201
Assignment ChE 8
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Due by electronic submission on Friday November 30, 2007 11:55pm E-mail from your Princeton account to [e-mail] this Word document, with answers and code entries filled out. Name: ______________________________________ Problem 1 (20%) Consider the data in this file. (a) Plot the data as a 3-D stem plot and fit an interpolated planar surface through the data. (b) Plot a 2-D "cut" through the interpolated surface for the plane x=2 from y=0 to y=20.
Problem 2 (20%) Image processing Consider this image (from the Princeton Univ. communications office), shown as a reduced-resolution "thumbnail" to the right. (a) Produce separate grayscale images for the red, blue and green components of the picture e.g. the "blue" component is shown on the right. Please make certain no tick marks or axes indicators are shown in the pictures you report and that they have the correct aspect ratio. Include full- size (not reduced) pictures in your solution. Produce a "false-color" image of the differences between green and blue color throughout the image, as in the example to the right for green - red differences (your image will look different than the example!).
(b)
Report all commands and operations that you did to achieve your results.
ChE 201
Assignment 8
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Problem 3 (25%) Consider the 3-D "parametric" curve discussed in class, x=t; y=sin(2*t); z=cos(3*t); Produce an animation of this curve for t=0 to t=10 in increments of 0.1 (100 frames). sure Make to label your axes and set the range of x, y and z for all plots to be the same so that one sees a point moving through space. Also, select a viewpoint different from the default one.
Problem 4 (35%) = x
2
Consider the function f
+ 2x + 1 x
3
+ 1
.
(a)
Compute (symbolically) the indefinite integral the resulting function in the interval [-10 10].
f
dx and obtain a plot of
+10
(b)
Compute (numerically) the definite integral
- 10
f
dx . Do this in two ways,
first using the result of (a) and second using the ML function quad on f directly. The second method may fail if it does, explain why and comment on the validity of the result of the integration using the analytical expression from (a).
+
(c)
Compute (numerically) the definite integral
0
f
dx .
ChE 201
Assignment 8
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APPENDIX MATLAB COMMANDS AND M-FILES You can copy and paste directly from the MATLAB command window. Please use "format compact" to eliminate extra lines in the output and semicolons (;) to suppress long uninteresting responses. Also include all M-Files that you wrote. --------------------------------------------------------------------------------------------Problem 1 >> ... --------------------------------------------------------------------------------------------Problem 2 >> -------------------------------------------------------------------------------------------Problem 3 >> ... --------------------------------------------------------------------------------------------Problem 4 >> ...