| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| ITKT 6313 | Advanced Course of Integral Equations | Екінші курс | 6 | 180 | 1 | 2 |
Purpose of the discipline: Fredholm Integral Equations of Type I and Type II. Numerical methods for solving Integral Equations. The Abel equation. Abel's integral equation. Integral Equations of Volterra type 1. The concept of an integral equation. The relationship between an integral equation and a Linear Differential Equation. Finding the solution of an integral equation by the PiCar method. Develops effective mathematical methods for finding the resolventum for a fredholm integral equation with a special core. Uses modern methods of solving Integral Equations.
narrative, exchange of views, discussion, problem methods
| 1 | Uses a systematic approach and methods of harmonic and intelligent analysis in solving applied problems (LO8); |
| 2 | Develops effective mathematical methods for solving applied problems of mathematics, physics, mechanics, economics and management (LO9); |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Concepts of Integral Equations. The relationship between linear differential equations and Integral Equations. | |
| 2 | Resolvent of the Volterra equation. Solving an integral equation using rubelventa. Approximation with a chain. | |
| 3 | Equations in the form of Rolls. Application of the Laplace Transform. | |
| 4 | Application of the winding theorem to solving problems given by the constraint (X,∞). Volterra 1 Integral Equations of type. | |
| 5 | Euler integral. | |
| 6 | Abel report. Abel's integral equation. Winding Volterra Integral Equations of Type 1. | |
| 7 | Concepts of Integral Equations. The relationship between linear differential equations and Integral Equations. | |
| 8 | Concepts of Integral Equations of fredholm 2 types. Fredholm determinant method. Creating a resolution of repeated nuclei. | |
| 9 | Integral Equations with rotating nuclei. Gammerstein equation. | |
| 10 | Eigenvalues, eigenvalues. Homogeneous integral equation with variable nuclei. | |
| 11 | Inhomogeneous symmetric equations. Fredholm alternatives. | |
| 12 | Construction of the green function and its application to solving edge problems. | |
| 13 | Bringing parametric edge problems to an integral equation. Singular Integral Equations. | |
| 14 | Methods for approximating Integral Equations | |
| 15 | Approximate finding of eigenvalues. 1.The Ritz method. 2. trail method. 3.Kellogg method. |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 |
|---|
| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | Шишкин Г.А. Линейные интегро-дифференциальные уравнения Фредгольма: Учеб.пособие по спецкурсу и спецсеминару.– Улан-Удэ: Издательство Бурятского госуниверситета, 2007. – 195 с. | |
| 2 | Владимиров В.С. Уравнения математической физики – М.: Нука, 1988 | |
| 3 | Михлен С.Г. Курс математической физики. – СПб.: Питер, изд-во «Лань», 2002 | |
| 4 | Петровскмй И.Г. Лекции по теории обыкновенных дифференциальных уравнений. – М.: изд-во МГУ, 1984 |