HW2 phy 286

• All code must be uploaded via canvas.
  • You can ONLY upload files with specified (allowed) filename extensions
  • Only one submission needed per team (One member can upload)
• Grading will consist of using the following criteria:
  • Accuracy and correctness of code input/output: 30%
  • Clarity and legibility of code: 20%
  • Use of comments, annotation and help provided to use the code: 20%
  • Logic, computational approach or design used: 30%
• Uploading code that does not work, needs manual corrections for execution, or code with invalid MATLAB variable names, scripts or functions will lose at least 40-50% of assigned points.
• Label plots clearly so it is easy/obvious to understand what is being done
• Comment your code
• Display calculations and/or output (in Command Window) so it is easily readable.
• Test your code before submitting.

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Problem 1 [50 points]: Calculating second derivatives.

In class, we examined how it is possible to compute forward, backward or central differences to calculate the derivatives of a function with one variable. Here, you will extend that approach to calculate the second derivative of a given function.

For a given set of vector inputs $[$ x , f ( x ) ], construct a script (HW2problem1.m) that calculates the absolute mean error in $f$ ″ ( x ) for a specified range of values $x$. Calculate $f$ ″ ( x ) by calling functions forward_fprime.m, backward_fprime.m and/or central_fprime.m, twice. There are 9 possible ways to then numerically calculate the second derivative of $f$ ( x ).

Your script should output the mean absolute error $|$ f t r u e ″ ( x ) − f n u m ″ ( x ) | when $f$ ( x ) = log ⁡ ( x ) and for $x$ defined in MATLAB as:

>> x = linspace(1, 2, 20);

For each of the 9 methods, display clearly how the second derivative was computed and the mean absolute errors computed. For e.g. your display can read:

Second derivative: Forward, Forward, |mean error| = xx.yy;
Second derivative: Forward, Backward: |mean error| = mm.nn;
...

Remember to pay close and careful attention to the range of the returned $x$ vectors and the first derivatives, while using these functions.