FACULTY OF ARTS AND SCIENCES
Department of Mathematics
SOCIAL MEDIA
MATH 207 | Course Introduction and Application Information
| Course Name |
Introduction to Differential Equations I
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 207
|
Fall
|
2
|
2
|
3
|
5
|
| Prerequisites |
|
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| Course Language |
English
|
|||||||||
| Course Type |
Required
|
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| Course Level |
First Cycle
|
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| Mode of Delivery | face to face | |||||||||
| Teaching Methods and Techniques of the Course | Problem SolvingCase StudyQ&A | |||||||||
| Course Coordinator | ||||||||||
| Course Lecturer(s) | ||||||||||
| 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;
|
| 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. |
|
|
Core Courses |
X
|
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 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. |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| 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 |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
2
|
32
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
2
|
32
|
| Study Hours Out of Class |
14
|
3
|
42
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
0
|
||
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
12
|
24
|
| Final Exam |
1
|
20
|
20
|
| Total |
150
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. |
X | ||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. |
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| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. |
X | ||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. |
X | ||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. |
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| 6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. |
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| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. |
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| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. |
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| 9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. |
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| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. |
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| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. |
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| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
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| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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