gibson:teaching:fall-2012:math445:lab3
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gibson:teaching:fall-2012:math445:lab3 [2012/09/05 19:45] gibson |
gibson:teaching:fall-2012:math445:lab3 [2012/12/05 09:11] (current) gibson [Problem F] |
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| labeling different lines in the same plot via the ''legend'' command. | labeling different lines in the same plot via the ''legend'' command. | ||
| - | A. Write a function ''mysort.m'' that will take in a vector of any size and sort | + | ==== Problem A==== |
| + | Write a function ''mysort.m'' that will take in a vector of any size and sort | ||
| it from least to greatest. Use the strategy of comparing neighbors and swapping | it from least to greatest. Use the strategy of comparing neighbors and swapping | ||
| them if necessary. If this process is done throughout the entire vector | them if necessary. If this process is done throughout the entire vector | ||
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| then by switching the outer loop to use a ''while'' command. | then by switching the outer loop to use a ''while'' command. | ||
| - | B. Suppose you opened a savings account that promised a 100% interest rate | + | ==== Problem B==== |
| + | Suppose you opened a savings account that promised a 100% interest rate | ||
| (typical rates are closer to 2.25% today). We are going to try and calculate | (typical rates are closer to 2.25% today). We are going to try and calculate | ||
| how much money that account would have after one year depending on how the | how much money that account would have after one year depending on how the | ||
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| quartely, monthly, and bi-weekly. Hint: one of your answers should be 26130.35. | quartely, monthly, and bi-weekly. Hint: one of your answers should be 26130.35. | ||
| - | C. Now we will compound the interest weekly. Let's use a ''for'' loop to | + | |
| + | ==== Problem C ==== | ||
| + | Now we will compound the interest weekly. Let's use a ''for'' loop to | ||
| compute not only how much money we will have in our account at the end of | compute not only how much money we will have in our account at the end of | ||
| the year but each week as well. Use the command | the year but each week as well. Use the command | ||
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| get the exact same plot and a final value of 26925.97 for B(53) . | get the exact same plot and a final value of 26925.97 for B(53) . | ||
| - | Bonus: Can you think of a way to calculate the same vector ''B'' in one line, | + | **Bonus:** Can you think of a way to calculate the same vector ''B'' in one line, |
| without using a loop? | without using a loop? | ||
| - | D. As the number of compounds increases, the final amount appears to be get | + | ==== Problem D ==== |
| + | As the number of compounds increases, the final amount appears to be get | ||
| closer to some final value. In order to check this, let's compound the interest | closer to some final value. In order to check this, let's compound the interest | ||
| every second. Compute the result of compounding the interest every second on | every second. Compute the result of compounding the interest every second on | ||
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| commonly in exponential and natural logarithms. | commonly in exponential and natural logarithms. | ||
| - | E. At this point I am going to make a guess that | + | ====Problem E==== |
| + | At this point I am going to make a guess that | ||
| <latex> | <latex> | ||
| - | (1 + 1.00/n)^n ≈ e. | + | (1 + 1.00/n)^n \approx e. |
| </latex> | </latex> | ||
| Line 125: | Line 131: | ||
| values for ''n'' where $n_j = 2^j$ with //j = 1, ..., 20//. Then for each of | values for ''n'' where $n_j = 2^j$ with //j = 1, ..., 20//. Then for each of | ||
| the values of n, again using a ''for'' loop, calculate | the values of n, again using a ''for'' loop, calculate | ||
| - | $a_j = (1 + 1.00/n_j )^{n_j}$ for ''j = 1, ..., 20''. Plot the values of //a//. | + | $a_j = (1 + 1.00/n_j )^{n_j}$ for //j = 1, ..., 20//. Plot the values of //a//. |
| Next plot //e − a//. You should see a graph that is not very informative | Next plot //e − a//. You should see a graph that is not very informative | ||
| since the values quickly go to zero. Instead we will plot the graph on a log | since the values quickly go to zero. Instead we will plot the graph on a log | ||
| Line 134: | Line 140: | ||
| Turn in all plots. | Turn in all plots. | ||
| - | Bonus: What happens if you let ''j = 1, ..., 60''? What happens if when you | + | **Bonus:** What happens if you let //j = 1, ..., 60//? What happens if when you |
| - | let $n_j = 10^j$ for ''j = 1,...,16''? Can you make a reasonable guess as to | + | let $n_j = 10^j$ for //j = 1,...,16//? Can you make a reasonable guess as to |
| what's happening here? | what's happening here? | ||
| - | F. Using the same procedure as in the previous problem, confirm that | + | ==== Problem F ==== |
| + | Using the same procedure as in the previous problem, confirm that | ||
| <latex> | <latex> | ||
| - | \lim_{n\rightarrow \infty} (1 + 0.754/n)^nn = e^{0.754} | + | \lim_{n\rightarrow \infty} (1 + 0.754/n)^n= e^{0.754} |
| </latex> | </latex> | ||
| Line 149: | Line 156: | ||
| the command ''exp(0.754)''. | the command ''exp(0.754)''. | ||
| - | G. We have used several MATLAB functions so far. Now we are going to write our | + | ==== Problem G ==== |
| + | |||
| + | We have used several MATLAB functions so far. Now we are going to write our | ||
| own function. In the main MATLAB window click File → New → Script | own function. In the main MATLAB window click File → New → Script | ||
| (or File → New → m-file depending on your version of MATLAB). This will open a | (or File → New → m-file depending on your version of MATLAB). This will open a | ||
| Line 185: | Line 194: | ||
| the last line. Turn in the code for your function. | the last line. Turn in the code for your function. | ||
| - | H. Enter the command ''format long'' then verify the following properties of | + | ==== Problem H ==== |
| + | |||
| + | Enter the command ''format long'' then verify the following properties of | ||
| exponentials and logarithms by testing the appropriate MATLAB functions with | exponentials and logarithms by testing the appropriate MATLAB functions with | ||
| the parameters indicated: | the parameters indicated: | ||
| Line 198: | Line 209: | ||
| <latex> | <latex> | ||
| - | log(ab) = log(a) + log(b), \text{ for } a = 0.1, b = 5 | + | \log(ab) = \log(a) + \log(b), \text{ for } a = 0.1, b = 5 |
| </latex> | </latex> | ||
| <latex> | <latex> | ||
| - | log(a^b) = b log(a), \text{ for } a = 3, b = 3 | + | \log(a^b) = b \log(a), \text{ for } a = 3, b = 3 |
| </latex> | </latex> | ||
| Note the ''log'' function in matlab is the natural logarithm. How would you | Note the ''log'' function in matlab is the natural logarithm. How would you | ||
| - | calculate $\log_{10}$ , $log_2$ , or $log_5$? | + | calculate $\log_{10}$ , $\log_2$ , or $\log_5$? |
gibson/teaching/fall-2012/math445/lab3.1346899528.txt.gz · Last modified: 2012/09/05 19:45 by gibson
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