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ME3255S2017/lecture_04/lecture_4.md

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## When using the command prompt, anything in your path or working directory can be run either as a script, function or class (to define objects)
Questions from last class:
- I downloaded GitHub to my desktop but I cannot sign into my UConn account like I can online.
- I checked my grades on HuskyCt recently and I received a 0 / 100 for Homework 1.
- It is very hard to tell if what I'm doing on github is right or wrong.
- How often will be using our laptops during the lecture?
- How many frogs would it take to move a car that is stuck in the snow? And what would be the approximate cost to do so
$m_{frog}$=22.7 g (https://en.wikipedia.org/wiki/Common_frog)
$v_{frog}$=17 kph = 4.72 m/s (http://purelyfacts.com/question/14/is-a-toad-faster-than-a-frog?DDA=113&DDB=40)
$m_{car}$=1000 kg (reasonable guess)
conservation of momentum:
$mv_{1} +mv_{2} = mv_{1}'+mv_{2}' = m_{total}v_{2}'$
```matlab
number_of_frogs = 1;
v2=0;
while v2 < 1 % 1 m/s
m_frogs=number_of_frogs*22.7e-3;
number_of_frogs=number_of_frogs+1;
p1=(m_frogs)*4.72; % momentum 1
v2=p1/(m_frogs+1000); % p2=p1, so v2=p1/m_total
end
number_of_frogs
```
number_of_frogs =
11844
```matlab
%myscript
```
```matlab
%plot --format svg
```
When using the GUI, your command history is saved, but it is better to save your work either as a script or a function or combination of both
Creating a default graph script: `setdefaults.m`
```matlab
set(0, 'defaultAxesFontSize', 16)
set(0,'defaultTextFontSize',14)
set(0,'defaultLineLineWidth',3)
```
```matlab
set(0, 'defaultAxesFontSize', 16)
set(0,'defaultTextFontSize',14)
set(0,'defaultLineLineWidth',3)
```
```matlab
t_linear=linspace(0,10,100);
plot(t_linear,t_linear.^2)
xlabel('time (s)')
ylabel('displacement (m)')
```
![png](lecture_4_files/lecture_4_7_0.png)
#EOL
## Graphics can be produced with a number of functions
2-D plots, 3-D plots, contour plots, 3D contour plots ...
```matlab
x=linspace(-1,1,21); y=linspace(-1,1,21);
[X,Y]=meshgrid(x,y);
Z=(X.*Y.^3-X.^3.*Y)
```
Z =
Columns 1 through 7
0 0.1710 0.2880 0.3570 0.3840 0.3750 0.3360
-0.1710 0 0.1224 0.2016 0.2430 0.2520 0.2340
-0.2880 -0.1224 0 0.0840 0.1344 0.1560 0.1536
-0.3570 -0.2016 -0.0840 0 0.0546 0.0840 0.0924
-0.3840 -0.2430 -0.1344 -0.0546 0 0.0330 0.0480
-0.3750 -0.2520 -0.1560 -0.0840 -0.0330 0 0.0180
-0.3360 -0.2340 -0.1536 -0.0924 -0.0480 -0.0180 0
-0.2730 -0.1944 -0.1320 -0.0840 -0.0486 -0.0240 -0.0084
-0.1920 -0.1386 -0.0960 -0.0630 -0.0384 -0.0210 -0.0096
-0.0990 -0.0720 -0.0504 -0.0336 -0.0210 -0.0120 -0.0060
0 0 0 0 0 0 0
0.0990 0.0720 0.0504 0.0336 0.0210 0.0120 0.0060
0.1920 0.1386 0.0960 0.0630 0.0384 0.0210 0.0096
0.2730 0.1944 0.1320 0.0840 0.0486 0.0240 0.0084
0.3360 0.2340 0.1536 0.0924 0.0480 0.0180 0.0000
0.3750 0.2520 0.1560 0.0840 0.0330 0 -0.0180
0.3840 0.2430 0.1344 0.0546 -0.0000 -0.0330 -0.0480
0.3570 0.2016 0.0840 0 -0.0546 -0.0840 -0.0924
0.2880 0.1224 0 -0.0840 -0.1344 -0.1560 -0.1536
0.1710 0.0000 -0.1224 -0.2016 -0.2430 -0.2520 -0.2340
0 -0.1710 -0.2880 -0.3570 -0.3840 -0.3750 -0.3360
Columns 8 through 14
0.2730 0.1920 0.0990 0 -0.0990 -0.1920 -0.2730
0.1944 0.1386 0.0720 0 -0.0720 -0.1386 -0.1944
0.1320 0.0960 0.0504 0 -0.0504 -0.0960 -0.1320
0.0840 0.0630 0.0336 0 -0.0336 -0.0630 -0.0840
0.0486 0.0384 0.0210 0 -0.0210 -0.0384 -0.0486
0.0240 0.0210 0.0120 0 -0.0120 -0.0210 -0.0240
0.0084 0.0096 0.0060 0 -0.0060 -0.0096 -0.0084
0 0.0030 0.0024 0 -0.0024 -0.0030 0
-0.0030 0 0.0006 0 -0.0006 0 0.0030
-0.0024 -0.0006 0 0 0.0000 0.0006 0.0024
0 0 0 0 0 0 0
0.0024 0.0006 -0.0000 0 0 -0.0006 -0.0024
0.0030 0 -0.0006 0 0.0006 0 -0.0030
0 -0.0030 -0.0024 0 0.0024 0.0030 0
-0.0084 -0.0096 -0.0060 0 0.0060 0.0096 0.0084
-0.0240 -0.0210 -0.0120 0 0.0120 0.0210 0.0240
-0.0486 -0.0384 -0.0210 0 0.0210 0.0384 0.0486
-0.0840 -0.0630 -0.0336 0 0.0336 0.0630 0.0840
-0.1320 -0.0960 -0.0504 0 0.0504 0.0960 0.1320
-0.1944 -0.1386 -0.0720 0 0.0720 0.1386 0.1944
-0.2730 -0.1920 -0.0990 0 0.0990 0.1920 0.2730
Columns 15 through 21
-0.3360 -0.3750 -0.3840 -0.3570 -0.2880 -0.1710 0
-0.2340 -0.2520 -0.2430 -0.2016 -0.1224 -0.0000 0.1710
-0.1536 -0.1560 -0.1344 -0.0840 0 0.1224 0.2880
-0.0924 -0.0840 -0.0546 0 0.0840 0.2016 0.3570
-0.0480 -0.0330 0.0000 0.0546 0.1344 0.2430 0.3840
-0.0180 0 0.0330 0.0840 0.1560 0.2520 0.3750
-0.0000 0.0180 0.0480 0.0924 0.1536 0.2340 0.3360
0.0084 0.0240 0.0486 0.0840 0.1320 0.1944 0.2730
0.0096 0.0210 0.0384 0.0630 0.0960 0.1386 0.1920
0.0060 0.0120 0.0210 0.0336 0.0504 0.0720 0.0990
0 0 0 0 0 0 0
-0.0060 -0.0120 -0.0210 -0.0336 -0.0504 -0.0720 -0.0990
-0.0096 -0.0210 -0.0384 -0.0630 -0.0960 -0.1386 -0.1920
-0.0084 -0.0240 -0.0486 -0.0840 -0.1320 -0.1944 -0.2730
0 -0.0180 -0.0480 -0.0924 -0.1536 -0.2340 -0.3360
0.0180 0 -0.0330 -0.0840 -0.1560 -0.2520 -0.3750
0.0480 0.0330 0 -0.0546 -0.1344 -0.2430 -0.3840
0.0924 0.0840 0.0546 0 -0.0840 -0.2016 -0.3570
0.1536 0.1560 0.1344 0.0840 0 -0.1224 -0.2880
0.2340 0.2520 0.2430 0.2016 0.1224 0 -0.1710
0.3360 0.3750 0.3840 0.3570 0.2880 0.1710 0
```matlab
contour(X,Y,Z)
```
![png](lecture_4_files/lecture_4_12_0.png)
```matlab
mesh(X,Y,Z)
```
![png](lecture_4_files/lecture_4_13_0.png)
```matlab
pcolor(X,Y,Z)
```
![png](lecture_4_files/lecture_4_14_0.png)
## Functions
So far, everything has been executed as a script, or calling a built-in function. Now we begin building our own functions.
Functions are saved in memory (or better yet) in a folder in your path or current directory
Example of storing function in memory
$f(x,y) = (xy^{3}-x^{3}y)$
```matlab
f= @(x,y) (x.*y.^3-x.^3.*y)
```
f =
@(x,y)(x.*y.^3-x.^3.*y)
```matlab
f(0.1,-0.5)
```
ans =
-0.0120
Here we will save a function called `my_function` as `my_function.m`
```matlab
function [vx,vy] = my_function(x,y,t)
% 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
vx=zeros(length(t),1);
vy=zeros(length(t),1);
vx(1:end-1) = diff(x)./diff(t); % calculate vx as delta x/delta t
vy(1:end-1) = diff(y)./diff(t); % calculate vy as delta y/delta t
vx(end) = vx(end-1);
vy(end) = vy(end-1);
end
```
```matlab
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
```matlab
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);
```
```matlab
yyaxis left
plot(t(1:10:end),vx(1:10:end),'o',t,3*t.^2)
ylabel('v_{x}')
yyaxis right
plot(t(1:10:end),vy(1:10:end),'s',t, t)
ylabel('v_{y}')
xlabel('time')
```
![png](lecture_4_files/lecture_4_22_0.png)
Now, create a new function that calls 'my_function' called, `my_caller.m`
```matlab
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 = velocity in x-direction
ay = velocity in y-direction
```matlab
[ax,ay]=my_caller(x,y,t);
```
```matlab
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_{x}')
xlabel('time')
axis([0,10,0,3])
```
![png](lecture_4_files/lecture_4_26_0.png)
```matlab
diff_match_dims(x,t)
```
Undefined function 'diff_match_dims' for input arguments of type 'double'.

```matlab
```