Charts in "Matkada" - construction and research

MathCAD has been providing stable support for its functions for many years. In this computing environment, economists, scientists, students and other specialists who work in applied and analytical mathematics work. Since not everyone understands the mathematical language, and not everyone is able to learn it in a short time, the program becomes difficult for novice users to perceive. The loaded interface and a large number of nuances push people away from using this product, but in fact, understanding any working environment is possible - just have a desire. In this article, we will analyze such an important topic as the construction of graphs of functions in the Matkada. This is a simple procedure that very often helps with calculations.

Chart Types

In addition to the fact that MathCAD defines fast graphics that are called using hot keys, there are other graphics applications. For example, the user can find the "Insert" section in the program header, and in it the "Graph" subsection, in which you can view all available graphs in the "Matkad":

• Graph XY - shows the dependence of one quantity on another. The most common type that allows you to quickly evaluate and explore dependencies.
• Polar graph - uses polar coordinates. The essence of the graph is to show the dependence of one variable on another only in the polar coordinate plane.
• Surface Plot - Creates a surface in space.
• Vector field, 3-D scatter graph, 3-D bar graph are used for other special purposes.

Function graphing

It is impossible to learn how to work with a computing environment without examples, so we will understand MatchCAD on a template.

Suppose that a function f (x) = (e ^ x / (2x-1) ^ 2) -10 is given in the interval [-10; 10], which must be constructed and carried out the study. Before proceeding with the construction of a function graph, it is necessary to translate this function into a mathematical form in the program itself.

1. After the function has been set, you should call the quick chart window with the Shift + 2 key. A window appears in which there are 3 black squares vertically and horizontally.
2. Vertical: the top and bottom are responsible for the intervals of values ​​that can be adjusted, the middle sets the function by which the user can build a graph in the Matkad. We leave the extreme black squares unchanged (the values ​​will be automatically assigned after construction), and in the middle we write our function.
3. Horizontal: extreme ones are responsible for the intervals of the argument, and in the middle you need to enter "x".
4. After the steps taken, a graph of the function is drawn.

Plotting points on the Matkada

It is sometimes difficult to specify a function or calculate its value, therefore, the range method is used to construct it. Only the range of values ​​over which the image needs to be reproduced can be given in the technical task.

1. We set the range of values ​​for the argument, in the case under consideration x: = - 10, -8.5 .. 10 (the symbol ".." is placed when the ";" key is pressed).
2. For convenience, we can display the resulting values ​​of "x" and "y". For the first case, we use the mathematical formulation "x =", and for the second - "f (x)". We observe two columns with corresponding values.
3. Let's plot using the keyboard shortcut Shift + 2.

Note that the part of the graph that rushed up disappeared, and a continuous function formed in its place. The thing is that in the first construction, the function underwent a gap at a certain point. The second graph was built on points, but it is obvious that a point that did not belong to the graph is not displayed here - this is one of the features of graphing on the basis of points.

Graph tab

In order to get rid of the situation where the function is undergoing a gap, it is necessary to tabulate the graph in Matkad and its values.

1. Take the interval we know from -10 to 10.
2. Now we write the command for the variable range - x: = a, a + 1 .. b (do not forget that the colon is the result of pressing the ";" key).
3. Looking at the given function, we can conclude that with the value "x = 1" division by zero will occur. To control the function without problems, it is worth excluding this operation as shown in the picture.
4. Now you can visually display the values ​​in the columns, as we did with the construction by points. The tabulation is completed, now all values ​​in increments of one unit correspond to their arguments. Note that on "x = 1" the value of the argument is not defined.

Minimum and maximum function

To find the minimum and maximum functions in the selected section of the graph in the Matkad, you should use the Given auxiliary block. Using this block, it is necessary to set the search interval and initial values.

1. In this case, the initial value x: = 9.
2. We write a working command to find the maximum value - X _max = Maximize (f, x) and calculate the value through the equal sign.
3. Using the Given block, we write the condition for x.
4. We set the minimum of the function by analogy with the maximum.
5. The results were as follows: the minimum value on the chart with the indicated interval f (x) = 2.488 * 10 ¹⁹⁸ , and the minimum value f (x) = -10.