Project: Restructuring/Restructuration of Basic Disciplines in the Engineering Grade

 

BAZO COSTAMILAN, Gerson1, LUCIA MOURA ALVES, Gloria2, MARIA PRADO DAMACENO, Nadya3 & SALDANHA MOTTA, Valeria4

1 Praca General Tiburcio 80, RJ/RJ, Brazil. Instituro Militar de Engenharia, gerson@leblon.ime.eb.br
2 Praca General Tiburcio 80, RJ/RJ, Brazil. Instituto Militar de Engenharia, gloria@aquarius.ime.eb.br, http://www.ime.eb.br/~gloria
3 Praca General Tiburcio 80, RJ/RJ, Brazil. Instituto Militar de Engenharia, nadya@taurus.ime.eb.br
4 Praca General Tiburcio 80, RJ/RJ, Brazil. Instituto Militar de Engenharia, valeria@aquarius.ime.eb.br

 

Abstract: The Department of Fundamental Sciences, Radiation and Environment (DECIFRAME) of the Military Institute of Engineering (IME) in the pursuit of motivate the studies in Mathematics and Physics and achieve an integration between the initial and professional phases of the Graduation Grade, has combined efforts to restructure the fundamental disciplines. This project is being developed in two main lines:teaching methodology change and Interdisciplinary.

Keywords: methodology, interdisciplinary, maple, integration

 

1  Introduction

Analyses of current technological developments have shown the importance of solid background on Basic Sciences for professionals of technological areas. Only with a solid conceptual basis may these professionals be able to face the fast changes and the interdisciplinary aspects, which surround modern technologies.

The Department of Fundamental Sciences, Radiation and Environment (DECIFRAME) of the Military Institute of Engineering (IME) in the pursuit of motivate the studies in Mathematics and Physics and achieve an integration between the initial and professional phases of the Graduation Grade, has combined efforts to restructure the fundamental disciplines. This project is being developed in two main lines:

2  Teaching methodology changes

The implementation of methodology changes is intended, in the context of potential contributions that shall be given to the learning process of disciplines taught in the major areas of Physics and Mathematics. The core idea of the project is to enhance the utilization of microcomputers as back up elements. This equipment will be used with two different accomplishments: audiovisual resources and simulations.

Within the audiovisual resources, the Powerpoint software is detached. With the help of this software, the theory to be taught is transformed into electronic slides and presented in the classroom with the aid of proper projectors connected to the microcomputers where the slides are being generated.

Among other simulation software, the Maple V is detached for the purposes of this project, in connection with its simulation accomplishments. The Maple V software is intended to be used as a learning back up device, in which phenomena pertaining academic program contents are properly depicted and explained, with the purpose of stimulating analytical and visual capabilities on the part of the students.

Those are some of the works in progress, are present in subsection follows.

2.1 Maple V in the modernization of Calculus

Professor: Lucia Moura Alves, Gloria

Traditional basic disciplines courses emphasize the learning of mathematics through rote work, memorization, and mastery of hand methods of solving problems. Although this can result in creating a good human calculator, it is not conducive to in-depth and substantive understanding of concepts. Many prospective students are concerned that if they take classes, they will not actually learn how to do any of the math, since "The computer does all the work for you." Fortunately, this is simply not true. Students cannot just present a problem to Maple V and have the computer solve it from beginning to end. They must understand the problem well enough to be able to give Maple the right instructions to solve it. In cases where Maple has a higer-level function that is capable of doing all the work such as Maple's Integrate command, students learn to break it apart and see how the computer does the work on a lower level. Maple V is not a magic wand that can be waved at a math problem; it is a tool that requires as much thought and care to use effectively as pencil, paper, and calculator.

MAPLE V in the Modernization of Calculus is a subproject to develop the understanding of calculus through Maple V.

Students use Maple V software to help them step through the boring routines of traditional mathematical learning, they are free to achieve a better conceptual understanding of the material while still gaining a good knowledge of the methods of problem-solving. The end result is a student who really understands the material he or she is working on.

The command of Maple V to representation of Fourier Serie of the function

is present follow. 

> restart:
> with(plots):
> w:=proc(x) if x>=-Pi and x<=0 then (Pi/2)+x elif x>0 and x<=Pi then (Pi/2)-x fi;end; 
> S1:=(4/Pi)*cos(x);
> S2:=S1+(4/(9*Pi))*cos(3*x);
> P0:=plot(w,-2*Pi..2*Pi,style=LINE,color=BLACK):
> P1:=plot(S1,x=-2*Pi..2*Pi,style=LINE,color=RED):
> P2:=plot(S2,x=-2*Pi..2*Pi,style=LINE,color=BLUE):
> display([P0,P1,P2],insequence=true,title='Animation');

Visit the page O Maple na Modernizacao do Calculo to more examples in portuguese.

2.2 Applications of Maple V in Physics

Professor: BAZO COSTAMILAN, Gerson

Application of Maple V in Physics help students forge a bridge between concepts and reasoning.

It is not only tell students how physics works, it show them, and it give them the opportunity to show what they have learned by testing their understanding of the concepts and applying them to real-world scenarios. Concept checkpoints, sample problems and electronic computations -all of these skill-building signposts have been developed to help students establish a connection between conceptual theories and application.

The pedagogical benefits of Maple V are evident to students and researchers alike because of its symbolic, numeric and plotting capabilities.

Examples with application of Maple in Physics is presented follow.

Wave Propagation with Maple V 

> restart;
> f:=exp(-x^2);

[Maple Math] 

> plot(f,x,color=blue);

[Maple Plot]

X Dislocated : X -> X - 2 

> g(x):= exp(-(x-2)^2);

[Maple Math] 

> plot({f(x),g(x)},x);

[Maple Plot]

Time Dislocated 

> h(x,t):=exp(-(x-t)^2);
> with(plots):
> animate(h(x,t),x=-8..8,t=-5..5,frames=50,color=blue);

 

2.3  Linear Algebra with Maple V

Professor: SALDANHA MOTTA, Valeria

The role of the work Linear Algebra with Maple V is to assist in the exploration of problems and to provide support materials for the Linear Algebra course. It's emphasized the importance of using the software to solve problems and to develop the concepts learned and the importance of the background acquired in normal classes. The students realize that "the software doesn't work by itself".

The command of Maple V to analytical and graphical solution, figure 3, of the linear system is presented follow. 

> b:=({x+y+3*z=5,2*x-y+4*z=11,-y+z=3});

b := {-y + z = 3, 2 x - y + 4 z = 11, x + y + 3 z = 5} 

> S:=solve(b);

S := {y = -7/5, x = 8/5, z = 8/5}

Graphical illustration 

> plot3d ({(5-x-y)/3, (y-2*x+11)/4, y+3}, x=-10..10,

y=-10..10, grid=[20,20],

3  Interdisciplinary

The goals of to give emphasis in interdisciplinary in this reformulation is to give opportunity to the students perceive the importance of integration between of courses in yours futures careers like Engineers.

3.1 Integrating Calculus and Physics

Professor: BAZO COSTAMILAN, Gerson & LUCIA MOURA ALVES, Gloria

Physics naturally comes to mind a discipline in which calculus is applied. Many students, including prospective mathematics, physics, and engineering majors, take separate calculus and physics courses concurrently. We have been part of a growing movement to integrate introductory calculus and physics courses into a unified curriculum.

This integrate is done through of "class couple" with Calculus and Physics teachers.

3.2 Final Project of the Basic Course(mathematics and physics)

Professor: BAZO COSTAMILAN, Gerson & LUCIA MOURA ALVES, Gloria

The Final Project of the Basic Course has by objective to promote integration between discipline of engineering course in to level:

Some works of this Project are in the site: http://www.ime.eb.br/~webde1/projfinal

3.3  Integration between Physics and Engineering Laboratories

Professor: Maria Prado Damasceno, Nadya

In the Integration Between Physics and Engineering Laboratories it is intended that students will discover that problems physics are important natural parts of the process of reaching conclusions through :

3.4 Integration between Linear Algebra and Physics/Chemistry

Professor: Saldanha Motta, Valeria

Linear Algebra with its theoretical contents, when applied to a engineering course, usually generates a question in the class: "What is the practical application of Linear Algebra?"

In the course, examples with subjects of Physics, Chemistry, Economy and so on are used, but the question continues. With the integration between Physics and Chemistry, the class understands the Linear Algebra as a tool solution of several problems. So, the initial question is answered.

4  Conclusion

The fundamental aim of this work is twofold: to communicate complex engineering and science knowledge and to enable students to receive more immediate and active feedback customized to their individual learning needs.

The project described above have been demonstrated a beneficial supplement facilitating teaching and learning in any class, it also has the potential to be incorporated into new teaching methodologies better designed to give students important skills for career life.

One last consideration is relevant to this context.

The computer is not the only way to improve quality of learning/teaching. As said by BELHOT, "The computer is not a substitute to the professor, but a resource to improve teaching activity".