Visualization of functions of two variables using Mathematica: (Exploring the pedagogical possibilities of the system beyond what is evident)

Functions of two variables appear frequently in engineering studies. Students have particular difficulties in understanding how the graphs of these functions are. This paper presents a sequential mode to analyze and reconstruct the graphical information in a function of two variables, up to display its three-dimensional image. This is done by representing the cuts of the graph of the function with a family of horizontal planes, but placing each contour line in the corresponding sectional plane. Cuts of the graph of the function with different vertical planes are also shown: those with parallel planes to the axial ones, OYZ and OXZ, and those with vertical planes through the axis OZ. The combined display of all these curves produces a much better idea of how the graph of the function under study is.