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diff --git a/lecture_03/file.txt b/lecture_03/file.txt
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+computational mechanics
+the dog had 4 legs and weighed 10.0 lbs
+are you awake?computational mechanics
+the dog had 4 legs and weighed 10.0 lbs
+are you awake?
diff --git a/lecture_03/lecture_03.ipynb b/lecture_03/lecture_03.ipynb
diff --git a/lecture_03/lecture_03.md b/lecture_03/lecture_03.md
diff --git a/lecture_03/octave-workspace b/lecture_03/octave-workspace
diff --git a/lecture_03/output_58_0.png b/lecture_03/output_58_0.png
diff --git a/lecture_03/output_63_0.svg b/lecture_03/output_63_0.svg
diff --git a/lecture_03/output_64_0.svg b/lecture_03/output_64_0.svg
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diff --git a/lecture_04/lecture_4.md b/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)
+```
+
+    [0;31mUndefined function 'diff_match_dims' for input arguments of type 'double'.
+    [0m
+
+
+```matlab
+
+```
diff --git a/lecture_04/lecture_4.pdf b/lecture_04/lecture_4.pdf
diff --git a/lecture_04/lecture_4_files/lecture_4_12_0.png b/lecture_04/lecture_4_files/lecture_4_12_0.png
diff --git a/lecture_04/lecture_4_files/lecture_4_13_0.png b/lecture_04/lecture_4_files/lecture_4_13_0.png
diff --git a/lecture_04/lecture_4_files/lecture_4_14_0.png b/lecture_04/lecture_4_files/lecture_4_14_0.png
diff --git a/lecture_04/lecture_4_files/lecture_4_22_0.png b/lecture_04/lecture_4_files/lecture_4_22_0.png
diff --git a/lecture_04/lecture_4_files/lecture_4_26_0.png b/lecture_04/lecture_4_files/lecture_4_26_0.png
diff --git a/lecture_04/lecture_4_files/lecture_4_7_0.png b/lecture_04/lecture_4_files/lecture_4_7_0.png
diff --git a/lecture_04/myscript.m b/lecture_04/myscript.m
@@ -0,0 +1,11 @@
+f=100;
+
+for i=1:10
+  g=i^2;
+  if f==g
+    fprintf('we made it\n')
+  else
+    fprintf('not yet\n')
+  end
+end
+