Monte Carlo Integration Method to the N-Dimensional Integral
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Monte Carlo Integration Method to the N-Dimensional Integral
Apply the Monte Carlo integration method to the N-dimensional integral (a) Compare the result to the
Apply the Monte Carlo integration method to the N-dimensional integral (a) Compare the result to the analytical value of the integral for increasing dimensions N. Plot the error as a function of the number of sample points for N = 3, N = 4, N = 5, and so on.
(b) Compare the accuracy of the Monte Carlo integration method to the product midpoint rule for increasing dimensions. (c) Is there a dimension for which the Monte Carlo is more accurate than the midpoint rule for the same number of integration points?
RUBRIC
Excellent Quality
95-100%
Introduction 45-41 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Literature Support
91-84 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Methodology
58-53 points
Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.
Average Score
50-85%
40-38 points
More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.
83-76 points
Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.
52-49 points
Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.
Poor Quality
0-45%
37-1 points
The background and/or significance are missing. No search history information is provided.
75-1 points
Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.
48-1 points
There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met
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Monte Carlo Integration Method to the N-Dimensional Integral