ARTIFICIAL INTELLIGENCE ENGINEERING
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT2062 Differential Equations Spring 3 0 3 6
The course opens with the approval of the Department at the beginning of each semester

Basic information

Language of instruction: En
Type of course: Must Course
Course Level: Bachelor
Mode of Delivery: Face to face
Course Coordinator : Dr. Öğr. Üyesi GÜLSEMAY YİĞİT
Course Lecturer(s): Prof. Dr. NAFİZ ARICA
Course Objectives: This course covers the fundamental concepts of an introductory level of elementary differential equations with basic concepts, theory, solution methods and applications. Main goal is to develop the basics of modeling at an introductory level and connect this step to the theoretical and methodological resource of mathematics.

Learning Outputs

The students who have succeeded in this course;
1. Classify differential equations and determine the existence and uniqueness of solutions of Initial Value Problems
2. Solve first order separable and linear differential equations
3. Use substitution methods to solve homogeneous and Bernoulli equations
4. Solve exact differential equations
5. Solve the higher order linear homogeneous and nonhomogeneous differential equations
6. Solve the systems of linear differential equations
7. Solve differential equations by using Laplace transform method

Course Content

In this course basic concepts of elementary differential equations will be covered. The solution techniques for the different types of first order differential equations will be given and the solution methods will be taught. The higher order linear differential equations and solution methods will be discussed. The systems of linear equations will be covered with different techniques. Finally, the Laplace Transform method will be taught to solve linear differential equations.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Classification of differential equations, Explicit solution, implicit solution, Initial Value Problems, Integrals as General and Particular Solutions.
2) Existence and Uniqueness of Solution. Separable Differential Equations.
3) First Order Linear Differential Equations.
4) Substitutions methods. Homogeneous Differential Equations. Bernoulli Differential Equations.
5) Exact Differential Equations.
6) Population models. Reducible second order equations.
7) Theory of Higher Order Linear Differential Equations, Existence and Uniqueness Theorem, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Cases.
8) Homogeneous Linear Equations with Constant Coefficients. Euler Equations.
9) Solution of Nonhomogeneous Linear Differential Equations. Method of Undetermined Coefficients.
10) Solution of Nonhomogeneous Linear Differential Equations. Method of Variation of Parameters.
11) Theory of Systems of Linear Differential Equations.
12) The Eigenvalue Method for Systems of Linear Differential Equations.
13) Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform. Inverse Laplace Transform.
14) Solution of Differential Equations by using Laplace Transform.

Sources

Course Notes: Differential Equations with Boundary Value Problems by C. Henry Edwards & D. E.Penney, sixth edition
References: Introduction to Ordinary Differential Equations” by Shepley L. Ross. Fourth Edition, John Wiley and Sons.

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 0 % 0
Laboratory 0 % 0
Application 0 % 0
Field Work 0 % 0
Special Course Internship (Work Placement) 0 % 0
Quizzes 2 % 20
Homework Assignments 0 % 0
Presentation 0 % 0
Project 0 % 0
Seminar 0 % 0
Midterms 1 % 35
Preliminary Jury 0 % 0
Final 1 % 45
Paper Submission 0 % 0
Jury 0 % 0
Bütünleme % 0
Total % 100
PERCENTAGE OF SEMESTER WORK % 55
PERCENTAGE OF FINAL WORK % 45
Total % 100

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Have sufficient background in mathematics, science and artificial intelligence engineering. 5
2) Use theoretical and applied knowledge in the fields of mathematics, science and artificial intelligence engineering together for engineering solutions. 5
3) Identify, define, formulate and solve engineering problems, select and apply appropriate analytical methods and modeling techniques for this purpose.
4) Analyse a system, system component or process and design it under realistic constraints to meet desired requirements; apply modern design methods in this direction.
5) Select and use modern techniques and tools necessary for engineering applications.
6) Design and conduct experiments, collect data, and analyse and interpret results.
7) Work effectively both as an individual and as a multi-disciplinary team member.
8) Access information via conducting literature research, using databases and other resources
9) Follow the developments in science and technology and constantly update themself with an awareness of the necessity of lifelong learning.
10) Use information and communication technologies together with computer software with at least the European Computer License Advanced Level required by their field.
11) Communicate effectively, both verbal and written; know a foreign language at least at the European Language Portfolio B1 General Level.
12) Have an awareness of the universal and social impacts of engineering solutions and applications; know about entrepreneurship and innovation; and have an awareness of the problems of the age.
13) Have a sense of professional and ethical responsibility.
14) Have an awareness of project management, workplace practices, employee health, environment and work safety; know the legal consequences of engineering practices.