Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
3MATH257DIFFERENTIAL EQUATIONS4+046

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course Differential equations are the main tools in modeling real-world phenomena and the area of study and development of several fundamental mathematical methods by great mathematicians of the past. The equations formulate some physical, chemical, etc. laws in compact form, and the solution of these equations allows us to predict the behavior of the corresponding system for different times, space, and other variables. The goal of the course is to make students acquainted with the main types of ordinary differential equations, methods of solving these equations, and applications of the equations to modeling some problems from science and engineering. The course will prepare students to study partial differential equations, differential geometry, dynamical systems, modeling and other applied mathematics subjects.
Course Content Introduction to Differential Equations, Solutions to First-Order Differential Equations and Initial Value Problems, Direction Fields and Autonomous ODE, Basic Theory of Second and Higher-Order Linear Differential Equations, Methods for Solving Linear Homogeneous and Nonhomogeneous ODE, Modeling with Second and Higher-Order Differential Equations, Series Solutions of Linear Equations, The Laplace Transform Approach to Linear ODE, Basic Theory of Systems of Linear First-Order Differential Equations, Solving Homogeneous and Nonhomogeneous Linear Systems.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator Prof.Dr. Şirin Atılgan Büyükaşık
Name of Lecturers Prof.Dr. ŞİRİN ATILGAN BÜYÜKAŞIK
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Elementary Differential Equations and Boundary Value Problems, W. E. Boyce and R. C. Di Prima, WILEY, 10-th Edition, 2012
A First Course in Differential Equations with Modeling Applications, D. G. Zill, CENGAGE Learning, 2016.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 60
Quizzes 4 % 10
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 30
Total
7
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 3 14 42
Exams and Exam Preparations 1 140 140
Total Work Load   Number of ECTS Credits 6 182

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To understand the problem and geometry of differential equations
2 To be able to recognize and solve certain first-order ODE
3 To understand the basic theory of higher-order linear ODE
4 To be able to find homogeneous and particular solutions to certain linear ODE
5 To be able to apply the Series solution method to linear ODE
6 To be able to apply Laplace transform to linear IVPs
7 To understand the basic concepts and theory of linear systems
8 To be able to find and analyze solutions to certain linear first-order systems


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Introduction to Differential Equations A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
2 Solutions to ODE and Initial Value Problems A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
3 Direction Fields and First-Order Autonomous ODE A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
4 Separable, Linear and Exact First Oder ODE A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
5 Integrating Factors, Bernoulli's Equation A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
6 Modeling with First-Order Equations A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
7 Basic Theory of Second and Higher-Order Linear ODE A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
8 Reduction of Order, Homogeneous ODE with Constant Coefficients A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
9 Method of Undetermined Coefficients, Variation of Parameters A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
10 Modeling with Second and Higher-Order Differential Equations A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
11 Series Solutions of Linear Equations A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
12 The Laplace Transform A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
13 Solution of Initial Value Problems by the Laplace Transform A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.
14 Systems of Linear First-Order Differential Equations A First Couse in Differential Equations with Modeling Applications, D.G. Zill, CENGAGE Learning, 2016.


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 3 3 4 3 2
C2 3 3 3 3 3 4 4 4 3 3
C3 3 3 3 3 3 4 3
C4 3 3 3 3 3 4 3 4 3 3
C5 3 3 3 3 4 3
C6 3 3 3 3 3 4 3
C7 3 3 3 3 3 4 3
C8 3 3 3 3 4 3 4 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=255953&lang=en