PrattWiki - User contributions [en]

MATLAB:Plotting Surfaces

2010-09-27T00:40:23Z

Geo4:

There are many problems in engineering that require examining a 2-D
domain. For example, if you want to determine the distance from a
specific point on a flat surface to any other flat surface, you need
to think about both the ''x'' and ''y'' coordinate. There are various
other functions that need ''x'' and ''y'' coordinates.

== Individual Patches ==
One way to create a surface is to generate lists of the x, y, and z coordinates for each location of a patch. MATLAB will plot intersections at each location specified by the matrices and will then connect the intersections by linking the values next to each other in the matrix. For example, if x, y, and z are 2x2 matrices, the surface commands will generate a single patch:
<source lang=matlab>
clear; format short e
x = [ 1 3;...
2 4];
y = [ 5 6;...
7 8];
z = [ 9 12;...
10 11]
meshc(x, y, z)
xlabel('x'); ylabel('y'); zlabel('z');
axis equal; axis([1 6 5 9 9 12])
</source>
<center>
[[File:PatchExOrig.png|400 px]]
</center>

Note that the four "corners" above are not all co-planar; MATLAB will thus create the patch using two triangles - to show this more clearly, you can tell MATLAB to change the view by specifying the azimuth and elevation:
<source lang=matlab>
view([136, 32])
</source>
which yields the following image:
<center>
[[File:PatchExRot.png|400 px]]
</center>

You can add more patches to the surface by increasing the size of the matrices. For example, adding another column will add two more intersections to the surface:
<source lang="matlab">
x = [x [ 5; 6]];
y = [y [ 5; 9]];
z = [z [12; 12]];
meshc(x, y, z)
xlabel('x'); ylabel('y'); zlabel('z');
axis equal; axis([1 6 5 9 9 12])
</source>
<center>
[[File:PatchExTwo.png|400 px]]
</center>

== The meshgrid Command==
Much of the time, rather than specifying individual patches, you will have functions of two parameters to plot. The '''meshgrid''' command is specifically used to create matrices that will represent two parameters. For example, note the output to the
following MATLAB command:
<source lang="matlab">
[x, y] = meshgrid(-2:1:2, -1:.25:1)
</source>
<source lang="text">
x =

-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2

y =

-1.0000 -1.0000 -1.0000 -1.0000 -1.0000
-0.7500 -0.7500 -0.7500 -0.7500 -0.7500
-0.5000 -0.5000 -0.5000 -0.5000 -0.5000
-0.2500 -0.2500 -0.2500 -0.2500 -0.2500
0 0 0 0 0
0.2500 0.2500 0.2500 0.2500 0.2500
0.5000 0.5000 0.5000 0.5000 0.5000
0.7500 0.7500 0.7500 0.7500 0.7500
1.0000 1.0000 1.0000 1.0000 1.0000
</source>

The first argument gives the range that the first output variable
should include, and the second argument gives the range that the
second output variable should include. Note that the first output
variable <code>x</code> basically gives an <code>x</code> coordinate and the second output
variable <code>y</code> gives a <code>y</code> coordinate. This is useful if you want to
plot a function in 2-D.

== Examples Using 2 Independent Variables ==
For example, to plot <code>z=x+y</code> over the ranges of <code>x</code>
and <code>y</code> specified above - the code would be:
<source lang="matlab">
[x, y] = meshgrid(-2:1:2, -1:.25:1);
z = x + y;
meshc(x, y, z);
xlabel('x');
ylabel('y');
zlabel('z');
title('z = x + y');
</source>
and the graph is:
<center>
[[Image:SurfExp01.png|400px]]
</center>

To find the distance ''r'' from a particular point, say <code>(-1,-0.5)</code>, you just need
to change the function. Since the distance between two points <math>(x, y)</math> and <math>(x_0, y_0)</math> is given by
<math>
r=\sqrt{(x-x_0)^2+(y-y_0)^2}
</math>
the code could be:
<source lang="matlab">
[x, y] = meshgrid(-2:1:2, -1:.25:1);
r = sqrt( (x-(-1)).^2 + (y-(-0.5)).^2 );
meshc(x, y, r);
xlabel('x');
ylabel('y');
zlabel('r');
title('r = Distance from (-1,-0.5)');
</source>
and the plot is
<center>
[[Image:SurfExp02.png|400px]]
</center>

== Examples Using Refined Grids ==
You can also use a finer grid to make a better-looking plot:
<source lang="matlab">
[x, y] = meshgrid(linspace(-1.2, 1.2, 20));
r = sqrt( (x-(-1)).^2 + (y-(-0.5)).^2 );
meshc(x, y, r);
xlabel('x');
ylabel('y');
zlabel('r');
title('r = Distance from (-1,-0.5)');
</source>
and the plot is:
<center>
[[Image:SurfExp03.png|400px]]
</center>

Note that the <code>meshgrid</code> command was given only one
argument - in that case, the range of <code>x</code> and <code>y</code> will be the same.

== Finding Minima and Maxima in 2-D ==
You can also use these 2-D structures to find minima and maxima. For
example, given the grid in the code directly above, you can find the
minimum and maximum distances and where they occur:
<source lang="matlab">
MinDistance = min(r(:))
MaxDistance = max(r(:))
XatMin = x(find(r == MinDistance))
YatMin = y(find(r == MinDistance))
XatMax = x(find(r == MaxDistance))
YatMax = y(find(r == MaxDistance))
</source>

<source lang="text">
MinDistance =
0.0782
MaxDistance =
2.7803
XatMin =
-0.9474
YatMin =
-0.4421
XatMax =
1.2000
YatMax =
1.2000
</source>

If there are multiple maxima or minima, the <code>find</code> command will
report them all. For example, with the following code,
<source lang="matlab">
[x, y] = meshgrid(linspace(-1, 1, 31));
z2 = exp(-sqrt(x.^2+y.^2)).*cos(4*x).*cos(4*y);
meshc(x, y, z2);
xlabel('x');
ylabel('y');
zlabel('z');
title('z = e^{-(x^2+y^2)^{0.5}} cos(4x) cos(4y)');
MinVal = min(min(z2))
MaxVal = max(max(z2))
XatMin = x(find(z2 == MinVal))
YatMin = y(find(z2 == MinVal))
XatMax = x(find(z2 == MaxVal))
YatMax = y(find(z2 == MaxVal))
</source>
which gives a graph of:
<center>
[[Image:SurfExp04.png|400px]]
</center>
the matrix <code>z2</code> has four entries with the same minimum value and one with the maximum value:
<source lang="text">
MinVal =
-0.4699

MaxVal =
1

XatMin =
-0.7333
0
0
0.7333

YatMin =
0
-0.7333
0.7333
0

XatMax =
0

YatMax =
0
</source>

== Higher Refinement ==
As seen in creating line plots [[MATLAB:Plotting#Using_Different_Scales| using different scales]], you may want to use a more highly-refined
grid to locate maxima and minima with greater precision. This may
include reducing the overall domain of the function as well as
including more points. For example, the changing the grid to have 1001 points in either direction makes for a more refined grid. The code below demonstrates how to increase the
refinement:
<source lang="matlab">
[xp, yp] = meshgrid(linspace(-1.2, 1.2, 1001));
z2p = exp(-sqrt(xp.^2+yp.^2)).*cos(4*xp).*cos(4*yp);
MinValp = min(min(z2p))
MaxValp = max(max(z2p))
XatMinp = xp(find(z2p == MinValp))
YatMinp = yp(find(z2p == MinValp))
XatMaxp = xp(find(z2p == MaxValp))
YatMaxp = yp(find(z2p == MaxValp))
</source>
The results obtained are:
<source lang="text">
MinValp =
-0.4703

MaxValp =
1

XatMinp =
-0.7248
0
0
0.7248

YatMinp =
0
-0.7248
0.7248
0

XatMaxp =
0

YatMaxp =
0
</source>

Note that ''graphing'' the more refined points would be a bad idea -
there are now over one million nodes and MATLAB will have a hard time
rendering such a surface.

== Using Other Coordinate Systems ==
The plotting commands such as <code>meshc</code> and <code>surfc</code> generate surfaces based on matrices of x, y, and z coordinates, respectively, but you can also use other coordinate systems to calculate where the points go. As an example, the surface above could be plotted on a circular domain using polar coordinates. To do that, ''r'' and <math>\theta</math> coordinates could be generated using meshgrid and the appropriate x, y, and z values could be obtained by noting that <math>x=r\cos(\theta)</math> and <math>y=r\sin(\theta)</math>. z can then be calculated from any combination of x, y, r, and <math>\theta</math>:
<source lang="matlab">
[r, theta] = meshgrid(...
linspace(0, 1.7, 60), ...
linspace(0, 2*pi, 73));
x = r.*cos(theta);
y = r.*sin(theta);
z = exp(-r).*cos(4*x).*cos(4*y);
m(x, y, z);
x('x');
y('y');
z('z');
</source>
produces:
<center>
[[Image:SurfExp06a.png|400px]]
</center>
though in this case, an interpolated surface plot might look better:
<source lang="matlab">
surfc(x, y, z);
shading interp
xlabel('x');
ylabel('y');
zlabel('z');
</source>
<center>
[[Image:SurfExp06b.png|400px]]
</center>

== Questions ==
{{Questions}}

== External Links ==

== References ==
<references />

[[Category:EGR 53]]

MATLAB:Plotting Surfaces

2010-09-27T00:37:29Z

Geo4:

There are many problems in engineering that require examining a 2-D
domain. For example, if you want to determine the distance from a
specific point on a flat surface to any other flat surface, you need
to think about both the ''x'' and ''y'' coordinate. There are various
other functions that need ''x'' and ''y'' coordinates.

== Individual Patches ==
One way to create a surface is to generate lists of the x, y, and z coordinates for each location of a patch. MATLAB will plot intersections at each location specified by the matrices and will then connect the intersections by linking the values next to each other in the matrix. For example, if x, y, and z are 2x2 matrices, the surface commands will generate a single patch:
<source lang=matlab>
clear; format short e
x = [ 1 3;...
2 4];
y = [ 5 6;...
7 8];
z = [ 9 12;...
10 11]
meshc(x, y, z)
xlabel('x'); ylabel('y'); zlabel('z');
axis equal; axis([1 6 5 9 9 12])
</source>
<center>
[[File:PatchExOrig.png|400 px]]
</center>

Note that the four "corners" above are not all co-planar; MATLAB will thus create the patch using two triangles - to show this more clearly, you can tell MATLAB to change the view by specifying the azimuth and elevation:
<source lang=matlab>
view([136, 32])
</source>
which yields the following image:
<center>
[[File:PatchExRot.png|400 px]]
</center>

You can add more patches to the surface by increasing the size of the matrices. For example, adding another column will add two more intersections to the surface:
<source lang="matlab">
x = [x [ 5; 6]];
y = [y [ 5; 9]];
z = [z [12; 12]];
meshc(x, y, z)
xlabel('x'); ylabel('y'); zlabel('z');
axis equal; axis([1 6 5 9 9 12])
</source>
<center>
[[File:PatchExTwo.png|400 px]]
</center>

== The meshgrid Command==
Much of the time, rather than specifying individual patches, you will have functions of two parameters to plot. The '''meshgrid''' command is specifically used to create matrices that will represent two two parameters. For example, note the output to the
following MATLAB command:
<source lang="matlab">
[x, y] = meshgrid(-2:1:2, -1:.25:1)
</source>
<source lang="text">
x =

-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2

y =

-1.0000 -1.0000 -1.0000 -1.0000 -1.0000
-0.7500 -0.7500 -0.7500 -0.7500 -0.7500
-0.5000 -0.5000 -0.5000 -0.5000 -0.5000
-0.2500 -0.2500 -0.2500 -0.2500 -0.2500
0 0 0 0 0
0.2500 0.2500 0.2500 0.2500 0.2500
0.5000 0.5000 0.5000 0.5000 0.5000
0.7500 0.7500 0.7500 0.7500 0.7500
1.0000 1.0000 1.0000 1.0000 1.0000
</source>

The first argument gives the range that the first output variable
should include, and the second argument gives the range that the
second output variable should include. Note that the first output
variable <code>x</code> basically gives an <code>x</code> coordinate and the second output
variable <code>y</code> gives a <code>y</code> coordinate. This is useful if you want to
plot a function in 2-D.

== Examples Using 2 Independent Variables ==
For example, to plot <code>z=x+y</code> over the ranges of <code>x</code>
and <code>y</code> specified above - the code would be:
<source lang="matlab">
[x, y] = meshgrid(-2:1:2, -1:.25:1);
z = x + y;
meshc(x, y, z);
xlabel('x');
ylabel('y');
zlabel('z');
title('z = x + y');
</source>
and the graph is:
<center>
[[Image:SurfExp01.png|400px]]
</center>

To find the distance ''r'' from a particular point, say <code>(-1,-0.5)</code>, you just need
to change the function. Since the distance between two points <math>(x, y)</math> and <math>(x_0, y_0)</math> is given by
<math>
r=\sqrt{(x-x_0)^2+(y-y_0)^2}
</math>
the code could be:
<source lang="matlab">
[x, y] = meshgrid(-2:1:2, -1:.25:1);
r = sqrt( (x-(-1)).^2 + (y-(-0.5)).^2 );
meshc(x, y, r);
xlabel('x');
ylabel('y');
zlabel('r');
title('r = Distance from (-1,-0.5)');
</source>
and the plot is
<center>
[[Image:SurfExp02.png|400px]]
</center>

== Examples Using Refined Grids ==
You can also use a finer grid to make a better-looking plot:
<source lang="matlab">
[x, y] = meshgrid(linspace(-1.2, 1.2, 20));
r = sqrt( (x-(-1)).^2 + (y-(-0.5)).^2 );
meshc(x, y, r);
xlabel('x');
ylabel('y');
zlabel('r');
title('r = Distance from (-1,-0.5)');
</source>
and the plot is:
<center>
[[Image:SurfExp03.png|400px]]
</center>

Note that the <code>meshgrid</code> command was given only one
argument - in that case, the range of <code>x</code> and <code>y</code> will be the same.

== Finding Minima and Maxima in 2-D ==
You can also use these 2-D structures to find minima and maxima. For
example, given the grid in the code directly above, you can find the
minimum and maximum distances and where they occur:
<source lang="matlab">
MinDistance = min(r(:))
MaxDistance = max(r(:))
XatMin = x(find(r == MinDistance))
YatMin = y(find(r == MinDistance))
XatMax = x(find(r == MaxDistance))
YatMax = y(find(r == MaxDistance))
</source>

<source lang="text">
MinDistance =
0.0782
MaxDistance =
2.7803
XatMin =
-0.9474
YatMin =
-0.4421
XatMax =
1.2000
YatMax =
1.2000
</source>

If there are multiple maxima or minima, the <code>find</code> command will
report them all. For example, with the following code,
<source lang="matlab">
[x, y] = meshgrid(linspace(-1, 1, 31));
z2 = exp(-sqrt(x.^2+y.^2)).*cos(4*x).*cos(4*y);
meshc(x, y, z2);
xlabel('x');
ylabel('y');
zlabel('z');
title('z = e^{-(x^2+y^2)^{0.5}} cos(4x) cos(4y)');
MinVal = min(min(z2))
MaxVal = max(max(z2))
XatMin = x(find(z2 == MinVal))
YatMin = y(find(z2 == MinVal))
XatMax = x(find(z2 == MaxVal))
YatMax = y(find(z2 == MaxVal))
</source>
which gives a graph of:
<center>
[[Image:SurfExp04.png|400px]]
</center>
the matrix <code>z2</code> has four entries with the same minimum value and one with the maximum value:
<source lang="text">
MinVal =
-0.4699

MaxVal =
1

XatMin =
-0.7333
0
0
0.7333

YatMin =
0
-0.7333
0.7333
0

XatMax =
0

YatMax =
0
</source>

== Higher Refinement ==
As seen in creating line plots [[MATLAB:Plotting#Using_Different_Scales| using different scales]], you may want to use a more highly-refined
grid to locate maxima and minima with greater precision. This may
include reducing the overall domain of the function as well as
including more points. For example, the changing the grid to have 1001 points in either direction makes for a more refined grid. The code below demonstrates how to increase the
refinement:
<source lang="matlab">
[xp, yp] = meshgrid(linspace(-1.2, 1.2, 1001));
z2p = exp(-sqrt(xp.^2+yp.^2)).*cos(4*xp).*cos(4*yp);
MinValp = min(min(z2p))
MaxValp = max(max(z2p))
XatMinp = xp(find(z2p == MinValp))
YatMinp = yp(find(z2p == MinValp))
XatMaxp = xp(find(z2p == MaxValp))
YatMaxp = yp(find(z2p == MaxValp))
</source>
The results obtained are:
<source lang="text">
MinValp =
-0.4703

MaxValp =
1

XatMinp =
-0.7248
0
0
0.7248

YatMinp =
0
-0.7248
0.7248
0

XatMaxp =
0

YatMaxp =
0
</source>

Note that ''graphing'' the more refined points would be a bad idea -
there are now over one million nodes and MATLAB will have a hard time
rendering such a surface.

== Using Other Coordinate Systems ==
The plotting commands such as <code>meshc</code> and <code>surfc</code> generate surfaces based on matrices of x, y, and z coordinates, respectively, but you can also use other coordinate systems to calculate where the points go. As an example, the surface above could be plotted on a circular domain using polar coordinates. To do that, ''r'' and <math>\theta</math> coordinates could be generated using meshgrid and the appropriate x, y, and z values could be obtained by noting that <math>x=r\cos(\theta)</math> and <math>y=r\sin(\theta)</math>. z can then be calculated from any combination of x, y, r, and <math>\theta</math>:
<source lang="matlab">
[r, theta] = meshgrid(...
linspace(0, 1.7, 60), ...
linspace(0, 2*pi, 73));
x = r.*cos(theta);
y = r.*sin(theta);
z = exp(-r).*cos(4*x).*cos(4*y);
m(x, y, z);
x('x');
y('y');
z('z');
</source>
produces:
<center>
[[Image:SurfExp06a.png|400px]]
</center>
though in this case, an interpolated surface plot might look better:
<source lang="matlab">
surfc(x, y, z);
shading interp
xlabel('x');
ylabel('y');
zlabel('z');
</source>
<center>
[[Image:SurfExp06b.png|400px]]
</center>

== Questions ==
{{Questions}}

== External Links ==

== References ==
<references />

[[Category:EGR 53]]

User:Geo4

2010-09-19T19:01:51Z

Geo4:

==About Me==
I am a student at Duke University who is studying engineering. Currently I plan to major in mechanical engineering and earn my certificate in aerospace engineering, but we know how these things tend to change. My post graduation plans are...unsolidified to say the least. Roughly they include either continuing on to a graduate degree, working and then returning to school for an MBA, or law school to study patent law.

==Pronunciation of My Name==
===First Name===
There are no tricks here: Grant. You may stress the first or last syllable, seeing as there is only one to choose from.
===Last Name===
Slightly more complicated: Oakley. It's two syllables. The "oak" part is the stressed portion and pronounced like the tree. The "ley" portion comes second, and is not stressed. It rhymes with "tree." If more help is needed, consult your nearest sunglasses retailer.

==Favorite MATLAB Demonstration==
===Creating Graphical User Interfaces===
I thought this section was interesting because the ability to actually display windows to the screen like any other programming language shows the versatility of MATLAB. I assumed it was purely for number crunching operations, but apparently one can also create a program that would allow another user to easily utilize functions and scripts like they would other computer applications.

==Interests==
I like to keep my interests diverse and at all times fairly random. That way nothing ever gets old.
*Engineering, obviously! I became interested in engineering doing projects at home and while trying to teach myself computer programming.
*Mountaineering, rock climbing, and hiking. These are ''slightly'' more accessible at home than in North Carolina, but I'll be sure to do as much as I can on breaks.
*Slacklining, juggling, unicycling, and other circus skills.
*Music. I play the tuba, bass, and piano. Unfortunately my band had to break up to go to school, so for now its only tuba with the school.
*Amateur computer programming. I spent a few too many hours of my summer learning to write in Processing (a very fun but utterly useless Java distribution).
*Morse Code .. | .-.. --- ...- . | .-- .... --- | -.-. .- -. | .-. . .- --. | - .... .. ...

==Classes==
I figured I would post these in case anybody wanted to study together or discuss the class.
*Engineering 53 (Section 002)
*Engineering Lab (Section 06)
*Chemistry 43 (Section 001)
*Chemistry 43 Lab (Section 12)
*Math 103 (Section 12)
*German 2 (Section 01)
*Endurance Swimming (Section 01)
*Symphony Orchestra

==Grand Challenges of Engineering Article==
Here is a link to a page on the National Academy of Engineering website. It discusses the need for engineers to design and create devices to further scientific research in fields such as biology and particle physics, and how these devices will allow researchers to better understand life and the universe.
*[http://www.engineeringchallenges.org/cms/8996/8965.aspx Engineering the Tools of Scientific Discovery], National Academy of Engineering, updated 15 February 2008, accessed 3 September 2010 (Engineering the Tools of Scientific Discovery), is one of fourteen grand challenges, all of which can be found at [http://www.engineeringchallenges.org/ www.engineeringchallenges.org].

==Shameless Promotion of my Band==
I figure that my band counts as personal information, so it wouldn't be out of line to direct you to our webpages.
*The main page is on MySpace (I know, not very trendy these days). [http://www.myspace.com/olaf3 Olaf Olaf Olaf on MySpace]
*I also tried to make a wiki-style page, for those who are truly bored. [http://olafolafolaf.wikidot.com/ Olaf Wiki]

User:Geo4

2010-09-19T18:53:02Z

Geo4:

==About Me==
I am a student at Duke University who is studying engineering. Currently I plan to major in mechanical engineering and earn my certificate in aerospace engineering, but we know how these things tend to change. My post graduation plans are...unsolidified to say the least. Roughly they include either continuing on to a graduate degree, working and then returning to school for an MBA, or law school to study patent law.

==Pronunciation of My Name==
===First Name===
There are no tricks here: Grant. You may stress the first or last syllable, seeing as there is only one to choose from.
===Last Name===
Slightly more complicated: Oakley. It's two syllables. The "oak" part is the stressed portion and pronounced like the tree. The "ley" portion comes second, and is not stressed. It rhymes with "tree." If more help is needed, consult your nearest sunglasses retailer.

==Interests==
I like to keep my interests diverse and at all times fairly random. That way nothing ever gets old.
*Engineering, obviously! I became interested in engineering doing projects at home and while trying to teach myself computer programming.
*Mountaineering, rock climbing, and hiking. These are ''slightly'' more accessible at home than in North Carolina, but I'll be sure to do as much as I can on breaks.
*Slacklining, juggling, unicycling, and other circus skills.
*Music. I play the tuba, bass, and piano. Unfortunately my band had to break up to go to school, so for now its only tuba with the school.
*Amateur computer programming. I spent a few too many hours of my summer learning to write in Processing (a very fun but utterly useless Java distribution).
*Morse Code. .. | .-.. --- ...- . | .-- .... --- | -.-. .- -. | .-. . .- --. | - .... .. ...

==Classes==
I figured I would post these in case anybody wanted to study together or discuss the class.
*Engineering 53 (Section 002)
*Engineering Lab (Section 06)
*Chemistry 43 (Section 001)
*Chemistry 43 Lab (Section 12)
*Math 103 (Section 12)
*German 2 (Section 01)
*Endurance Swimming (Section 01)
*Symphony Orchestra

==Grand Challenges of Engineering Article==
Here is a link to a page on the National Academy of Engineering website. It discusses the need for engineers to design and create devices to further scientific research in fields such as biology and particle physics, and how these devices will allow researchers to better understand life and the universe.
*[http://www.engineeringchallenges.org/cms/8996/8965.aspx Engineering the Tools of Scientific Discovery], National Academy of Engineering, updated 15 February 2008, accessed 3 September 2010 (Engineering the Tools of Scientific Discovery), is one of fourteen grand challenges, all of which can be found at [http://www.engineeringchallenges.org/ www.engineeringchallenges.org].

==Shameless Promotion of my Band==
I figure that my band counts as personal information, so it wouldn't be out of line to direct you to our webpages.
*The main page is on MySpace (I know, not very trendy these days). [http://www.myspace.com/olaf3 Olaf Olaf Olaf on MySpace]
*I also tried to make a wiki-style page, for those who are truly bored. [http://olafolafolaf.wikidot.com/ Olaf Wiki]

User:Geo4

2010-09-02T16:42:27Z

Geo4:

==About Me==
I am a student at Duke University who is studying engineering. Currently I plan to major in mechanical engineering and earn my certificate in aerospace engineering, but we know how these things tend to change. My post graduation plans are...unsolidified to say the least. Roughly they include either continuing on to a graduate degree, working and then returning to school for an MBA, or law school to study patent law.

==Interests==
I like to keep my interests diverse and at all times fairly random. That way nothing ever gets old.
*Engineering, obviously! I became interested in engineering doing projects at home and while trying to teach myself computer programming.
*Mountaineering, rock climbing, and hiking. These are ''slightly'' more accessible at home than in North Carolina, but I'll be sure to do as much as I can on breaks.
*Slacklining, juggling, unicycling, and other circus skills.
*Music. I play the tuba, bass, and piano. Unfortunately my band had to break up to go to school, so for now its only tuba with the school.
*Amateur computer programming. I spent a few too many hours of my summer learning to write in Processing (a very fun but utterly useless Java distribution).
*Morse Code. .. | .-.. --- ...- . | .-- .... --- | -.-. .- -. | .-. . .- --. | - .... .. ...

==Classes==
I figured I would post these in case anybody wanted to study together or discuss the class.
*Engineering 53 (Section 002)
*Engineering Lab (Section 06)
*Chemistry 43 (Section 001)
*Chemistry 43 Lab (Section 12)
*Math 103 (Section 12)
*German 2 (Section 01)
*Endurance Swimming (Section 01)
*Symphony Orchestra

==Grand Challenges of Engineering Article==
Here is a link to a page on the National Academy of Engineering website. It discusses the need for engineers to design and create devices to further scientific research in fields such as biology and particle physics, and how these devices will allow researchers to better understand life and the universe.
*[http://www.engineeringchallenges.org/cms/8996/8965.aspx Engineering the Tools of Scientific Discovery], National Academy of Engineering, updated 15 February 2008, accessed 3 September 2010 (Engineering the Tools of Scientific Discovery), is one of fourteen grand challenges, all of which can be found at [http://www.engineeringchallenges.org/ www.engineeringchallenges.org].

==Shameless Promotion of my Band==
I figure that my band counts as personal information, so it wouldn't be out of line to direct you to our webpages.
*The main page is on MySpace (I know, not very trendy these days). [http://www.myspace.com/olaf3 Olaf Olaf Olaf on MySpace]
*I also tried to make a wiki-style page, for those who are truly bored. [http://olafolafolaf.wikidot.com/ Olaf Wiki]

User:Geo4

2010-09-02T16:36:30Z

Geo4:

==About Me==
I am a student at Duke University who is studying engineering. Currently I plan to major in mechanical engineering and earn my certificate in aerospace engineering, but we know how these things tend to change. My post graduation plans are...unsolidified to say the least. Roughly they include either continuing on to a graduate degree, working and then returning to school for an MBA, or law school to study patent law.

==Interests==
I like to keep my interests diverse and at all times fairly random. That way nothing ever gets old.
*Engineering, obviously! I became interested in engineering doing projects at home and while trying to teach myself computer programming.
*Mountaineering, rock climbing, and hiking. These are ''slightly'' more accessible at home than in North Carolina, but I'll be sure to do as much as I can on breaks.
*Slacklining, juggling, unicycling, and other circus skills.
*Music. I play the tuba, bass, and piano. Unfortunately my band had to break up to go to school, so for now its only tuba with the school.
*Amateur computer programming. I spent a few too many hours of my summer learning to write in Processing (a very fun but utterly useless Java distribution).
*Morse Code. .. | .-.. --- ...- . | .-- .... --- | -.-. .- -. | .-. . .- --. | - .... .. ...

==Classes==
I figured I would post these in case anybody wanted to study together or discuss the class.
*Engineering 53 (Section 002)
*Engineering Lab (Section 06)
*Chemistry 43 (Section 001)
*Chemistry 43 Lab (Section 12)
*Math 103 (Section 12)
*German 2 (Section 01)
*Endurance Swimming (Section 01)
*Symphony Orchestra

==Grand Challenges of Engineering Article==
Here is a link to a page on the National Academy of Engineering website. It discusses the need for engineers to design and create devices to further scientific research in fields such as biology and particle physics, and how these devices will allow researchers to better understand life and the universe.
*[http://www.engineeringchallenges.org/cms/8996/8965.aspx Engineering the Tools of Scientific Discovery] is one of fourteen grand challenges, all of which can be found at [http://www.engineeringchallenges.org/ www.engineeringchallenges.org].

==Shameless Promotion of my Band==
I figure that my band counts as personal information, so it wouldn't be out of line to direct you to our webpages.
*The main page is on MySpace (I know, not very trendy these days). [http://www.myspace.com/olaf3 Olaf Olaf Olaf on MySpace]
*I also tried to make a wiki-style page, for those who are truly bored. [http://olafolafolaf.wikidot.com/ Olaf Wiki]

User:Geo4

2010-09-02T16:30:19Z

Geo4:

User:Geo4

2010-08-31T19:02:35Z

Geo4:

==Bio==
I am a student at Duke University who is studying engineering. Currently I plan to major in mechanical engineering and earn my certificate in aerospace engineering, but we know how these things tend to change. My post graduation plans are...unsolidified to say the least. Roughly they include either continuing on to a graduate degree, working and then returning to school for an MBA, or law school to study patent law.

==Interests==
I like to keep my interests diverse and at all times fairly random. That way nothing ever gets old.
*Engineering, obviously! I became interested in engineering doing projects at home and while trying to teach myself computer programming.
*Mountaineering, rock climbing, and hiking. These are ''slightly'' more accessible at home than in North Carolina, but I'll be sure to do as much as I can on breaks.
*Slacklining, juggling, unicycling, and other circus skills.
*Music. I play the tuba, bass, and piano. Unfortunately my band had to break up to go to school, so for now its only tuba with the school.
*Amateur computer programming. I spent a few too many hours of my summer learning to write in Processing (a very fun but utterly useless Java distribution).
*Morse Code. .. | .-.. --- ...- . | .-- .... --- | -.-. .- -. | .-. . .- --. | - .... .. ...