The main course information for this course is available through
Canvas, with some residual
information on the public-facing
main 216 website.
Pencasts
These are a bit rough around the edges,
but are provided in case they are useful. If you have questions,
please let us (in particular, Gavin LaRose:
<glarose(at)umich(dot)edu>) know.
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[sec5.1] Linear independence of vector functions:
Discusses linear independence and using the Wronskian to
demonstrate linear independence.
[video]
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[sec5.2] Eigenvalues and eigenvectors:
Discusses the linear algebra behind eigenvalues and eigenvectors,
and how and why we find eigenvalues for a matrix.
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[sec5.2] Eigenvalues and eigenvectors:
Given the discussion of eigenvalues, looks at eigenvectors and how
and why we find them for a given matrix.
[video]
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[sec5.2] Eigenvalues and eigenvectors and solving differential
equations:
Uses the discussion of eigenvalues and eigenvectors to solve a
system of differential equations
[video]
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[sec5.2] Solving a 3x3 system. This has both a real and a complex
conjugate pair of eigenvalues. It's also over 6 minutes; sorry.
Also note that when solving for v for the eigenvalue
-1+i there is a typo in the matrix
A-lambda I: the first entry in the second row
should be 1, not -1.
[video]
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[sec6.1] Finding critical points for a nonlinear system.
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[sec6.2] Linear analysis near the critical point (0,0) for this
system. (Note that at the end of this video, I say something like
"trajectories become parallel to the (0,1) direction," when I
should say "(1,0).")
[video]
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[sec6.2] Linear analysis near the critical point (7,0) for this
system.
[video]
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[sec6.2] Linear analysis near the critical points (0,1) and (1,3)
for this system.
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[sec6.2] Sketch of the phase portrait for the nonlinear system,
given the linear analyses from above.
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[sec7.2] Solution to a differential equation using Laplace
transforms.
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[sec7.6] Another solution to an initial value problem using Laplace
transforms. This is more involved, and includes a delta function.
Also a long video (9+ minutes). Get a cup of coffee before hitting
play. Note: there is a sign error in this when the term
-4s-25 is moved to the right-hand-side of the equation; it
should be 4s+25, instead of 4s-25.
[video]
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