DEGREE PROGRAMS  Associate's Degree (Short Cycle)  Bachelor’s Degree (First Cycle)  Master’s Degree (Second Cycle)

Course Description Course Name : Operational Mathematics I Course Code : MT 467 Course Type : Optional Level of Course : First Cycle Year of Study : 4 Course Semester : Fall (16 Weeks) ECTS : 5 Name of Lecturer(s) : Asst.Prof.Dr. ŞEHMUS FINDIK Learning Outcomes of the Course : Knows the definition of Laplace transform. Is able to calculate the Laplace transform of a function. Knows the definition of Fourier Series. Finds the Fourier Series of a function. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : To teach the students the concepts Laplace Transform, Transform of derivative and Fourier series with examples. Course Contents : 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. Language of Instruction : Turkish Work Place : Faculty of Science Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Laplace transform Review of the relevant pages from sources Lecture and discussion 2 Piecewise continuous functions and exponential order Review of the relevant pages from sources Lecture and discussion 3 Transforms of derivatives, the Gamma function Review of the relevant pages from sources Lecture and discussion 4 Inverse transforms and their properties Review of the relevant pages from sources Lecture and discussion 5 Piecewise continuous functions, regular point of discontinuity, even and odd functions Review of the relevant pages from sources Lecture and discussion 6 Fourier Series and Dirichlet conditions Review of the relevant pages from sources Lecture and discussion 7 Fourier series of odd and even functions Review of the relevant pages from sources Lecture and discussion 8 Mid-term exam Review of the topics discussed in the lecture notes and sources again Written exam 9 Complex Fourier series, Fourier series on the interval [a,b] Review of the relevant pages from sources Lecture and discussion 10 Fourier series of the functions defined on half intervals Review of the relevant pages from sources Lecture and discussion 11 The Problem of Convergence of Fourier Series, (C,1) summability. Review of the relevant pages from sources Lecture and discussion 12 L² theory for Fourier Series, Bessel´s Inequality Review of the relevant pages from sources Lecture and discussion 13 Convolution and Parseval´s Theorem Review of the relevant pages from sources Lecture and discussion 14 General Review Review of the relevant pages from sources Lecture and discussion 15 Solving problems Review of the relevant pages from sources Lecture and discussion 16/17 Final exam Review of the topics discussed in the lecture notes and sources again Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Operational Mathematics, Author: R.V. Churchill Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 100     Homeworks/Projects/Others 0 0 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Is able to prove Mathematical facts encountered in secondary school. 4 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 5 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 2 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 1 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 4 6 Expresses clearly the relationship between objects while constructing a model 3 7 Draws mathematical models such as formulas, graphs and tables and explains them 4 8 Is able to mathematically reorganize, analyze and model problems encountered. 4 9 Knows at least one computer programming language 4 10 Uses effective scientific methods and appropriate technologies to solve problems 0 11 Knows programming techniques and is able to write a computer program 1 12 Is able to do mathematics both individually and in a group. 0 13 Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 0 14 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 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 3 42 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 119 Total Workload / 25 (h): 4.76 ECTS Credit: 5