
MTH243 (Calculus
for Functions of Several Variables)
MATHEMATICA. Chapter 12:
Functions of Several Variables
Vladimir A. Dobrushkin,Lippitt
Hall 202C, 8745095,dobrush@uri.edu
In this course we will use Mathematica computer algebra system (CAS), which is available in computer labs at URI. The Mathematica projects are created to help you learn new concepts. Mathematica is very useful in visualizing graphs and surfaces in three dimensions. Matlab commercial software is also available at engineeering labs. Its free version is called Octave. A student can also use free CASs: SymPy (based on Python) or Sage.

Section 12.2. Graphs of Functions of two Variables
Example 1. Plotting the Graph of the Function \( F (x, y) = x^2+y^2 \)
Plot3D[(x^2 + y^2), {x, 3, 3}, {y, 3, 3}, Axes > True,
PlotStyle > Green]
Now we create a new graph:
\( g (x, y) = x^2 + y^2 + 3 \)
Plot3D[(x^2 + y^2 + 3), {x, 3, 3}, {y, 3, 3}, Axes > True]
Another graph of \( h(x, y) = 5  x^2  y^2 \)
Plot3D[(5  x^2  y^2), {x, 3, 3}, {y, 3, 3}, Axes > True,
PlotStyle > Orange]
One more: \( k (x, y) = x^2 + (y  1)^2 \)
Plot3D[(x^2 + (y  1)^2), {x, 3, 3}, {y, 3, 3}, PlotStyle > None]
Example 2. Plotting the Graph of the Function \( G(x,y)=e^{(x^2+y^2)} \)
Plot3D[(E^(x^2 + y^2)), {x, 5, 5}, {y, 5, 5},
PlotStyle > Opacity[.8]]
Cross Sections and the Graph of a Function where x=2
Plot3D[{(x^2 + y^2), (4 + y^2)}, {x, 3, 3}, {y, 3, 3}]
 