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Abstracts

XXIII conference

The way to solve a mathematical problem, depending on the purpose of education

Pyrkova O.A.

Moscow Institute of Physics and Technology (State University), Section of Higher Mathematics, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russian Federation, +7(095)408-81-72, E-mail: omukha@mail.ru

Deliberately planned training results that have assimilated the knowledge, skills, abilities, development of creative thinking, humanity and other qualities required of the person as a subject of social, work and family life is the purpose of education. The method of solving the problem should be based primarily on those skills and competencies that we want to develop, strengthen, refresh their memory and finally create in accordance with the definition of learning objectives.

Consider the boundary value problems for ordinary second order differential equation with a small parameter at the higher derivative for example. Limit of solving this problem must be found in the small parameter tends to zero the right or left. Two solutions can be used for this purpose. The first method is based on the a direct solution of the problem, followed by taking to the limit. The second method is based on the proof of the corresponding theorem reduces to the solution of two Cauchy problem for the first order equations.

The second method of solving develops creative thinking, expanding scientific horizon of students, introducing the concept of the boundary layer in addition to saving time in the solution of the problem. The first method relies on the ability to solve integration of second order differential equations, using an expansion in Taylor's formula. The second solution uses the same skills in the proof of the theorem.

It seems reasonable to use a second method of solution with increasing trend in the acquisition of encyclopedic knowledge, because it makes us think not only about the algorithm for the solution, but within its application.

Literature:

1. A.A. Abramov, V.I. Ulyanov, "A method for solving biharmonic type equation with a singularly within a small parameter", Computational Mathematics and Mathematical Physics, 1992, 32:4, 481–487

2. Diesperov VN Differential and difference equations: Educational handbook. - M .: Fiztech-Polygraph, 2007. - 58 p.

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