On the Usage of Different Coordinate Systems for 3D Plots of Functions of Two Real Variables

Autor: David G. Zeitoun, Thierry Dana-Picard
Rok vydání: 2018
Předmět:
Zdroj: Mathematics in Computer Science. 13:311-327
ISSN: 1661-8289
1661-8270
DOI: 10.1007/s11786-018-0359-z
Popis: Students learning towards a degree in a STEM related domain learn quite early a course in Advanced Calculus, i.e. a course where the main object of study are multivariate functions. It happens that students do not see the connection between the properties of the function such as continuity or differentiability and the 3-dimensional graphical representation. In particular, difficulties appear in classroom for functions having different limits at a point, according to the path approaching the point. One of the ways for this analysis is to use different coordinate systems to study the behavior of the function. Constraints exist on the hardware, the software and on the numerical approximation methods, which may lead to completely different graphs for the same function, when using two different coordinate systems. In this contribution we analyze the different types of graphs created with a CAS such as MATLAB 14 and Maple 2017 for different coordinate systems, in terms of properties of the 2-variable function under study. We prove that when the function is continuous, the 3D graphical representation does not depend on the coordinate system in use. However, when the function is discontinuous,the graphical representation depends strongly on the coordinate system and on the type of discontinuity (point singularity, line singularity, multiple singularity, etc.). Moreover, without a suitable analysis prior to plotting, the 3D graph may be uncorrect. The software shows a strange behavior around the singular points. It happens also that a line singularity is replaced either by a point singularity or by no singularity. We analyse the software behavior using numerical analysis of the meshing algorithm.
Databáze: OpenAIRE
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