gibson:teaching:spring-2016:math445:lab3
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| - | ====== Math 445 lab 3: scripts, plotting, and publishing ====== | + | ====== Math 445 lab 3: scripts, log-linear relations ====== |
| Write a single Matlab script file that solves the following problems, and use the [[http://www.mathworks.com/help/matlab/matlab_prog/publishing-matlab-code.html | Matlab ''publish'']] function to create a nice-looking PDF of your code and graphs to turn in. Be sure to label each problem with comments like ''<nowiki> %% Problem 1%% </nowiki>'' so that the problems are separated and labeled in the PDF. | Write a single Matlab script file that solves the following problems, and use the [[http://www.mathworks.com/help/matlab/matlab_prog/publishing-matlab-code.html | Matlab ''publish'']] function to create a nice-looking PDF of your code and graphs to turn in. Be sure to label each problem with comments like ''<nowiki> %% Problem 1%% </nowiki>'' so that the problems are separated and labeled in the PDF. | ||
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| **Problem 3:** Make a plot of $y(x) = 0.3 \log x + 2$ over the range $1 \leq x \leq 10^5$ using a dot-dashed cyan line. Chose an appropriate plotting function that best displays the functional relationship between $x$ and $y$. For this plot, it's best to create the ''x'' vector with ''logspace'' rather than ''linspace''; e.g. ''x = logspace(0,5,20)'' will set ''x'' to 20 points between $1 = 10^0$ and $10^5$ which are uniformly spaced on a logarithmic plot. Label the axes, set the $y$ range of the plot to $2 \leq y \leq 6$, and place a coordinate grid within the plot. Title the plot as in previous problems. | **Problem 3:** Make a plot of $y(x) = 0.3 \log x + 2$ over the range $1 \leq x \leq 10^5$ using a dot-dashed cyan line. Chose an appropriate plotting function that best displays the functional relationship between $x$ and $y$. For this plot, it's best to create the ''x'' vector with ''logspace'' rather than ''linspace''; e.g. ''x = logspace(0,5,20)'' will set ''x'' to 20 points between $1 = 10^0$ and $10^5$ which are uniformly spaced on a logarithmic plot. Label the axes, set the $y$ range of the plot to $2 \leq y \leq 6$, and place a coordinate grid within the plot. Title the plot as in previous problems. | ||
| - | **Problem 4:** Make a plot of $y(x) = 10 x^{-3}$ over the range $10 \leq x \leq 10^4$ using a solid green line. Chose an appropriate plotting function that best displays the functional relationship between $x$ and $y$. Use the ''logspace'' function for ''x'' as in problem 3. Label the axes, set the $x$ range of the plot to $0 \leq x \leq 10^5$, and place a coordinate grid within the plot. Title the plot as in previous problems. | + | **Problem 4:** Make a plot of $y(x) = 10 x^{-3}$ over the range $10 \leq x \leq 10^4$ using a solid green line. Chose an appropriate plotting function that best displays the functional relationship between $x$ and $y$. Use the ''logspace'' function for ''x'' as in problem 3. Label the axes, set the $x$ range of the plot to $10^0 \leq x \leq 10^5$, and place a coordinate grid within the plot. Title the plot as in previous problems. |
| - | **Problems 5,6,7:** For these problems you will deduce the functional relationship between variables in data sets using graphical analysis. The data sets are given as // N x 2// matrices with //x// as the first column and //y// as the second. For each data set, you will find a function //y(x)// that fits the data, using the following steps: | + | **Instructions for problems 5,6,7:** For these problems you will deduce the functional relationship between variables in data sets using graphical analysis. The data sets are given as // N x 2// matrices with //x// as the first column and //y// as the second. For each data set, you will find a function //y(x)// that fits the data, using the following steps: |
| - Download or cut & paste the data set to a text file with an appropriate name, e.g. ''earthquake_magnitude.asc'' for problem 1. | - Download or cut & paste the data set to a text file with an appropriate name, e.g. ''earthquake_magnitude.asc'' for problem 1. | ||
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| * appropriate labels for each axis and a title | * appropriate labels for each axis and a title | ||
| - | and specify the function form of | + | and provide an explicit formula for $y(x)$. |
| - | **Problem 2: The distribution of earthquake magnitudes, by Moment Magnitude scale.** | + | **Problem 5: The distribution of earthquake magnitudes, by Moment Magnitude scale.** |
| Big earthquakes are rare, and little earthquakes are frequent. In fact, there is a | Big earthquakes are rare, and little earthquakes are frequent. In fact, there is a | ||
| very clean empirical law that governs how many earthquakes of a given magnitude | very clean empirical law that governs how many earthquakes of a given magnitude | ||
| Line 53: | Line 53: | ||
| Using Matlab plotting commands, deduce the form of the functional relationship //N(M)//. Estimate the constants in the relationship by estimating the slope and the //y//-intercept, and then fine-tuning by matching the plot of your estimate against the plot of the data. | Using Matlab plotting commands, deduce the form of the functional relationship //N(M)//. Estimate the constants in the relationship by estimating the slope and the //y//-intercept, and then fine-tuning by matching the plot of your estimate against the plot of the data. | ||
| - | **Problem 2: The distribution of earthquake magnitudes, by energy.** The moment magnitude scale is logarithmic, in that an earthquake of magnitude //M+1// releases about 32 times more energy than an earthquake of magnitude //M//. The following dataset gives the number //N// of earthquakes in a given | + | **Problem 6: The distribution of earthquake magnitudes, by energy.** The moment magnitude scale is logarithmic, in that an earthquake of magnitude //M+1// releases about 32 times more energy than an earthquake of magnitude //M//. The following dataset gives the number //N// of earthquakes in a given |
| year of energy //E// measured in Joules. | year of energy //E// measured in Joules. | ||
| <file - earthquake_energy.asc> | <file - earthquake_energy.asc> | ||
| Line 64: | Line 64: | ||
| 2e09 49000 | 2e09 49000 | ||
| 6e07 365000 | 6e07 365000 | ||
| - | <1e06 2920000 | + | 1e06 2920000 |
| </file> | </file> | ||
| Line 70: | Line 70: | ||
| and fine-tune the constants in the relation, just as in problem 1. | and fine-tune the constants in the relation, just as in problem 1. | ||
| - | **Problem 3: World population.** The following data set provides the human population //P// of the earth at a given time //t//, measured in years A.D. | + | **Problem 7: World population.** The following data set provides the human population //P// of the earth at a given time //t//, measured in years A.D. |
| <file - world_population.asc> | <file - world_population.asc> | ||
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