|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 Coordinator||Dr. Lec. Uyesi Leyla BUGAY|
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.
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
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
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
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|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|
|Textbook||Diferansiyel Denklemler ve Uygulamaları, mehmet Aydın, Gönül Gündüz,Beno Kuryel|
Differentiel Equuations, L.Shipley Ross
Differentiel Equuations, Frank Ayres
Differential Equations, Lester R. Ford