods will be taught. Also, solution methods for higherorder ordinary differential equations will be analyzed. |
| Related Sustainable Development Goals | |
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| Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 1 | Description and Classification of differential equations. Separable Differential Equations. First - Order Linear Differential Equations. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 1.1, 2.2, 2.3 |
| 2 | Exact Differential Equations. Non- Exact Differential Equations. Bernoulli Differential Equations. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section: 2.4, 2.5 |
| 3 | Homogeneous Constant Coefficient Second Order Differential Equations. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.2 |
| 4 | Non-homogeneous Constant Coefficient Second Order Differential Equations. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.4 |
| 5 | Non-homogeneous Constant Coefficient Second Order Differential Equations. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.6, 4.7, 6.3, 6.4 |
| 6 | Systems of Linear Differential Equations | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5 |
| 7 | Systems of Linear Differential Equations/ Matrix Exponential | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.8 |
| 8 | Midterm Exam | |
| 9 | Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform Inverse Laplace Transforms. Solving Initial Value Problems by Laplace Transforms. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 7.2, 7.3. 7.4, 7.5. |
| 10 | Laplace Transform: Systems of Linear Differential Equations (Including Non-homogeneous Case) | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 7.9 |
| 11 | Series Solutions of Differential Equations. Power Series Solutions: Series Solutions around an Ordinary Point. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 6.1. |
| 12 | Series Solutions around a Singular Point. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 8.3 |
| 13 | Boundary Value Problems | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 1.1, 2.4, 2.5 |
| 14 | Approximate methods of solving first-order equations: The method of successive approximations. The Euler method. The improved Euler method. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Sect. 11.3, 11.4 |
| 15 | Semester review | |
| 16 | Final exam |
| Course Notes/Textbooks | Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), ISBN-13: 978-0321747747. |
| Suggested Readings/Materials | Shepley L. Ross, ''Introduction to Ordinary Differential Equations'', Fourth Edition, (John Wiley and Sons,1989), ISBN-13: 978-0471032953. |
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 2 | 60 |
| Final Exam | 1 | 40 |
| Total |
| Weighting of Semester Activities on the Final Grade | 2 | 60 |
| Weighting of End-of-Semester Activities on the Final Grade | 1 | 40 |
| Total |
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Course Hours (Including exam week: 16 x total hours) | 16 | 2 | 32 |
| Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | 2 | |
| Study Hours Out of Class | 14 | 3 | 42 |
| Field Work | |||
| Quizzes / Studio Critiques | |||
| Portfolio | |||
| Homework / Assignments | |||
| Presentation / Jury | |||
| Project | |||
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 2 | 12 | |
| Final Exams | 1 | 20 | |
| Total | 150 |
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
| 1 | Being able to transfer knowledge and skills acquired in mathematics and science into engineering, | |||||
| 2 | Being able to identify and solve problem areas related to Food Engineering, | |||||
| 3 | Being able to design projects and production systems related to Food Engineering, gather data, analyze them and utilize their outcomes in practice, | |||||
| 4 | Having the necessary skills to develop and use novel technologies and equipment in the field of food engineering, | |||||
| 5 | Being able to take part actively in team work, express his/her ideas freely, make efficient decisions as well as working individually, | |||||
| 6 | Being able to follow universal developments and innovations, improve himself/herself continuously and have an awareness to enhance the quality, | |||||
| 7 | Having professional and ethical awareness, | |||||
| 8 | Being aware of universal issues such as environment, health, occupational safety in solving problems related to Food Engineering, | |||||
| 9 | Being able to apply entrepreneurship, innovativeness and sustainability in the profession, | |||||
| 10 | Being able to use software programs in Food Engineering and have the necessary knowledge and skills to use information and communication technologies that may be encountered in practice (European Computer Driving License, Advanced Level), | |||||
| 11 | Being able to gather information about food engineering and communicate with colleagues using a foreign language ("European Language Portfolio Global Scale", Level B1) | |||||
| 12 | Being able to speak a second foreign language at intermediate level. | |||||
| 13 | Being able to relate the knowledge accumulated during the history of humanity to the field of expertise | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
