Застосування математичного моделювання при викладанні вищої математики студентам інженерних спеціальностей

Abstract

Mathematical modeling applying in teaching of engineering specialties students

O.Yu. Dyuzhenkova

An important component of quality training of future engineers is to increase their level of mathematical education. This approach includes understanding of the basic concepts and statements that are studied in the course of higher mathematics, their interpretation in various sciences, the ability to construct mathematical models and apply mathematical methods for solving of applied problems. In the article we describe the general approach and features of mathematical modeling in teaching of higher mathematics for students of engineering specialties. It’s emphasized the importance of the problems using which illustrates the need to introduce basic mathematical concepts for motivation and stimulating learning of mathematics. Great attention should be given to applied problems that contribute to the development of research skills of future specialists for the implementation of the professional direction of the course of higher mathematics. In addition, mathematical modeling is important to establish interdisciplinary connections and the formation of scientific and holistic perception of the world.

In the article we consider the examples of the use of mathematical models in the study of the derivative function, definite integral, differential equations. It emphasized the advisability of combined tasks, which connect different sections of higher mathematics. In particular, we consider the problems, which solving needs the material from linear algebra, analytical geometry and mathematical analysis.

Each new mathematical concept should be introduced only after consideration of various tasks, which are leading to the need to introduce this concept. Mathematical modeling can be used in the study of all sections of higher mathematics. For students of engineering specialties there are many interesting problems, which solving uses the differential equations. For example, determine the current dependence  on time  in the electrical circuit, which consists of a series enabled DC power supply that has a voltage, resistance  and self-induction and switch, if .

The current in the electrical circuit under given conditions determined by the equation. So the problem is reduced to solving of differential equation with separable variables. Considering the initial condition, we obtain that the current in the electrical circuit is defined by the function.

To form research skills it’s advisable to consider different ways for solve of the task. Solving the same problem in different ways, the student learns to analyze, simulate and use different mathematical methods to solve constructed model.

For example, find the least distance from the lake shore, which is described by function, to the highway, determined as straight line .

Obviously, determine of the distance between the curve and the straight reduced to finding of the distance between the point on curve  and line : , which is calculated by the formula . So, the solving of this problem provides for find of the minimum function of two variables  on condition that. In the article we consider three ways to solve this problem.

To establish connections between different sections of higher mathematics course it’s suggested to consider the combined problem which solution needs of material from higher algebra, analytic geometry and mathematical analysis. Such tasks can be used for final control of student’s knowledge.