Czech

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The student is required to understand commands and functions of the mathematical programme MATLAB as numeric and symbolic computation, as high-level programming and as advanced graphics and visualization and they are able to apply in solution to practical problems. Students solve such practical problems where non-trivial and meaningful use of computers is required it is where:
" computers help with routine and time-consuming calculations (the theoretical background has been discussed earlier),
" computers revise discussed subject matter using another non-traditional procedures (the tasks can't be solved with computer support without any theoretical background),
"computers can illustrate theoretical problems or dependencies (often with graphical support),
"computer can solve tasks that can't be solved by students themselves.
For example, in the first problem, a polynomial of the fifth degree is in the denominator, and students are not able to solve it. They have to find the roots of this polynomial with the help of MATLAB and then make the partial-fraction expansion, for which they need to know the relevant theory. In the third problem they have to draw the relevant area in order to be able to formulate the integral, which will give the solution of their problem. Ignorance of the relevant theory and mere mechanical computation of the integral generally leads to an incorrect result. Similarity we can get incorrect graphical illustration of surfaces, conic sections and so on.

It is assumed that students passed out subjects Mathematics I and Chemical Informatics I. From Mathematics students know Differential and Integral Calculus of a real function of one real variable, Linear Algebra and Analytical Geometry. From Computer Technology basic skills and experience of using the computer, managing files in MS Windows and fundamentals of the typography of the technical text.

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Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Attendance, activity, acceptation of five partial tasks and one semester project and succesful passing of the sciential test.
Student can have from the task n. 1 totally 4 points, for acceptable he (she) must get at least 2 points. From task n. 2 student can have totally 6 points, for acceptable he (she) must get at least 3 points. From task n. 3 (course of function) student can have totally 15 points, for acceptable he (she) must get at least 8 points. From task n. 4 student can have totally 4 points, for acceptable he (she) must get at least 2 points. From task n. 5 student can have totally 4 points, for acceptable he (she) must get at least 2 points. From semester project student can have totally 50 points, for acceptable he (she) must get at least 25 points. From sciential test student can have totally 15 points, for acceptable he (she) must get at least 8 points. Student can give from attendance 1 point, for acceptable he (she) must have only excused absence. From activity, when student solved some voluntary tasks, he (she) can give other points. For acceptable student does not need to solve any voluntary task.

1) Introduction to MATLAB - MATLAB as numeric and symbolic computation, MATLAB as high-level programming, MATLAB as advanced graphics and visualization. Elementary functions of MATLAB. Partial task n. 1.
2) Operation with polynomials.
3) Elaboration of data set. Basic of programming. Approximation of functions.
4) Matrix operations. Partial task n. 2.
5) Operation with functions. Graph a real function of one real variable (Partial task n. 3).
6) Solution of non-linear equations, zero points, maximum, minimum, derivative.
7) Graph a real function of one real variable, asymptotes, convexity and concavity and other characteristics.
8) MATLAB as advanced graphic and visualization. Partial task n. 4.
9) Operation with vectors. Applications. Partial task n. 5.
10) Conic sections.
11) Quadratic surfaces.
12) Instructions for elaborate the semester project. Semester project.
13) Semester project.

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The objective of the course is to provide students with the basic knowledge and skills from the work by the mathematical program MATLAB as numeric and symbolic computation, as high-level programming and as advanced graphics and visualization to be able to solve problems from profession. Attention is focused on such problems where non-trivial and meaningful use of computers is required. Students work with different forms and different applications in the solution particular problems and this way they learn to put the text, data or pictures from different applications into one document. Students should demonstrate in their semester project, that they know how to use computer technology in the creation of a written document, that they are able to use the mathematical program MATLAB in solution of mathematical problems, that they are able to graphically illustrate results obtained and to present them not only in plane, but also in three-dimensional space and that they are ready to take responsibility for the results obtained. The computer exercises should contribute both to better independence of students and to increasing interest in mathematics. Students should demonstrate that they are able to apply the knowledge they have learnt in the solution of unseen problems, that they understand the connection of mathematics with other technical subjects, that they are able to solve problems and analyse the results. The application of acquire knowledge in chemical practice is emphasized.

Five partial tasks and one semester project (individual problem)
DU1 - word problem with chemical respectively physical application, (general solution, conditions, units, concrete numerical solution)
DU2 - interpolation respectively approximation of measured data (calculation of basic statistic quantity, graphic presentation)
DU3 - numerically and graphically solution of a graph a real function of one real variable (15 items including tangent lines and asymptotes)
DU4 - practical word problem, in which student must find maximum respectively minimum (student must find the function, then he (she) it generally resolve extreme including conditions and units and in the end he (she) fund concrete numerical solution)
DU5 - finding of the volume and surface area of the solid, the height of the solid and the area of the base surface of body
SP - five task
ad1. - finding of the function of speed and change of this speed in given time interval, (partial-fraction expansion, in denominator is polynomial of five degree, integration of particular fractions);
ad2. - finding of the price of the chemical elements, (system of eight equations in eight unknowns)
ad3. - finding surface area of the foil, which is bounded by given curves including graphically presentation;
ad4. - finding trajectories of two mass points respectively its common points, (student must find the central respectively vertex form of given conic sections, find all characteristic elements and graphically represent including description respectively points of intersection);
ad5. - determination and graphically representation of given surface
Method of check:
DU1 - input in electronic form by e-mail, output in written form - 4 points
DU2 - input in electronic form by e-mail, data on e-learning and Internet, output statistic characterization in written form, graph as m-file to reserved directory on faculty intranet respectively by e-mail - 6 points
DU3 - input in electronic form by e-mail, output numerical solution in written form, graph as m-file to reserved directory on faculty intranet respectively by e-mail - 30 points
DU4 - input in electronic form by e-mail, output in written form - 4 points
DU5 - input in electronic form by e-mail, output in written form - 4 points
SP - input in electronic form, e-lerning, Internet, output ONLY in electronic form to reserved directory on faculty direction respectively by e-mail - 50 points

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