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Prerequisites 
 
Course Language  English  
Course Type  Required  
Course Level  First Cycle  
Mode of Delivery    
Teaching Methods and Techniques of the Course  Problem Solving Case Study Q&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  
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  Nonhomogeneous 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  Nonhomogeneous 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 Nonhomogeneous 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 firstorder 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), ISBN13: 9780321747747. 
Suggested Readings/Materials  Shepley L. Ross, ''Introduction to Ordinary Differential Equations'', Fourth Edition, (John Wiley and Sons,1989), ISBN13: 9780471032953. 
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 EndofSemester 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  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 selfimprove 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 nonexperts 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