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
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;
  • will be able to classify the differential equations.
  • will be able to use solution methods of first order ordinary differential equations.
  • will be able to solve higher order linear differential equations with constant coefficients.
  • will be able to understand the Laplace transform method of linear differential equations.
  • will be able to analyze series solutions of linear differential equations.
  • will be able to solve systems of linear differential equations.
  • will be able to analyze approximate methods of solving first-order equations by using the method of succesive approximations and the Euler method.
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.

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

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, Addison-Wesley,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, Addison-Wesley,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, Addison-Wesley,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, Addison-Wesley,Section 4.2,4.3
6 Solution of Non-homogeneous 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, Addison-Wesley,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, Addison-Wesley,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, Addison-Wesley,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 first-order 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, Addison-Wesley,Section , Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons.
Suggested Readings/Materials None

 

EVALUATION SYSTEM

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 End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

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

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
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 up-to-date, 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

 

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