For each function given below in (i)-(iii), perform the following steps in Mathematica (do not forget to comment/text your steps). (i) f(x, y) = x sin (2y) + y sin 2x (ii) f(x, y) = (sin x)(cos y)e-√²+y²/8 (iii) f(x, y) = y² + y³ – x³ (a) Plot the surface z = f(x, y) (you can use either ContourPlot3D or Plot3D, make sure to use the proper parameters in either case, use "Help"). Choose appropriate range for the variables so that the graph features are clearly seen in the figure. (b) Plot several level curves of f(x, y) using Contour Plot.
For each function given below in (i)-(iii), perform the following steps in Mathematica (do not forget to comment/text your steps). (i) f(x, y) = x sin (2y) + y sin 2x (ii) f(x, y) = (sin x)(cos y)e-√²+y²/8 (iii) f(x, y) = y² + y³ – x³ (a) Plot the surface z = f(x, y) (you can use either ContourPlot3D or Plot3D, make sure to use the proper parameters in either case, use "Help"). Choose appropriate range for the variables so that the graph features are clearly seen in the figure. (b) Plot several level curves of f(x, y) using Contour Plot.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:For each function given below in (i)-(iii), perform the following steps in Mathematica
(do not forget to comment/text your steps).
(i) f(x, y) = x sin (2y) + y sin 2x
(ii) f(x, y) = (sin x)(cos y)e-√²+y²/8
(iii) f(x, y) = y² + y³ – x³
(a) Plot the surface z = f(x, y) (you can use either ContourPlot3D or Plot3D, make
sure to use the proper parameters in either case, use "Help"). Choose appropriate
range for the variables so that the graph features are clearly seen in the figure.
(b) Plot several level curves of f(x, y) using Contour Plot.
Expert Solution
Introduction
As per the question we are given the following three bivariate functions :
- f(x, y) = x sin(2y) + y sin(2x)
- f(x, y) = (sin x)(cos y)e-√(x²+y²)/8
- f(x, y) = y2 + y3 - x3
And we have to plot their 3d surfaces along with the level curves using the commands : "Plot3D" & "ContourPlot" in mathematica.
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