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)}} | ||
+ | {{PDF Table Item|filename=ExampleOddTri.pdf|title=FS for f(x}=ODD Triangle, x \in (0,1)}} | ||
+ | [http://dl.dropbox.com/u/31308033/AEM/OddTriangle.mpg Animation of the successive superposition of 380 modes] | ||
+ | |||
+ | [http://dl.dropbox.com/u/31308033/AEM/OddTriangleSlow.mpg Slower animation of the successive superposition of 380 modes] | ||
+ | {{PDF Table Item|filename=ExampleEvenTri.pdf|title=FS for f(x}=Even Triangle, x \in (0,1)}} | ||
+ | {{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] | ||
+ | |||
====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] | ||
====Application of Fourier Transform/Series==== | ====Application of Fourier Transform/Series==== | ||
[http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cts=1330962524014&ved=0CDMQtwIwAQ&url=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DUkotZy3lQqo&ei=7t9UT5DlHYSJsQKS9fDvBQ&usg=AFQjCNEsEOy9rzRrgn2xnt0NopUhgjTYwQ&sig2=4zt2FQTRYSoEhyNcM-PPtQ Aliasing - Plane] | [http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cts=1330962524014&ved=0CDMQtwIwAQ&url=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DUkotZy3lQqo&ei=7t9UT5DlHYSJsQKS9fDvBQ&usg=AFQjCNEsEOy9rzRrgn2xnt0NopUhgjTYwQ&sig2=4zt2FQTRYSoEhyNcM-PPtQ Aliasing - Plane] | ||
+ | |||
[http://youtu.be/rVSh-au_9aM Aliasingish - Helicopter] | [http://youtu.be/rVSh-au_9aM Aliasingish - Helicopter] | ||
+ | |||
[http://youtu.be/jq8YCCqYvX0 Aliasing - Wheel animation] | [http://youtu.be/jq8YCCqYvX0 Aliasing - Wheel animation] | ||
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[http://en.wikipedia.org/wiki/Green's_function Green's Function - Wikipedia] | [http://en.wikipedia.org/wiki/Green's_function Green's Function - Wikipedia] | ||
{{PDF Table Item|filename=FreqResponseHO.pdf|title= Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125} }} | {{PDF Table Item|filename=FreqResponseHO.pdf|title= Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125} }} | ||
+ | |||
+ | ===Sampling, Nyquist and Aliasing=== | ||
+ | |||
+ | [http://en.wikipedia.org/wiki/Aliasing Aliasing - Wikipedia] | ||
+ | |||
+ | [http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem Nyquist Shannon Sampling Theorem - Wikipedia] | ||
+ | |||
+ | [http://www.youtube.com/watch?v=Y9Px9EAhyss&feature=fvwp&NR=1 Aliasing - Plane Prop] | ||
+ | |||
+ | [http://www.youtube.com/watch?v=Fy9dJgGCWZI Aliasing - Sinusoid Signal] | ||
+ | |||
+ | [http://www.youtube.com/watch?v=YpMtanpsVeE Aliasing - Fan] | ||
+ | |||
+ | [http://www.youtube.com/watch?v=qgvuQGY946g&feature=related Aliasing - Helicopter] | ||
+ | |||
+ | [http://www.youtube.com/watch?v=A-19SxqZ8Qs Aliasing - String] | ||
+ | |||
+ | [http://www.youtube.com/watch?v=Z8123NdNnM4 Aliasing - Audio] | ||
==Partial Differential Equations== | ==Partial Differential Equations== | ||
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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] | ||
− | [http:// | + | [http://youtu.be/gWGLAAYdbbc Shock Wave (Plane) - You Tube ] |
− | + | ||
− | + | ||
[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] | ||
− | [http:// | + | [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:// | + | [http://youtu.be/_EKSFLkcOq8 Shockwave Slowmo] |
+ | |||
+ | [http://youtu.be/iCwMNm447RI Not Shockwaves but interesting] | ||
+ | |||
+ | [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 :)] | ||
+ | |||
+ | [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
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