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  None  
Course Language  English  
Course Type  Required  
Course Level  First Cycle  
Mode of Delivery    
Teaching Methods and Techniques of the Course  
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 Managment Skills Courses  
Transferable Skill Courses 
Week  Subjects  Required Materials 
1  Classification of differential equations. Exact Differential Equations. Non Exact Differential Equations.  Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, AddisonWesley,Section 1.1, 2.4, 2.5. 
2  Separable Differential Equations, Homogeneous Differential Equations. First  Order Linear Differential Equations.  Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, AddisonWesley,Section 2.2, 2.3, 2.6. 
3  Bernoulli Differential Equations. Substitutions and Transformations. Equations with Linear Coefficients.  Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 2.3, 2.4. 
4  Theory of Higher Order Linear Differential Equations, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Case.  Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, AddisonWesley,Section 6.1. 
5  Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Midterm Exam 1.  Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 4.2. Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, AddisonWesley,Section 4.2,4.3 
6  Solution of Nonhomogeneous Differential Equations: Method of Undetermined Coefficients, Method of Variation of Parameters.  Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, AddisonWesley,Section 4.4, 4.6,4.7. 
7  Cauchy Euler Differential Equations. Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform.  Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, AddisonWesley,Section 8.5, 7.2, 7.3. 
8  Inverse Laplace Transforms. Solving Initial Value Problems by Laplace Transforms.  Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, AddisonWesley,Section 7.4, 7.5. 
9  Series Solutions of Differential Equations. Power Series Solutions: Series Solutions around an Ordinary Point.  Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 6.1. 
10  Series Solutions around a Singular Point. Method of Frobenius. Midterm Exam 2.  Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 6.2. 
11  Systems of Linear Differential Equations: Differential Operators and an Operator Method.  Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons, Section 7.1. 
12  Basic Theory of Linear Systems in Normal Form: Two Equations in Two Unknown Functions. Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions.  Introduction to Ordinary Differential Equations by Shepley L. Ross. 4thEdit., John Wiley and Sons, Sect. 7.3,7.4 
13  The Matrix Method for Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions, n Equations in n Unknown Functions.  Introduction to Ordinary Differential Equations by Shepley L. Ross. 4thEdition, John Wiley and Sons, Sect. 7.6, 7.7 
14  Approximate methods of solving firstorder equations: The method of successive approximations. The Euler method. The improved Euler method.  Introduction to Ordinary Differential Equations by Shepley L. Ross. 4thEdition, John Wiley and Sons, Sect. 8.3, 8.4, 8.5 
15  Review of the semester.  
16  Final Exam 
Course Notes/Textbooks  Fundamentals of Differential Equations and Boundary Value Problems, 6th Edition by Nagle, Saff and Snider, Pearson, AddisonWesley,Section , Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons. 
Suggested Readings/Materials  None 
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  4  64 
Laboratory / Application Hours (Including exam week: 16 x total hours)  16  
Study Hours Out of Class  16  1  
Field Work  
Quizzes / Studio Critiques  
Portfolio  
Homework / Assignments  
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterms  2  10  
Final Exams  1  30  
Total  130 
#  Program Competencies/Outcomes  * Contribution Level  
1  2  3  4  5  
1  To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics.  X  
2  To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics,  X  
3  To be able to define and analyze problems and to find solutions based on scientific methods,  X  
4  To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials,  X  
5  To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,  X  
6  To be able to criticize and renew her/his own models and solutions,  X  
7  To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way,  X  
8  To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge uptodate, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,  X  
9  To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,  
10  To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,  X  
11  To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,  
12  By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,  X  
13  To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,  
14  To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,  
15  To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. 
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest