COURSE INFORMATON
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 Type
Course Coordinator Assoc.Prof.Dr. Şehmus FINDIK
Instructors
Doç.Dr.ŞEHMUS FINDIK1. Öğretim Grup:A
Doç.Dr.ŞEHMUS FINDIK2. Öğretim Grup:A
 
Assistants
Goals
To teach the students the concepts Laplace Transform, Transform of derivative and Fourier series with examples.
Content
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.

Learning Outcomes
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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
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.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
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
TextbookOperational Mathematics, Yazar: R.V. Churchill Lipschutz, Differential Geometry (Schaum´s outline series)
Additional Resources