COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Differential Equations * MT   235 3 4 4 6

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Dr. Lec. Uyesi Leyla BUGAY
Instructors
Dr. Öğr. ÜyesiLEYLA BUGAY1. Öğretim Grup:A
Dr. Öğr. ÜyesiLEYLA BUGAY2. Öğretim Grup:A
 
Assistants
Goals
Students recognize differential equations and its clasifications, first order differantial equations, exact differantial equations; they recognize and solve linear differantial equations, Bernoulli differantial equations, Cauchy- Euler equations, systems of linear differantial equations, and Laplace transformations.
Content
Differential equations and their solutions, clasification of differential equations, initial value problems, boundary value problems and existence of solutions, exact differential equations and integrating factor, seperable equations and equations reducible to this form, Linear equations ve Bernoulli equations, explicit methods of solving higher order linear differantial equations, homogeneous linear equations with constant coefficients, the method of undetermined coefficients, variations of parameters, Cauchy- Euler equations, system of linear differantial equations, Laplace transformations, Basic properties of Laplace transformations

Learning Outcomes
-


Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
X
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.
X

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Differential equations and their solutions Required readings
2 Classification of differential equations Required readings
3 Initial value problems, Boundary value problems and existence of solutions Required readings
4 Exact differential equations and integrating factor Required readings
5 Seperable equations and equations reducible to this form Required readings
6 Linear equations ve Bernoulli equations Required readings
7 Explicit methods of solving higher order linear differantial equations Required readings
8 Mid-term Exam Review of the topics discussed in the lecture notes and sources again
9 The homogeneous linear equations with constant coefficients Required readings
10 The method of undetermined coefficients Required readings
11 Variations of parameters Required readings
12 Cauchy - Euler equations Required readings
13 System of linear differantial equations Required readings
14 Laplace transformations Required readings
15 Basic properties of Laplace transformations Required readings
16-17 Final Exam Review of the topics discussed in the lecture notes and sources again

Recommended or Required Reading
TextbookDiferansiyel Denklemler ve Uygulamaları, mehmet Aydın, Gönül Gündüz,Beno Kuryel
Additional Resources
Differentiel Equuations, L.Shipley Ross
Differentiel Equuations, Frank Ayres
Differential Equations, Lester R. Ford