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Math 340 Exam 2Dec. 8, 2008Name:Student number:
<Text-field style="Heading 1" layout="Heading 1"> Problem 1</Text-field>We would like to use the 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to fit the data
Although the model is not linear, it can be linearized as 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 by proper substitutions. Carry out the linearization and solve for 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 and 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 by LinearAlgebra[LeastSquares]. Plot the resulting function in the form of the original model along with the original data in the same graph.
<Text-field style="Heading 1" layout="Heading 1"> Problem 2</Text-field>Consider the following initial value problem of the ordinary differential 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(1) Solve the problem using Maple function "dsolve"(2) Compute an approximate solution by the Runge-Kutta program using 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plot the exact solution and the approximate solution together in the same graph.(3) Investigate the accuracy by plotting an error graph.(4) By trial and error, find the smallest 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 such that the error is less than 0.00002
<Text-field style="Heading 1" layout="Heading 1"> Problem 3</Text-field>The satellite of the moon is subject to the gravity of both earth and the moon with irregular trajectory. To simulate that, let the center of the earth be the origin (0,0) and the trajectory of the satellite be 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. For simplicity, consider the trajectory of the moon as a circle 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The following are useful constants: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 ODE for the satelite: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The initial location of the satelite is 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 and the initial velocity is (x'(0),y'(0))=(-100,0). We are interested in the trajectory of the first 100 hours (i.e. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2OVEkMTAwRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHRjcvJSp1bmRlcmxpbmVHRjcvJSpzdWJzY3JpcHRHRjcvJSxzdXBlcnNjcmlwdEdGNy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y3LyUrZXhlY3V0YWJsZUdGNy8lKXJlYWRvbmx5R0Y3LyUpY29tcG9zZWRHRjcvJSpjb252ZXJ0ZWRHRjcvJStpbXNlbGVjdGVkR0Y3LyUscGxhY2Vob2xkZXJHRjcvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRicvJSptYXRoY29sb3JHRkIvJS9tYXRoYmFja2dyb3VuZEdGRS8lK2ZvbnRmYW1pbHlHRjEvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUpbWF0aHNpemVHRjQtSSNtb0dGJDYzUScmc2RvdDtGJy8lJWZvcm1HUSZpbmZpeEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYnLyUncnNwYWNlR0Zpby8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobWF4c2l6ZUdRKWluZmluaXR5RicvJShtaW5zaXplR1EiMUYnLyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJTBmb250X3N0eWxlX25hbWVHRlYvJSVzaXplR0Y0LyUrZm9yZWdyb3VuZEdGQi8lK2JhY2tncm91bmRHRkUtRiw2OVElMzYwMEYnRi9GMkY1RjhGOkY8Rj5GQEZDRkZGSEZKRkxGTkZQRlJGVEZXRllGZW5GZ25Gam4tRl1vNjNRMSZJbnZpc2libGVUaW1lcztGJ0Zgb0Zjb0Zlb0Znb0Zqb0ZccEZecEZgcEZjcEZmcEZocEZqcEZccUZecUZgcUZicQ== seconds). Use the Runge-Kutta program to solve the initial value problem of the ODE system and plot the trajectory of the satellite.Extra credit: Plot the trajectory of the satellite and the moon in the same graph.Extra credit: Make a movie showing the movement of the satellite and the moon.