Update

HW3/README.md

@@ -0,0 +1,73 @@
+# Homework #3
+## due 2/15/17 by 11:59pm
+
+
+1. Create a new github repository called 'roots_and_optimization'. 
+
+    a. Add rcc02007 and pez16103 as collaborators.
+
+    b. Clone the repository to your computer.
+
+    c. Copy your `projectile.m` function into the 'roots_and_optimization' folder.
+    *Disable the plotting routine for the solvers*
+
+    d. Use the four solvers `falsepos.m`, `bisect.m`, `newtraph.m` and `mod_secant.m`
+    to solve for the angle needed to reach h=1.72 m, with an initial speed of 15 m/s. 
+
+    e. The `newtraph.m` function needs a derivative, calculate the derivative of your
+    function with respect to theta, `dprojectile_dtheta.m`. This function should
+    output d(h)/d(theta). 
+
+
+    f. In your `README.md` file, document the following under the heading `#
+    Homework #3`:
+
+        i. Compare the number of iterations that each function needed to reach an
+        accuracy of 0.00001%. Include a table in your README.md with:
+
+        ```
+        | solver | initial guess(es) | ea | number of iterations|
+        | --- | --- | --- | --- |
+        |falsepos   |  |  |  |
+        |bisect     |  |  |  |
+        |newtraph   |  |  |  |
+        |mod_secant |  |  |  |
+        ```
+
+        ii. Compare the convergence of the 4 methods. Plot the approximate error vs the
+        number of iterations that the solver has calculated. Save the plot as
+        `convergence.png` and display the plot in your `README.md` with:
+
+        `![Plot of convergence for four numerical solvers.](convergence.png)`
+
+        iii. In the `README.md` provide a description of the files used to create the
+        table and the convergence plot. 
+
+2. The Newton-Raphson method and the modified secant method do not always converge to a
+solution. One simple example is the function f(x) = x*exp(-x^2). The root is at 0, but
+using the numerical solvers, `newtraph.m` and `mod_secant.m`, there are certain initial
+guesses that do not converge. 
+
+    a. Calculate the first 5 iterations for the Newton-Raphson method with an initial
+    guess of x_i=2 for f(x)=x*exp(-x^2).
+
+    b. Add the results to a table in the `README.md` with:
+
+    ```
+    ### divergence of Newton-Raphson method
+
+    | iteration | x_i | approx error |
+    | --- | --- | --- |
+    | 0 | 2 | n/a |
+    | 1 |   |     |
+    | 2 |   |     |
+    | 3 |   |     |
+    | 4 |   |     |
+    | 5 |   |     |
+    ```
+
+    c. Repeat steps a-b for an initial guess of 0.2. (But change the heading from
+    'divergence' to 'convergence')
+
+3. Commit your changes to your repository. Sync your local repository with github. Then
+copy and paste the "clone URL" into the following Google Form [Homework 3](https://goo.gl/forms/UJBGwp0fQcSxImkq2)

README.md

@@ -74,8 +74,8 @@ general, I will not post homework solutions.
 |3|1/31||Consistent Coding habits|
 |   |2/2|5|Root Finding| 
 |4|2/7|6|Root Finding con’d|      
-|   |2/9|7|Optimization|      
-|5|2/14||Intro to Linear Algebra|
+|   |2/9|7| **Snow Day**|      
+|5|2/14|| Optimization |
 |   |2/16|8|Linear Algebra|
 |6|2/21|9|Linear systems: Gauss elimination|
 |   |2/23|10|Linear Systems: LU factorization|

lecture_05/lecture_05.md

@@ -1,4 +1,193 @@
 
+
+```octave
+%plot --format svg
+```
+
+## Questions from last class
+
+When you execute the given function 
+
+my_function.m:
+
+```matlab
+function [x,y] = my_function(max_time)
+    N=100;
+    t=linspace(0,max_time,N);
+    x=t.^2;
+    y=2*t;
+end
+```
+
+as 
+
+```>> [x,y] = my_function(20);```
+
+What variables are saved to your workspace?
+
+![responses](q1.png)
+
+How do you write a help description for a function?
+
+![responses to question 2](q2.png)
+
+
+How to keep our forked ME3255S page up to date with the original
+pretty tired this morning
+
+How do I use the Github Desktop?
+
+whats your favorite football team?
+
+Will UConn's github get updated to the newest version of github?
+As u said in class trail and error is the best way of learning.
+
+I believe the % is the same as matlab where it de-links your code into text
+
+Does the @ symbol designate a pointer? 
+
+Given the change of air pressure as altitude increases, how fast would a frisbee have to travel (and spin) to hit an airplane?
+
+What is a gui?
+
+
+could you go over a nested for loop example
+
+Can't seem to get this function to produce any graph and am not sure why
+
+When are these google forms due?
+
+how do I create a new function using Github on my desktop?
+
+Can you explain the first question more in class?
+
+What is the meaning of life?
+
+Should I just know how or what these topics are or will we learn them in the future?
+
+
+
+```octave
+f =@(x) x.^2
+
+
+```
+
+    f = 
+
+        @(x)x.^2
+
+
+
+```octave
+f([1:2:10])
+f(4)
+```
+
+    ans =
+
+         1     9    25    49    81
+
+
+    ans =
+
+        16
+
+
+
+```octave
+% nested for loop example
+for i = [1:6]
+    for j = [1:3]
+        fprintf('i=%i and j=%i\n',i,j)
+    end
+end
+        
+```
+
+    i=1 and j=1
+    i=1 and j=2
+    i=1 and j=3
+    i=2 and j=1
+    i=2 and j=2
+    i=2 and j=3
+    i=3 and j=1
+    i=3 and j=2
+    i=3 and j=3
+    i=4 and j=1
+    i=4 and j=2
+    i=4 and j=3
+    i=5 and j=1
+    i=5 and j=2
+    i=5 and j=3
+    i=6 and j=1
+    i=6 and j=2
+    i=6 and j=3
+
+
+# From last class 
+
+
+```octave
+help my_function
+```
+
+    Help documentation of "my_function"
+      This function computes the velocity in the x- and y-directions given
+      three vectors of position in x- and y-directions as a function of time
+      x = x-position
+      y = y-position
+      t = time
+      output
+      vx = velocity in x-direction
+      vy = velocity in y-direction
+
+
+
+```octave
+help my_caller
+```
+
+    Help documentation of "my_caller"
+      This function computes the acceleration in the x- and y-directions given
+      three vectors of position in x- and y-directions as a function of time
+      x = x-position
+      y = y-position
+      t = time
+      output
+      ax = acceleration in x-direction
+      ay = acceleration in y-direction
+
+
+
+```octave
+t=linspace(0,10,100)'; 
+x=t.^3; % vx = 3*t^2
+y=t.^2/2;  % vy = t
+[vx,vy]=my_function(x,y,t);
+[ax,ay]=my_caller(x,y,t);
+yyaxis left
+plot(t(1:10:end),ax(1:10:end),'o',t,6*t)
+ylabel('a_{x}')
+yyaxis right
+plot(t(1:10:end),ay(1:10:end),'s',t, 1*t./t)
+ylabel('a_{y}')
+xlabel('time')
+axis([0,10,0,3])
+```
+
+
+![png](lecture_05_files/lecture_05_11_0.png)
+
+
+
+```octave
+diff_match_dims(x,t)
+```
+
+    Undefined function 'diff_match_dims' for input arguments of type 'double'.
+    
+
 # Good coding habits
 ## naming folders and files
 
@@ -24,23 +213,18 @@ function i=code(j)
 end
 ```
 
+    Error: Function definitions are not permitted in this context.
+    
+
 
 ```octave
 help code
 ```
 
-    'code' is a command-line function
-
-     Example of bad variable names and bad function name
-
+    code not found.
 
-    Additional help for built-in functions and operators is
-    available in the online version of the manual.  Use the command
-    'doc <topic>' to search the manual index.
-
-    Help and information about Octave is also available on the WWW
-    at http://www.octave.org and via the help@octave.org
-    mailing list.
+    Use the Help browser search field to search the documentation, or
+    type "help help" for help command options, such as help for methods.
 
 
 ## Choose variable names that describe the variable
@@ -85,8 +269,8 @@ help counting_function
 1. Clone your homework_1 to your computer
 2. open Matlab (cli, jupyter or gui)
 3. Change working directory to homework_1 *e.g.* Windows:`cd('C:\Users\rcc02007\Documents\Github\homework_1')`, Mac: `cd('/Users/rcc02007/Documents/Github/homework_1')`
-4. You have already created your first script `myscript.m` (if not see lecture_4)
-5. Run `>> my_script.m`
+4. You have already created your first script `setdefaults.m` (if not see lecture_4)
+5. Run `>> setdefaults.m`
 6. Create a new m-file called nitrogen_pressure.m
 7. Create a function based upon the ideal gas law for nitrogen, Pv=RT
     1. R=0.2968 kJ/(kg-K)
@@ -96,14 +280,45 @@ help counting_function
 9. After file is 'committed', 'push' the changes to your github account
 
 for the command-line git user, this is steps 8 and 9:
-
 1. `$ git add *`
 2. `$ git commit -m 'added file nitrogen_pressure.m'`
 3. `$ git push -u origin master
     Username for 'https://github.uconn.edu':rcc02007 <enter>
-    `
+    Password for 'https://rcc02007@github.uconn.edu': `
 
 
+Now, use this function to plot the range of pressures that a pressure vessel would experience if it is 1000 gallons (3.79 m^3) with 10-20 kg of Nitrogen and temperatures range from -10 to 35 degrees C. 
+
+```matlab
+v=0.379/linspace(50,20,10);
+T=273.15+linspace(-10,35,10);
+[v_grid,T_grid]=meshgrid(v,T);
+P = nitrogen_pressure(v,T);
+pcolor(v_grid,T_grid,P)
+```
+
+
+```octave
+setdefaults;
+v=3.79./linspace(10,20,10);
+T=273.15+linspace(-10,35,10);
+[v_grid,T_grid]=meshgrid(v,T);
+P = nitrogen_pressure(v_grid,T_grid);
+pcolor(v_grid,T_grid-273.15,P-100)
+xlabel('specific volume (m^3/kg)')
+ylabel('Temperature (C)')
+%zlabel('Pressure (kPa)')
+
+%colormap winter
+%colormap summer
+%colormap jet
+colorbar()
+```
+
+
+![png](lecture_05_files/lecture_05_25_0.png)
+
+
 
 ```octave