| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| VK 42103 | The Calculus of Variations | төртінші курс | 5 | 150 | 1 | 2 |
The subject teaches students to use mathematical knowledge in research and solving real problems in the field of calculation of variations and methods of optimization. Students study the simplest calculus of variations, calculus of variations with higher derivatives, convex programming, global minimum theorem, and practice solving mathematical problems related to linear and non -linear programming.
Narrative, exchange of views, discussion, problem methods. For students with disabilities, together with structural divisions, the teaching methods, forms, type of control and amount of time for the introduction of specialized adaptive disciplines (modules) can be changed by the subject teacher.
| 1 | Uses classical methods of mathematics in solving fundamental and applied problems. (LO 7); |
| 2 | Uses methods of mathematical modeling to solve fundamental and applied practical problems(LO 8); |
| 3 | Solves the problem, correctly setting the performances of classical problems of fundamental mathematics;(LO 9); |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Basic concepts of variational curvature. Functions. Basic definitions and lemmas | презентация |
| 2 | Simple calculation of the variational curve. Necessary conditions for a weak minimum. Euler's equation. Stand-alone cases | презентация |
| 3 | Isoperimeter calculation. Conditional extremum. LaGrange report | презентация |
| 4 | The second variation of the functionality. Variational problems with moving edges | Жазбаша |
| 5 | Sufficient extreme conditions. Independent derivative variational problems | презентация |
| 6 | Problem statement. The Weierstrass theorems. Theorem 1-3 | презентация |
| 7 | Convex Programming. Elements of convex analysis. Convex sets. Convex functions | Жазбаша |
| 8 | The global minimum theorem. The criterion of effectiveness. Ways to transfer convex sets Projection of a point on a set. The Lagrange function. The dump point. The main lemma. The main theorem. Kuhn-Tucker theorems | презентация |
| 9 | The algorithm for the output of the convex programming problem. Nonlinear Programming. A necessary condition for efficiency. The algorithm for the output of a nonlinear programming problem | презентация |
| 10 | Linear programming. Problem statement | презентация |
| 11 | The simplex method. Choosing the direction. Creating a new simplex table. Creating a starting endpoint | Жазбаша |
| 12 | Numerical minimization methods in finite-dimensional space | Жазбаша |
| 13 | Gradient methods. The method of gradient projections. The conditional gradient method. The nodal gradient method Newton's method. The Lagrange multiplier method. The method of accusative functions | Жазбаша |
| 14 | Newton's method. The Lagrange multiplier method. The method of accusative functions | Жазбаша |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 | PÇ10 | PÇ11 |
|---|
| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | Negizgi ádebıetter: 1. T.Sh. Imanqul /Varıasıalyq qısap jáne tıimdilik ádisteri. Oqý qural. 2019j. 2. H.I.Ibrashev, Sh.T. Erkeǵulov. Matematıkalyq analız kýrsy. T.2. Oqý quraly. Almaty: 2014j. 3. Metody reshenıa matematıcheskıh zadach v Maple. Ýchebnoe posobıe. – Belgorod: Izd. Belaýdıt, 2015g. S.E.Savochenko, T.G.Kýzmıcheva | |
| 2 | Qosymsha ádebıetter: 1. Q.Aıtbaev./Varıasıalyq qısap jáne tıimdeý ádisteri. Oqý-ádistemelik qural. - Túrkistan 2014j. 2. S.T.Kasúk, A.A.Logvınova /Vysshaıa matematıka na kompútere v programme Maple 14. Chelábınsk, 2015g. |