| Сабақтың коды | Курс аты | Сынып | Академиялық кредит | Cағат | Апталық сабақ сағаттары (лекция) | Апталық сабақ сағаттары (практика) | Апталық сабақ сағаттары (зертханалық) |
|---|---|---|---|---|---|---|---|
| VK 42103 | Вариацияларды есептеу | 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 | Бағалау әдісі | |
|---|---|---|
| 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 | Жазбаша |
| 3 | Isoperimeter calculation. Conditional extremum. LaGrange report | Жазбаша |
| 4 | The second variation of the functionality. Variational problems with moving edges | презентация |
| 5 | Sufficient extreme conditions. Independent derivative variational problems | Жазбаша |
| 6 | Problem statement. The Weierstrass theorems. Theorem 1-3 | Жазбаша |
| 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 | Жазбаша |
| 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 | Жазбаша |
| 10 | Linear programming. Problem statement | Жазбаша |
| 11 | The simplex method. Choosing the direction. Creating a new simplex table. Creating a starting endpoint | презентация |
| 12 | Numerical minimization methods in finite-dimensional space | презентация |
| 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 | презентация |
| 14 | Newton's method. The Lagrange multiplier method. The method of accusative functions | презентация |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 | PÇ10 | PÇ11 |
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