MATH-348 Advanced Engineering Mathematics - Supplemental

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{{PDF Table Item|filename=Example11.1.1.pdf|title=FS for f(x}=x, x \in (-\pi,\pi)}}
 
{{PDF Table Item|filename=Example11.1.1.pdf|title=FS for f(x}=x, x \in (-\pi,\pi)}}
 
{{PDF Table Item|filename=Example11.1.2.pdf|title=FS for f(x}=Exp(Abs(x)), x \in (-\pi,\pi)}}
 
{{PDF Table Item|filename=Example11.1.2.pdf|title=FS for f(x}=Exp(Abs(x)), x \in (-\pi,\pi)}}
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{{PDF Table Item|filename=ExampleOddTri.pdf|title=FS for f(x}=ODD Triangle, x \in (0,1)}}
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[http://dl.dropbox.com/u/31308033/AEM/OddTriangle.mpg Animation of the successive superposition of 380 modes]
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[http://dl.dropbox.com/u/31308033/AEM/OddTriangleSlow.mpg Slower animation of the successive superposition of 380 modes]
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{{PDF Table Item|filename=ExampleEvenTri.pdf|title=FS for f(x}=Even Triangle, x \in (0,1)}}
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{{PDF Table Item|filename=ExampleEvenTri.mp3|title=FS for f(x}=Even Triangle, x \in (0,1)}}
 
[http://en.wikipedia.org/wiki/Fourier_series Fourier Series - Wikipedia]
 
[http://en.wikipedia.org/wiki/Fourier_series Fourier Series - Wikipedia]
 
[http://en.wikipedia.org/wiki/Gibbs_phenomenon  Gibbs Phenomenon - Wikipedia]
 
[http://en.wikipedia.org/wiki/Gibbs_phenomenon  Gibbs Phenomenon - Wikipedia]
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====Fourier Graphing====
 
====Fourier Graphing====
 
[http://ticc.mines.edu/csm/wiki/images/8/82/SimpleFSGraphing.nb Simple Mathematica Notebook for Fourier Series Graphing]
 
[http://ticc.mines.edu/csm/wiki/images/8/82/SimpleFSGraphing.nb Simple Mathematica Notebook for Fourier Series Graphing]
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[http://physics-animations.com/Physics/English/swa_txt.htm  Animation of Shock Wave Formation in Pressure Field]
 
[http://physics-animations.com/Physics/English/swa_txt.htm  Animation of Shock Wave Formation in Pressure Field]
  
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[http://www.youtube.com/watch?v=jZ3Hhdr8EjI&feature=PlayList&p=2AE42B05690BA5AD&playnext=1&playnext_from=PL&index=2  Shock Wave (Plane) - You Tube 1]
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[http://youtu.be/gWGLAAYdbbc Shock Wave (Plane) - You Tube ]
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[http://www.youtube.com/watch?v=QX04ySm4TTk&feature=PlayList&p=2AE42B05690BA5AD&index=3&playnext=2&playnext_from=PL Shock Wave (Plane) - You Tube 2]
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[http://www.youtube.com/watch?v=9r_2l5_FviU Shock Wave (Explosion) - You Tube 3]
 
[http://www.youtube.com/watch?v=9r_2l5_FviU Shock Wave (Explosion) - You Tube 3]
 
   
 
   
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[http://www.youtube.com/watch?v=GvVQEl_q2ZM Shock Wave (Explosion) - You Tube 4 : Ignore The the cartoon bubble]
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[http://youtu.be/eU8joiS62js Shock Wave (Explosion) - You Tube 4 ]
  
 
[http://www.youtube.com/watch?v=pz7lcHN7GxQ Shock Wave (Simulation) - You Tube 5 : Notice the distortion of the expanding wave-front]
 
[http://www.youtube.com/watch?v=pz7lcHN7GxQ Shock Wave (Simulation) - You Tube 5 : Notice the distortion of the expanding wave-front]
  
 
[http://youtu.be/_EKSFLkcOq8 Shockwave Slowmo]
 
[http://youtu.be/_EKSFLkcOq8 Shockwave Slowmo]
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[http://youtu.be/iCwMNm447RI Not Shockwaves but interesting]
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[http://youtu.be/-Zu5SGllmwc Sonic Boom Animation]
  
 
[http://exploration.grc.nasa.gov/education/rocket/shock.html NASA - Shock Wave Simulator]
 
[http://exploration.grc.nasa.gov/education/rocket/shock.html NASA - Shock Wave Simulator]
  
 
[http://www.tfarchive.com/cartoons/wallpapers/shockwave17.jpg Shockwave :)]
 
[http://www.tfarchive.com/cartoons/wallpapers/shockwave17.jpg Shockwave :)]
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[http://mesoscopic.mines.edu/~jscales/parametric_array.pdf Death Ray]
  
  
 
{{End PDF Table}}
 
{{End PDF Table}}

Latest revision as of 04:23, 15 February 2013

Main Page > Mathematical and Computer Sciences Course Wikis > Advanced Engineering Mathematics
Pdf.png These downloads require Adobe Acrobat Reader

Contents

Course Material

Solutions to ODD Problems

Thanks for taking AEM. If you are doing AEM problems from the text then here are solutions to the odd problems that didn't make it into the abridged edition.

Chapter 7,8,11,12 Odd Solutions for AEM
Solutions to suggested AEM problems from chapter 11

Minor ASI Information

Minor/ASI Information 2011-2012 UGrad Bulletin

Linear Algebra

Three Planes in Space

Three Planes in Space - Four Different Ways 
 Legend for the Animations
   Red = First Plane Equation
   Orange = Second Plane Equation
   Yellow = Third Plane Equation
   Green = Column Space of A (AKA the set of all linear combination of the pivot columns of A)
   Blue = Right Hand Side for non-homogeneous problem.

Animation : Ax=0 with oo-many solutions that form a line in space.

Animation : Ax=b with oo-many solutions that form a line in space.

Animation : Ax=b with a single solution

Animation : Ax=b with no solutions

Linear Algebra Software

Linear Algebra Toolkit

Fourier Methods

Review of Functions

Special Angles and the Unit Circle
A61.TrigIdentities

Odd and Even Functions (Wikipedia) : (see Also 09.LN)

Periodic Functions (Wikipedia) : (See Also 09.LN)

Notes on the Dirac delta "function"

Fourier Series

Fourier Orthogonality

Graphs of cos(pi x), cos(2pi x), sin(pi x), sin(2 pi x) and their various products
Graphs of cos(pi x), cos(2pi x), sin(pi x), sin(2 pi x) and the product of cos(pi x) and sin(pi x)
Graphs of cos(pi x), cos(2pi x), sin(pi x), sin(2 pi x) and the product of cos(pi x) and cos(2 pi x)
Graphs of cos(pi x), cos(2pi x), sin(pi x), sin(2 pi x) and the product of sin(pi x) and sin(pi x)

Fourier Series Examples

FS for f(x}=x, x \in (-\pi,\pi)
FS for f(x}=Exp(Abs(x)), x \in (-\pi,\pi)
FS for f(x}=ODD Triangle, x \in (0,1)

Animation of the successive superposition of 380 modes

Slower animation of the successive superposition of 380 modes

FS for f(x}=Even Triangle, x \in (0,1)
FS for f(x}=Even Triangle, x \in (0,1)

Fourier Series - Wikipedia Gibbs Phenomenon - Wikipedia

Fourier Graphing

Simple Mathematica Notebook for Fourier Series Graphing

Application of Fourier Transform/Series

Aliasing - Plane

Aliasingish - Helicopter

Aliasing - Wheel animation

Fourier Transform

Fourier Transform - Wikipedia

Wikipedia - Sinc Function

Mathworld - Sinc Function

Wikipedia - Nyquist-Shannon Sampling Theorem

Mathworld - Convolution (Animation)

Convolution and Diffraction (Animations)

Convolution and Diffraction (Animations)

Wikipedia - Convolution (Animation)

Green's Function - Wikipedia

Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125}

Sampling, Nyquist and Aliasing

Aliasing - Wikipedia

Nyquist Shannon Sampling Theorem - Wikipedia

Aliasing - Plane Prop

Aliasing - Sinusoid Signal

Aliasing - Fan

Aliasing - Helicopter

Aliasing - String

Aliasing - Audio

Partial Differential Equations

Ordinary Differential Equations

Review of Ordinary Differential Equations (DRAFT - 11/16/09)

Millennium Bridge - Wikipedia

You Tube Video - Millennium Bridge Resonance

Heat Equation

Homogeneous Evolutions

Heat Movie 1 - f(x)=abs(x), with B.C. u(0,t)=u(L,t)=0

Heat Movie 2 - f(x)=parabola, with B.C. u(0,t)=u(L,t)=0

Heat Movie 3 - f(x)Double V, with B.C. u(0,t)=u(L,t)=0

Inhomogeneous Evolutions

Heat Movie 4 - Forced Heat Equation with B.C. u(0,t)=u(L,t)=0

Heat Movie 5 - Forced Heat Equation with B.C. u_{x}(0,t)=u_{x}(L,t)=0

Wave Equation

1D Wave Equation

Wave on a 1-D Sting with Fixed Endpoints

Wave on a 1-D Sting with Fixed Endpoints - Animated with first 5 Fourier Modes (Fundamental Mode in Red)

Wave on a 1-D Sting with FLAT Endpoints from HW10

Wave on a 1-D Sting with FLAT Endpoints from HW10 - Animated with first 5 Fourier Modes (Fundamental Mode in Red)

Traveling Wave :u0(x) = − tanh(x): Red = Right Traveling, Blue=Left Traveling, Black = Superposition

2D Wave Equation Rectangular and Polar

Rectangular Membrane Movie 1 -Text Example pg577

Rectangular Membrane 2 -Text Example pg577

Applet - Pretty Cool

Rectangular Membrane Modes

Animations of Rectangular Membrane Modes - Pretty Good

Animations done by Dr. Russell - All sorts of stuff!


The Well-Tempered Timpani By Richard K. Jones

Vibrating Membrane1 - 12.9.1 Example

Vibrating Membrane2 - 12.9.1 Example

Vibrating Membrane3 - 12.9.1 Example

Vibrating Membrane4 - 12.9.1 Example


Nonlinear Wave Phenomenon

Wikipedia Article on Shock Waves

Animation of Shock Wave Formation in Pressure Field

Shock Wave (Plane) - You Tube

Shock Wave (Explosion) - You Tube 3

Shock Wave (Explosion) - You Tube 4

Shock Wave (Simulation) - You Tube 5 : Notice the distortion of the expanding wave-front

Shockwave Slowmo

Not Shockwaves but interesting

Sonic Boom Animation

NASA - Shock Wave Simulator

Shockwave :)

Death Ray


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