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GA 1.5 publish

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<h1 id="report-for-group-assignment-15">Report for Group Assignment 1.5</h1>
<p><em><a href="http://mude.citg.tudelft.nl/">CEGM1000 MUDE</a>: Week 1.5, Friday, Oct 4, 2024.</em></p>
<p>Remember there are &quot;Tips for Writing the Report&quot; in the <a href="https://mude.citg.tudelft.nl/2024/files/GA_1_3/README.html">GA 1.3 README</a>.</p>
<h2 id="questions">Questions</h2>
<h2 id="numerical-derivatives">Numerical Derivatives</h2>
<p><strong>Question 1</strong></p>
<p>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.</p>
<p><em>Write your answer here.</em></p>
<p><em>The time derivative represents the growth rathe of the ice thickness. From a visual data inspection, it seems that the first measures of ice thickness occur at the beginning of the year. At a certain moment of the year measurements stop, which represents that the ice layer broke. At this moment, the time derivative does not have physical sense as the next measurement corresponds to a new/different ice layer.</em></p>
<p><strong>Question 2</strong></p>
<p>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?</p>
<p><em>Write your answer here.</em></p>
<p><em>The time derivative is missing at the end of the data set using FE while using BE the information is missing at the first point. Central differences require that the distance between the evaluation point and those used to compute the derivative are equidistant, the measurements were not performed this way but CD can be evaluated between measurements (at the middle).</em></p>
<p><strong>Question 3</strong></p>
<p>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 FE/BE?</p>
<p><em>Insert image here</em></p>
<p><em>Write your answer here.</em></p>
<p><em>First, inherently CD is second order accurate while FE/BE are first order accurate. Second, defining CD between points reduces $\Delta x$ by half, making its evaluation even more accurate.</em></p>
<h2 id="taylor-series-expansion">Taylor Series Expansion</h2>
<p><strong>Question 4</strong></p>
<p>Insert an image of your derivation of the first four derivatives of Task 2.1.</p>
<p><em>Insert image here</em></p>
<p><em>See the solution in the notebook.</em></p>
<p><strong>Question 5</strong></p>
<p>Insert an image of your results corresponding to Task 2.5.</p>
<p><em>Insert image here</em></p>
<p><em>See the solution in the notebook.</em></p>
<p><strong>Question 6</strong></p>
<p>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)?</p>
<p><em>Write your answer here</em></p>
<p><em>Very close to $x_0$ every approximation seems accurate, as you increase the distance the larger orders retain a high accuracy. However, the farther you move, every solution diverge considerably. The higher orders show a faster acceleration. The approximation of harmonic functions using TSE is only reasonable if its done nearby the expansion point.</em></p>
<p><strong>Question 7</strong></p>
<p>Insert an image of your results corresponding to Task 3.1.</p>
<p><em>Insert image here</em></p>
<p><em>See the solution of Task 3.1</em></p>
<p><strong>Question 8</strong></p>
<p>Insert an image of your results corresponding to Task 3.3.</p>
<p><em>Insert image here</em></p>
<p><em>See the solution of Task 3.3</em></p>
<p><strong>Last Question: How did things go? (Optional)</strong></p>
<p><em>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.</em></p>
<p><strong>End of file.</strong></p>
<span style="font-size: 75%">
&copy; Copyright 2024 <a rel="MUDE" href="http://mude.citg.tudelft.nl/">MUDE</a>, TU Delft. This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY 4.0 License</a>.
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<h1 id="report-for-group-assignment-15">Report for Group Assignment 1.5</h1>
<h1 id="readme-for-group-assignment-15">README for Group Assignment 1.5</h1>
<p><em><a href="http://mude.citg.tudelft.nl/">CEGM1000 MUDE</a>: Week 1.5, Friday, Oct 4, 2024.</em></p>
<p>Remember there are &quot;Tips for Writing the Report&quot; in the <a href="https://mude.citg.tudelft.nl/2024/files/GA_1_3/README.html">GA 1.3 README</a>.</p>
<h2 id="questions">Questions</h2>
<h2 id="numerical-derivatives">Numerical Derivatives</h2>
<p><strong>Question 1</strong></p>
<p>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.</p>
<p><em>Write your answer here.</em></p>
<p><strong>Question 2</strong></p>
<p>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?</p>
<p><em>Write your answer here.</em></p>
<p><strong>Question 3</strong></p>
<p>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?</p>
<p><em>Insert image here</em></p>
<p><em>Write your answer here.</em></p>
<h2 id="taylor-series-expansion">Taylor Series Expansion</h2>
<p><strong>Question 4</strong></p>
<p>Insert an image of your derivation of the first four derivatives of Task 2.1.</p>
<p><em>Insert image here</em></p>
<p><strong>Question 5</strong></p>
<p>Insert an image of your results corresponding to Task 2.5.</p>
<p><em>Insert image here</em></p>
<p><strong>Question 6</strong></p>
<p>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)?</p>
<p><em>Write your answer here</em></p>
<p><strong>Question 7</strong></p>
<p>Insert an image of your results corresponding to Task 3.1.</p>
<p><em>Insert image here</em></p>
<p><strong>Question 8</strong></p>
<p>Insert an image of your results corresponding to Task 3.3.</p>
<p><em>Insert image here</em></p>
<p><strong>Last Question: How did things go? (Optional)</strong></p>
<p><em>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.</em></p>
<p><em>You can access this assignment with the following link: <a href="https://classroom.github.com/a/6VU2xhZR">classroom.github.com/a/6VU2xhZR</a>.</em></p>
<p>GA 1.5 focuses on fundamentals of numerical analysis.</p>
<p>There are several files to be aware of:</p>
<ol>
<li><code>README.md</code></li>
<li><code>Analysis.ipynb</code></li>
<li><code>Report.md</code></li>
<li><code>justIce.csv</code></li>
</ol>
<p>As before, you should complete the analysis in <code>Analysis.ipynb</code> then answer the questions in <code>Report.md</code>.</p>
<h2 id="working-method">Working Method</h2>
<ol>
<li>Clone the repository</li>
<li>Work with your group members to complete the tasks in the notebook.</li>
<li>Use VS Code LiveShare to quickly share code from one computer to another, or update the Report. Do not view and edit it very actively with all members simultaneously.</li>
<li>Keep track of who is working on each file to avoid merge conflicts, which take up valuable time. Don't try to merge notebooks; instead have one person work on them at a time and make a commit. If a second person is working on the notebook, use LiveShare to share code, or wait until a commit is pushed, then pull the commit to your computer and make your changes.</li>
<li>Remember to leave time at the end of the session to merge all branches, push all commits and sort out any issues that may arise.</li>
</ol>
<p>Your repository does <em>not</em> have an automatic Actions check. Just confirm that your notebook and report have been uploaded.</p>
<h2 id="grading-and-feedback">Grading and Feedback</h2>
<p><em>The grading and feedback system in previous works has failed, and we apologize for the delay. Starting this week the grading for GA's will be as described here.</em></p>
<p>The grade for this assignment will be determined by evaluating the overall quality of all questions in the report, as well as confirming that you complete the tasks in the notebook.information. A number of 0, 3, 6, 7.5, 9 or 10 will be assigned, along with a feedback document containing general comments about the GA results. You will be able to use this feedback and your score to help see where your GA could have been improved, as well as study for the exam.</p>
<p>Examples illustrating how the grades will be assigned:</p>
<ul>
<li>10 points: exceptional.</li>
<li>9 points: excellent, but of course there is always room for improvement.</li>
<li>7.5 points: good, but some of the answers are incorrect or do not provide sufficient quantitative information. Answers cover the concepts well but are limited in terms of application or relevance to the problem at hand and are not adapted from the information and context provided in the textbook.</li>
<li>6.0 points: sufficient, as there are many of the issues described in the previous item, or significant problems with the implemetnation.</li>
<li>3.0 points: insufficient.</li>
<li>0.0 points: no submission, or submissions with negligible apparent effort.</li>
</ul>
<p>As before, <strong>quality</strong> (and being <strong>quantitative</strong>) is much more important than being <strong>quantity.</strong></p>
<p><strong>End of file.</strong></p>
<span style="font-size: 75%">
&copy; Copyright 2024 <a rel="MUDE" href="http://mude.citg.tudelft.nl/">MUDE</a>, TU Delft. This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY 4.0 License</a>.
......
......@@ -377,7 +377,7 @@ code {
<p>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?</p>
<p><em>Write your answer here.</em></p>
<p><strong>Question 3</strong></p>
<p>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 FE/BE?</p>
<p>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?</p>
<p><em>Insert image here</em></p>
<p><em>Write your answer here.</em></p>
<h2 id="taylor-series-expansion">Taylor Series Expansion</h2>
......
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