gibson:teaching:spring-2018:math445:lab3
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| - 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. | ||
| - Load the dataset to Matlab with ''load''. For example, ''data = load('earthquake_magnitude.asc');''. | - Load the dataset to Matlab with ''load''. For example, ''data = load('earthquake_magnitude.asc');''. | ||
| - | - Extract the two columns of the loaded data into two appropriately named vectors, e.g. ''M = data(:,1);'' and ''N = data(:,2);'' will extract the M (magnitude) and N (number) columns of the earthquake-magnitude data matrix into vectors ''M'' and ''N'' for problem 1. For the remaining generic instructions I'll call these vectors ''x'' and ''y''. | + | - Extract the two columns of the loaded data into two appropriately named vectors, e.g. ''M = data(:,1);'' and ''N = data(:,2);'' will extract the M (magnitude) and N (number) columns of the earthquake-magnitude data matrix into vectors ''M'' and ''N'' for problem 5. For the remaining generic instructions I'll call these vectors ''x'' and ''y''. |
| - Experiment with ''plot'', ''semilogy'', ''semilogx'', and ''loglog'' to determine the functional relationship between ''y'' and ''x''. | - Experiment with ''plot'', ''semilogy'', ''semilogx'', and ''loglog'' to determine the functional relationship between ''y'' and ''x''. | ||
| - Estimate the constants in the log-linear relationship graphically to determine the specific functional relation between ''y'' and ''x''. | - Estimate the constants in the log-linear relationship graphically to determine the specific functional relation between ''y'' and ''x''. | ||
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| The first column is the [[http://en.wikipedia.org/wiki/Moment_magnitude_scale | moment magnitude]] //M//, and the second column is the number of earthquakes //N// of that magnitude that occur, on average, in a year. The last two entries are estimates, since it's impossible to detect every small earthquake around the world. The data are obtained from [[http://www.earthquake.ethz.ch/education/NDK/NDK|Earthquake Statistics and Earthquake Prediction Research]] by Stefan Wiemer, Institute of Geophysics, Zurich. | The first column is the [[http://en.wikipedia.org/wiki/Moment_magnitude_scale | moment magnitude]] //M//, and the second column is the number of earthquakes //N// of that magnitude that occur, on average, in a year. The last two entries are estimates, since it's impossible to detect every small earthquake around the world. The data are obtained from [[http://www.earthquake.ethz.ch/education/NDK/NDK|Earthquake Statistics and Earthquake Prediction Research]] by Stefan Wiemer, Institute of Geophysics, Zurich. | ||
| - | 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. Your final answer should be an explicit formula for //N(M)//. |
| **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 | **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 | ||
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| Deduce the form of the functional relation //E(N)// using Matlab plotting, then estimate | Deduce the form of the functional relation //E(N)// using Matlab plotting, then estimate | ||
| - | and fine-tune the constants in the relation, just as in problem 1. | + | and fine-tune the constants in the relation, and provide an explicit formula for //E(N)//. |
| **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. | **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. | ||
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| </file> | </file> | ||
| - | Deduce the form of the functional relation //P(t)// and determine the constants graphically. | + | Deduce the form of the functional relation //P(t)//, determine the constants graphically, and provide the explicit function //P(t)//. |
| Assume that the formula you derived for //P(t)// is valid indefinitely into the future and | Assume that the formula you derived for //P(t)// is valid indefinitely into the future and | ||
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