|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Operational Mathematics *||3||3||5|
|Prerequisites and co-requisites|
|Recommended Optional Programme Components||None|
|Language of Instruction||Turkish|
|Course Level||First Cycle Programmes (Bachelor's Degree)|
|Course Coordinator||Assoc.Prof.Dr. Şehmus FINDIK|
To teach the students the concepts Laplace Transform, Transform of derivative and Fourier series with examples.
The Laplace Transformation. Transforms of derivatives. The Gamma function. The inverse transformation. The other properties of transformation. Fourier series. Bessel´s inequality and Parseval´s equality. The derivative and integral of Fourier series. Solutions of the partial differential equation using Fourier 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||Laplace transform||Review of the relevant pages from sources|
|2||Piecewise continuous functions and exponential order||Review of the relevant pages from sources|
|3||Transforms of derivatives, the Gamma function||Review of the relevant pages from sources|
|4||Inverse transforms and their properties||Review of the relevant pages from sources|
|5||Piecewise continuous functions, regular point of discontinuity, even and odd functions||Review of the relevant pages from sources|
|6||Fourier Series and Dirichlet conditions||Review of the relevant pages from sources|
|7||Fourier series of odd and even functions||Review of the relevant pages from sources|
|8||Mid-term exam||Review of the topics discussed in the lecture notes and sources|
|9||Complex Fourier series, Fourier series on the interval [a,b]||Review of the relevant pages from sources|
|10||Fourier series of the functions defined on half intervals||Review of the relevant pages from sources|
|11||The Problem of Convergence of Fourier Series, (C,1) summability.||Review of the relevant pages from sources|
|12||L² theory for Fourier Series, Bessel´s Inequality||Review of the relevant pages from sources|
|13||Convolution and Parseval´s Theorem||Review of the relevant pages from sources|
|14||General Review||Review of the relevant pages from sources|
|15||Solving problems||Review of the relevant pages from sources|
|16-17||Final exam||Review of the topics discussed in the lecture notes and sources|
|Recommended or Required Reading|
|Textbook||Operational Mathematics, Yazar: R.V. Churchill Lipschutz, Differential Geometry (Schaum´s outline series)|