# Math 216 Pencasts

The main course information for this course is available through the main 216 website.

## Pencasts

These are in beta-testing: they are a bit rough around the edges at present, 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.

• [sec4.2] The Method of Elimination: [video]

• [sec5.1] Linear independence of vector functions: Discusses linear independence and using the Wronskian to demonstrate linear independence. [video]

• [sec5.2] Eigenvalues and eigenvectors: Discusses the linear algebra behind eigenvalues and eigenvectors, and how and why we find eigenvalues for a matrix. [video]

• [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]

• [sec5.2] Eigenvalues and eigenvectors and solving differential equations: Uses the discussion of eigenvalues and eigenvectors to solve a system of differential equations [video]

• [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]

• [sec6.1] Finding critical points for a nonlinear system. [video]

• [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]

• [sec6.2] Linear analysis near the critical point (7,0) for this system. [video]

• [sec6.2] Linear analysis near the critical points (0,1) and (1,3) for this system. [video]

• [sec6.2] Sketch of the phase portrait for the nonlinear system, given the linear analyses from above. [video]

• [sec7.2] Solution to a differential equation using Laplace transforms. [video]

• [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]

Math 216/pencasts