PHY 226
Mathematical Methods
Dr Phil Lightfoot
Email me or come to
see me any time
p.k.lightfoot@shef.ac.uk 2224533
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PHY226 Phils Problems
Lecture 1
Question 1 Question 2 Question 3 Question 4 Question 4graph Question 5
Lecture 2
Question 1 Question 2 Question 2end Question 3 Question 3end Question 4 Question 5
Question 6 Question 7 Question 8 Question 9
Lecture 3
Question 1 Question 2 Question 3 Question 4 Question 4graph
Lecture 4
Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7
Lecture
5-8
Question 1 Question 1end Question 2 Question 3 Question 3end Question 4 Question4end
Question 5 Question 5end Question 6 Question 7 Question 8 Question 9 Question 9end
Question 10 Question 10end Question 11 Question11end Question12
Lecture
9-11
Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8
Lecture
12
Lecture
13
Question 1 Question 2 Question 3 Question 4 Question 5 Question 5cont
Lecture
14
Question 1 Question 1more Question 1end Question 2 Question 2end Question 3
Lecture
15-16
Question 1 Question 2 Question 2cont
Lecture
17-18
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Homework 2 answers part1 part2
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Tutorial answers
Page6 Page7 Page8 Page9 Page10
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Presentations from
lectures
Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7
Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12 Lecture 13 Lecture 14special
Lecture15 Lecture16 lecture17 lecture18 lecture19 lecture20
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Complete
lecture notes with all spaces filled in
Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5-11 Lecture 9-11
Lecture 12 Lecture 13 Lecture14 lecture15-16 lecture17 lecture18 lecture19,20
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Past exam
papers
The
answers to 2007 paper (sorry no working) to have access to full working email
me your attempt
answers1 answers2 answers3 answers4
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Formula data sheet for the exam
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Interactive media
shown in lectures
Important
To access movie and
audio files right click on link,
save link as
filename, then open on desktop
2nd
Order Differential Equations
Tiger bounce (50Mb
movie showing resonance and phase shift in a forced undamped system)
Rally
suspension (explains the difference between spring preload and compression and
rebound damping)
http://uk.youtube.com/watch?v=CZeCuS4xzL0&feature=related
4x4
with no shock absorbers (demonstrates the effect of removing damping)
http://uk.youtube.com/watch?v=AKcTA5j6K80&feature=related
Bose
suspension (demonstrates the benefits of active suspension)
http://uk.youtube.com/watch?v=eSi6J-QK1lw
Crosswind
landing (demonstrates the need to ensure critical damping in aircraft landing
gear – Jumbos must not bounce)
http://uk.youtube.com/watch?v=n9yF09DMrrI
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Fourier Series
Audacity audio
software download from site below (allows you to record sounds, view waveforms,
and Fourier transform them into frequency distributions)
http://audacity.sourceforge.net/
Look at waveforms from
various instruments (This is a window media player file that I have made, but
its better to download
audacity and generate these waveforms yourselves).
Check your answers
with this software !!! (allows you to build a waveform using the first few sine
and cosine terms)
Fourier software
(allows you to make your own waveforms and add and remove harmonics at will
!!!)
http://www.univie.ac.at/future.media/moe/galerie/fourier/fourier.html
Fourier applet
(interactive demonstration)
http://www.falstad.com/fourier/
Fourier Quiz (Saturday
night in? Looking for an educational game to play with friends? Try this
Fourier Quiz, its great !!!!!!)
Close Encounters (How
Spielberg relied on the Fourier Series to make alien visits less tedious)
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Fourier
Transforms
A host of Applets on
Fourier series, Fourier transforms (demonstrates everything you can think of
!!!!!!)
http://www.jhu.edu/~signals/index.html
Convolution
(demonstrates the effect of convolving different signal pulses)
http://www.jhu.edu/~signals/convolve/index.html
Fourier Transforms
(shows the transform of a large number of sample pulses and repeat patterns)
http://www.jhu.edu/~signals/ctftprops/indexCTFTprops.htm
You have the best
Fourier transform devices already attached to your heads. Use them to pick out
the tracks from these mashed songs
Cat-napped (Join
the elite team of CSI Sheffield. Filter through the background noise in Jasons
message using Fast Fourier Transform to find evidence of the cat)
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Partial
Differential Equations
Our experiment (The
plot and figures collected during our lecture demonstration showing Diffusion
equation related to cooling of a bar)
Solution to the wave
equation along a 1D string (Applets allows you to chose the starting conditions
and then shows evolution of wave motion)
http://www.falstad.com/loadedstring/
Solution to the wave
equation in a 2D environment (Interactive Applet allows you to select the
boundary conditions, and quantum numbers of waves on a 2D surface)
http://www.falstad.com/membrane/
Solution to the wave
equation in a 3D box (Interactive Applet allows you to select the boundary
conditions, and quantum numbers of waves)
http://www.falstad.com/wavebox/
also see www.falstad.com/mathphysics.html
Solution to the
Schroedinger Equation in a (in)finite potential well
(Applet allows you
to select multiple energy states and plots wave function solution)
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Spherical
Harmonics
High order spherical
harmonics (pretty patterns of high order spherical harmonics)
http://www.lifesmith.com/spharmin.html
Movie of Spherical
Harmonic describing bouncing of water droplet on ground
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