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


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 Content  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 Management Skills Courses  
Transferable Skill Courses 
Week  Subjects  Related Preparation 
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. 4th Edit., 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. 4th Edition, 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. 4th Edition, John Wiley and Sons, Sect. 8.3, 8.4, 8.5. 
15  Review of the semester.  
16  Final Exam 
Course 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. 
References  None 
Semester Requirements  Number  Percentage 
Participation  
Laboratory / Application  
Field Work  
Quizzes / Studio Critiques  
Homework / Assignments  
Presentation / Jury  
Project  
Seminar / Workshop  
Portfolios  
Midterms / Oral Exams 
2

60

Final / Oral Exam 
1

40

Total 
Contribution of Semester Work to Final Grade  2 
60 
Contribution of Final Work to Final Grade  1 
40 
Total 
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  
Homework / Assignments  
Presentation / Jury  
Project  
Seminar / Workshop  
Portfolios  
Midterms / Oral Exams 
2

10


Final / Oral Exam 
1

30


Total 
130

#

Program Qualifications / Outcomes 
* Level of Contribution


1 
2 
3 
4 
5 

1  Adequate knowledge in Mathematics, Science and Civil Engineering; ability to use theoretical and applied information in these areas to model and solve Civil Engineering problems  
2  Ability to identify, define, formulate, and solve complex Civil Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose  
3  Ability to design a complex system, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose  
4  Ability to devise, select, and use modern techniques and tools needed for Civil Engineering practice  
5  Ability to design and conduct experiments, gather data, analyze and interpret results for investigating Civil Engineering problems  
6  Ability to work efficiently in Civil Engineering disciplinary and multidisciplinary teams; ability to work individually  
7  Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of two foreign languages  
8  Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself  
9  Awareness of professional and ethical responsibility  
10  Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development  
11  Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of Civil Engineering solutions 
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest