Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Having specialized output
Reexamination Certificate
1999-11-09
2003-04-15
Ngo, Chuong Dinh (Department: 2124)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Having specialized output
Reexamination Certificate
active
06549923
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to electronic apparatus having the function of displaying graphs and more particularly to a differentiation learning aiding apparatus with the function of displaying a graph, and a storage medium which contains a control program therefor.
2. Description of the Related Art
Recently, there are electronic calculating apparatus such as pocket or desk-top calculators which perform calculation utilizing a function, input a function expression per se, and display a graph of the inputted function.
When differentiation and/or calculation of a derived function are performed by such electronic calculating apparatus, it outputs a result of the calculation as a numerical value and further displays a graph of the derived function. However, it cannot display an increase-decrease table useful for displaying a graph.
Therefore, in learning, a learner must learn an increase-decrease table before understanding a graph. Thus, the learner must draw an increase-decrease table by hand for learning, which is very inefficient compared to displaying the graph.
SUMMARY OF THE INVENTION
The object of the present invention is to provide an electronic apparatus capable of displaying an increase-decrease table in the learning of differentiation.
(1) In order to solve the above mentioned problem, according to one aspect of the present invention, there is provided an electronic apparatus comprising:
function-setting means for setting a function;
first-order differentiating means for differentiating the function set by the function setting means to provide a first-derivative;
increase-decrease table data producing means for producing increase-decrease table data for displaying an increase-decrease table which contains an increase-decrease state of the function set by the function setting means, and positive and negative signs of values of the first-derivative function obtained by the first-order differentiating means, in predetermined domains; and
displaying means for displaying the increase-decrease table on the basis of the increase-decrease table data produced by the increase-decrease table data producing means.
According to this invention, the function is set by the function setting means. The set function is differentiated by the first-order differentiating means to provide a first derivative. The increase-decrease table data producing means produces the increase-decrease table data for displaying the increase-decrease table which contains the increase-decrease state of the function set by the function setting means, and the positive and negative signs of values of the first-derivative provided by the first-derivative differentiating means, in the predetermined domains. The increase-decrease table is then displayed on the displaying means on the basis of the increase-decrease table data produced by the increase-decrease table data producing means.
(2) The apparatus may further comprise second-order differentiating means for obtaining a second derivative of the function by further differentiating the first-derivative provided by the first-derivative differentiating means. The increase-decrease table data producing means may produce the increase-decrease table data for displaying the increase-decrease table which contains in the predetermined domain the increase-decrease state of the function set by the function setting means, positive and negative signs of values of the first-derivative obtained by the first-order differentiating means, and positive and negative signs of values of the second derivative obtained by the second-order differentiating means.
According to this invention, the second-order differentiating means further differentiates the first-derivative obtained by the first-order differentiating means to provide the second-derivative. As described above, the increase-decrease table data producing means may produce increase-decrease table data for displaying the increase-decrease table which contains in a predetermined domain an increase-decrease state of the function set by the function setting means, positive and negative signs of values of the first-derivative obtained by the first-order differentiating means, and positive and negative signs of values of the second derivative obtained by the second-order differentiating means.
Therefore, since the second derivative is obtained, and the increase-decrease table containing the first and second derivatives is displayed, the learner can understand not only increases and decreases in a graph of the original function which is indicated by the positive and negative signs of values of the first derivative, but also a form of the graph of the original function upward and downward convex which is indicated by the positive and negative signs of values of the second derivative. Therefore, the learner can easily produce a precise graph with a reduced quantity of handwork, thereby achieving a high learning effect and an effective learning of the graph of the function and differentiation.
(3) According to the present invention, the apparatus may further comprises:
display controlling means for controlling the displaying means to displaying the increase-decrease table in a state where a portion of the increase-decrease table data is hidden, when the increase-decrease table is displayed by the displaying means on the basis of the increase-decrease table data produced by the increase-decrease table data producing means,
increase-decrease table data inputting means for inputting data to the hidden data portion of the increase-decrease table displayed by the displaying means under control of the display controlling means; and
increase-decrease table data determining means for determining whether or not the data inputted by the increase-decrease table data inputting means coincides with the hidden data portion of the increase-decrease table data produced by the increase-decrease table data producing means to output a result of the determination.
According to this invention, the display controlling means controls the displaying means so as to display the increase-decrease table in the state where the portion of the increase-decrease table data is hidden, when the increase-decrease table is displayed by the displaying means on the basis of the increase-decrease table data produced by the increase-decrease table data producing means. The increase-decrease table data inputting means inputs the data to the hidden data portion of the increase-decrease table displayed by the displaying means under control of the display controlling means. The increase-decrease table data determining means determines whether or not the data inputted by the increase-decrease table data inputting means coincides with the hidden data portion of the increase-decrease table data produced by the increase-decrease table data producing means to output a result of the determination.
Therefore, when the increase-decrease table is displayed by the displaying means, the portion of data is displayed in the hidden state. When the hidden data is inputted, the determining means determines whether the inputted data is proper or not and displays the result of the determination. Thus, the learner can efficiently learn drawing the increase-decrease table. In this case, no trouble to draw the entire increase-decrease table by hand is required to be taken to reduce the learner's work. Moreover, when only the portion of data of the increase-decrease table is hidden, the learner can learn while viewing other displayed data, which is useful especially for elementary learning.
(4) The increase-decrease table data producing means may produce the decrease-decrease table data for displaying the increase-decrease table which represents the increase-decrease state of the function set by the function setting means, in two kinds of increase states and two kinds of decrease states in the predetermined domains, on the basis of the positive and negative signs of values of the first and second derivatives in the predetermined domains.
Th
Casio Computer Co. Ltd.
Frishauf Holtz Goodman & Chick P.C.
Ngo Chuong Dinh
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