| Course Name | Introduction to Differential Equations II |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| MATH 208 | Spring | 2 | 2 | 3 | 5 |
| Prerequisites |
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| Course Language | English | ||||||||
| Course Type | Required | ||||||||
| Course Level | First Cycle | ||||||||
| Mode of Delivery | - | ||||||||
| Teaching Methods and Techniques of the Course | Problem SolvingCase StudyQ&ASimulation | ||||||||
| Course Coordinator | - | ||||||||
| Course Lecturer(s) | |||||||||
| Assistant(s) | |||||||||
| Course Objectives | This course includes classification, applications and solution methods of partial differential equations. Fourier series for periodic functions, solution of heat and wave equation by separation method, solution methods of Laplace equation in rectangular and polar coordinates are aimed. |
| Learning Outcomes | The students who succeeded in this course;
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| Course Description | In this course basic concepts and classification of partial differential equations will be discussed. The heat, wave and Laplace equation will be given and the solution methods will be taught. |
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| Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 1 | Mathematical background for the study of partial differential equations | Erwin Kreyszig, “Advanced Engineering Mathematics”,10Th Edition, (John Wiley and Sons), Sections 9.5, 9.7, 9.8 |
| 2 | Description of partial differential equations. Classification and model definitions. First order partial differential equations | Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 1.1. to 1.7 |
| 3 | Modelling first order partial differential equations. Solving by the method of characteristics | Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 2.1. to 2.4 |
| 4 | Modelling continuity equation, wave equation and traffics flow and applications | Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 2.1. to 2.4 |
| 5 | Partial Laplace transform. Solving first order partial differential equations by partial Laplace transform. | “http://www.math.ttu.edu/~gilliam /ttu/s10/m3351_s10/c15_laplace_trans_pdes.pdf” Chapter 15 |
| 6 | Heat Equation. Solution by separation of variables. Existence and Uniqueness of Solutions. | Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.5. |
| 7 | Heat and diffusion equations examples and interpretation of the solution results | Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.5-10.7 |
| 8 | Midterm Exam I | |
| 9 | The wave equation. Solution by seperation of variables. Existence and Uniqueness of Solutions. | Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.6. |
| 10 | The Laplace's equation in rectangular coordinates. Solution by separation of variables. Existence and Uniqueness of Solutions. | Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.7. |
| 11 | Laplace's equation in polar coordinates and its solution by the method of separation of variables. | Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.7. |
| 12 | Solving second order partial differential equations by partial Laplace transform. | “http://www.math.ttu.edu/~gilliam/ttu/s10/m3351_s10/c15_laplace_trans_pdes.pdf” Chapter 15 |
| 13 | Numerical solutions of heat equation | David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), Sections: 9.1,9.2 |
| 14 | Numerical solutions of wave equation | David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), Sections: 9.1,9.2 |
| 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 | Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), ISBN-13:978-0-521-84886-2 Erwin Kreyszig, “Advanced Engineering Mathematics”,10Th Edition, (John Wiley and Sons), ISBN: 978-0-470-45836-5 David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), ISBN-10: 0-534-13014-3 |
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | 1 | 20 |
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 1 | 30 |
| Final Exam | 1 | 50 |
| Total |
| Weighting of Semester Activities on the Final Grade | 2 | 50 |
| Weighting of End-of-Semester Activities on the Final Grade | 1 | 50 |
| Total |
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Course Hours (Including exam week: 16 x total hours) | 16 | 4 | 64 |
| Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
| Study Hours Out of Class | 14 | 3 | 42 |
| Field Work | |||
| Quizzes / Studio Critiques | |||
| Portfolio | |||
| Homework / Assignments | 1 | 10 | |
| Presentation / Jury | |||
| Project | |||
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 1 | 14 | |
| Final Exams | 1 | 20 | |
| Total | 150 |
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
| 1 | To be able master and use fundamental phenomenological and applied physical laws and applications, | X | ||||
| 2 | To be able to identify the problems, analyze them and produce solutions based on scientific method, | X | ||||
| 3 | To be able to collect necessary knowledge, able to model and self-improve in almost any area where physics is applicable and able to criticize and reestablish his/her developed models and solutions, | X | ||||
| 4 | To be able to communicate his/her theoretical and technical knowledge both in detail to the experts and in a simple and understandable manner to the non-experts comfortably, | |||||
| 5 | To be familiar with software used in area of physics extensively and able to actively use at least one of the advanced level programs in European Computer Usage License, | |||||
| 6 | To be able to develop and apply projects in accordance with sensitivities of society and behave according to societies, scientific and ethical values in every stage of the project that he/she is part in, | |||||
| 7 | To be able to evaluate every all stages effectively bestowed with universal knowledge and consciousness and has the necessary consciousness in the subject of quality governance, | |||||
| 8 | To be able to master abstract ideas, to be able to connect with concreate events and carry out solutions, devising experiments and collecting data, to be able to analyze and comment the results, | |||||
| 9 | To be able to refresh his/her gained knowledge and capabilities lifelong, have the consciousness to learn in his/her whole life, | |||||
| 10 | To be able to conduct a study both solo and in a group, to be effective actively in every all stages of independent study, join in decision making stage, able to plan and conduct using time effectively. | |||||
| 11 | To be able to collect data in the areas of Physics and communicate with colleagues in a foreign language ("European Language Portfolio Global Scale", Level B1). | |||||
| 12 | To be able to speak a second foreign at a medium level of fluency efficiently | |||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
