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| MAT4023 | A first course in integral equations | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Doç. Dr. Elif BAŞKAYA | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Teach practice areas of the knowledges and abilities which are gained from lessons of Differential Equations and Mathematical Analysis. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Students can class integral equations | 1,3,5 | 1,3, | | LO - 2 : | Students learn linear, nonlinear integral equations and solving method of them | 1,3,5 | 1,3, | | LO - 3 : | Students learn Fredholm integral equations and solving method of them | 1,3,5 | 1,3, | | LO - 4 : | Students learn Volterra integral equations and solving method of them | 1,3,5 | 1,3, | | LO - 5 : | Students learn the relation between differential equations and integral equations | 1,3,5 | 1,3, | | LO - 6 : | Students learn singular integral equations | 1,3,5 | 1,3, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| The general terms about integral equations: The short history of integral equations, definition and classification; Solution of an integral equation; Converting Volterra Equation to an ordinary differential equation; Converting initial value problem to Volterra equation; Converting boundary value problem to Fredholm integral equation; Taylor series, Infinite geometric series, Solving Fredholm integral equation with using the Adomian decomposition method, the variational iteration method, the direct computation method, the successive approximations method, the method of successive substitutions; Homogeneous Fredholm integral equations; Fredholm integral equations of the first kind: The method of regularization; Solving Volterra integral equation with using he Adomian decomposition method, the variational iteration method, the series solution method, the successive approximations method, the method of successive substitutions; Volterra integral equations of the first kind: The series solution method, Conversion of first kind to second kind; Singular integral equations. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | The general terms about integral equations: The short history of integral equations, definition and classification | | | Week 2 | The classification of integral equations; Solution of an integral equation; Converting Volterra Equation to an ordinary differential equation; Converting initial value problem to Volterra equation | | | Week 3 | Converting boundary value problem to Fredholm integral equation; Taylor series, Infinite geometric series | | | Week 4 | Solving Fredholm integral equation with using the Adomian decomposition method | | | Week 5 | Solving Fredholm integral equation with using the variational iteration method, the direct computation method | | | Week 6 | Solving Fredholm integral equation with using the successive approximations method, the method of successive substitutions | | | Week 7 | Comparison between alternative methods for Fredholm integral equation | | | Week 8 | Homogeneous Fredholm integral equations; Fredholm integral equations of the first kind: The method of regularization | | | Week 9 | The quiz exam | | | Week 10 | Solving Volterra integral equation with using he Adomian decomposition method | | | Week 11 | Solving Volterra integral equation with using the variational iteration method, the series solution method | | | Week 12 | Solving Volterra integral equation with using the successive approximations method, the method of successive substitutions | | | Week 13 | Comparison between alternative methods for Volterra integral equation | | | Week 14 | Volterra integral equations of the first kind: The series solution method, Conversion of first kind to second kind | | | Week 15 | Singular integral equations | | | Week 16 | The final exam | | | |
| 1 | Wazwaz, AM. 2011; Linear and Nonlinear Integral Equations: Methods and Applications, Springer, New York. | | | |
| 1 | Yankovsky, G. 1971; Problems and Exercises in Integral Equations, MIR Publishers, Moscow. | | | 2 | Vernon Lovitt, W. 1924; Linear İntegral Equations, Mc Graw-Hill Book Comp., New York. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 22/11/2021 | 1 | 50 | | End-of-term exam | 16 | 12/01/2022 | 1 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Arasınav için hazırlık | 5 | 1 | 5 | | Arasınav | 2 | 1 | 2 | | Ödev | 1 | 14 | 14 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 173 |
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