MATHEMATICS
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

Basic information

Language of instruction: English
Type of course: Must Course
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator : Dr. Öğr. Üyesi GÜLSEMAY YİĞİT
Course Lecturer(s): Prof. Dr. NAFİZ ARICA
Recommended Optional Program Components: None
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 Outcomes

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 / Textbooks: 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
Quizzes 2 % 20
Midterms 1 % 35
Final 1 % 45
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) To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics 5
2) To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods, 5
3) To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials, 5
4) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, 4
5) To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way, 4
6) To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,
7) 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,
8) 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, 4
9) 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, 3
10) To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning, 3
11) To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school, 3
12) 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. 4