Teaching of differential equations // University Teaching

Introduction

There are many topics in what refers to infinitesimal calculation that have already been touched in my publications, now it is the turn of differential equations. It is necessary to remember a topic that we apply by mistake when we explain these topics and especially if we refer to the differential equations. If we only focus on solving the problem as if it were a solution that is sought without prior analysis to the resolution of the algebraic algorithm without measuring solutions that are framed in qualitative and intuitive ideas that are immersed in many differential equations and that before solving it we have than to formulate them under a net approach of logical mathematical thinking.

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How I teach (my proposal)

Differential review: Many of the universities of our country and especially in the branch of engineering present a curriculum in which the whole study of the calculation is covered by four curricular units that are: calculus I, calculus II, calculus III and calculus IV.
In calculus I all the subjects that are essential to have a solid base are met, for example: solving equations of first, second and third degree, polynomials, factoring of polynomials, set of real numbers, inequations, functions and basic notions of analytical geometry, and after these basic notions that will strengthen the following topics, it is proposed to cover what is properly calculus with the following topics: Limit and continuity of a real function, derivative and application of a real function. For calculation II, everything referring to series and successions, the concept and basic techniques of integration, which is an integral defined by applying the fundamental theorem of calculation, integration methods (substitution or change of variable, on the part, trigonometric functions, etc.) are covered. trigonometric substitution and simple fractions), improper integrals and finally applications of the integral: calculation of area, calculation of volume, calculation of mass and center of mass, moment of inertia of a flat figure and last calculation of work and energy with integrals ). Calculation III, this is one of the calculation units of more difficult understanding by students, and basically all the content of calculation I and calculation II is collected and it is focused with two and three variables, eye on many of the cases In some universities, what is related to differential equations is incorporated in this curricular unit. For the IV calculation, all the topics already included and related to differential equations are incorporated.

This whole account of how the topics covered by the infinitesimal calculus are divided in our universities is to analyze that since IV calculation is the last subject of the calculations that our students see, before entering to explain the differential equations it is necessary that we explain raising a teaching system remembering topics such as first and second degree equations, and most importantly, going back and reviewing the derivatives that will be a key point for understanding and understanding differential equations by students.

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Teaching of differential equations through a graphical and analytical approach using mathematical software:

It is very classic to teach differential equations under an approach that does not involve graphics, since its content lends itself to be seen that way, and since students may already reach this point a bit exhausted in the use of graphics in the plane and in the three-dimensional space, but let me tell you that this practice is wrong, because within the learning of calculation all the knowledge that is required to teach must start from a graphic analysis, of course without leaving other methods of understanding as they are the algebraic, it is more I could say that any element to use to teach the differential equations that results in the student's learning is valid, however I propose this proposal because to me in particular it has worked for me, these graphic analyzes support with the application of software, in previous articles I have already explained the importance in the use of softwre for teaching of mathematics:

https://steemit.com/education/@carlos84/importance-in-the-use-of-software-for-the-teaching-of-mathematics

In particular, he used the software geogebra for being a software of free use, although any other of his preference can be used.

Importance of learning differential equations

In all branches of knowledge is important the diversity of knowledge that we can acquire for its possible application in the labor field, in this sense differential equations especially in the branch of electrical engineering has multiple applications, and for us teachers should not knowledge about what is referred to this topic.

It is necessary to reinforce this field that this implicit also in the science and the experimental field, it is necessary to support it with the technology of the computers through the use of the different softwre, to establish parameters of comparison among them and to check the performance of the students in their evaluations and go in the middle of that process of trial and error discarding methods and staying with what results, and in this way apply as relevant as possible that goes in favor of meaningful learning of our university students that are fundamental pillar through the diverse engineering in the production of our world.

Greetings friends steemians.