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Functions and their curves
Published in John Bird, Engineering Mathematics, 2017
When a mathematical equation is known, co-ordinates may be calculated for a limited range of values, and the equation may be represented pictorially as a graph, within this range of calculated values. Sometimes it is useful to show all the characteristic features of an equation, and in this case a sketch depicting the equation can be drawn, in which all the important features are shown, but the accurate plotting of points is less important. This technique is called ‘curve sketching’ and can involve the use of differential calculus, with, for example, calculations involving turning points.
Functions and their curves
Published in John Bird, Higher Engineering Mathematics, 2017
When a mathematical equation is known, co-ordinates may be calculated for a limited range of values, and the equation may be represented pictorially as a graph, within this range of calculated values. Sometimes it is useful to show all the characteristic features of an equation, and in this case a sketch depicting the equation can be drawn, in which all the important features are shown, but the accurate plotting of points is less important. This technique is called ‘curve sketching’ and can involve the use of differential calculus, with, for example, calculations involving turning points.
Investigation of the effect of computer-supported instruction on students’ achievement on optimization problems
Published in International Journal of Mathematical Education in Science and Technology, 2023
The participants of the study consisted of prospective elementary mathematics teachers who were in their first year of study at a state university in Turkey. The participants were enrolled in two separate classes. The members of the two classes were randomly assigned to the experimental and control groups. The numbers of students in the experimental and control groups were 22 and 24, respectively. The study was conducted in a Calculus I course, for which the researcher was the instructor, that was offered in the first semester of the four-year program. The class meetings were held for two hours each week. Briefly, the content of the Calculus I course was composed of the following units, in order of presentation: the real number system; the concept of function; the concepts of limit and continuity and their applications; the concepts of derivative and differential; curve sketching; and optimization problems. Prior to the session in which the optimization problems were covered, the students had been taught how to find the local max–min. values of a function by using the first and second derivative tests. Moreover, this knowledge had also been used in sketching graphs of functions to specify extremum points.