Report for Group Assignment 1.5

CEGM1000 MUDE: Week 1.5, Friday, Oct 4, 2024.

Remember there are "Tips for Writing the Report" in the GA 1.3 README.

Questions

Numerical Derivatives

Question 1

Explain what the time derivative of the ice thickness represents and why it would be incorrect to compute it at once for the entire data set.

Write your answer here.

Question 2

Summarize the number of ice thickness measurements, number of intervals and number of values calculated for each numerical derivative. Note any differences about the time value at which each derivative is computed. Then, explain why there are differences between each method. For each method, at which points are the time derivative missing? Why can't Central Differences be evaluated at the same time/location as the data points?

Write your answer here.

Question 3

Insert the image of your results showing the measurements and the three numerical derivatives. What can you conclude of the accuracy of the growth rate estimation? In this case, what are the two reasons that make CD more (much more) accurate than FD/BD?

Insert image here

Write your answer here.

Taylor Series Expansion

Question 4

Insert an image of your derivation of the first four derivatives of Task 2.1.

Insert image here

Question 5

Insert an image of your results corresponding to Task 2.5.

Insert image here

Question 6

How do the errors behave for the four TSE? Which one is more accurate near $x_0$? Farther away $x_0+5$? What is your opinion about using TSE for approximating harmonic functions (as the one in this exercise)?

Write your answer here

Question 7

Insert an image of your results corresponding to Task 3.1.

Insert image here

Question 8

Insert an image of your results corresponding to Task 3.3.

Insert image here

Last Question: How did things go? (Optional)

Use this space to let us know if you ran into any challenges while working on this GA, and if you have any feedback to report.

End of file.

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