| Title | Summary |
|---|---|
| Explicit and Implicit Solutions via Matlab | Professor Lipsman (video) shows how to use the Matlab command
dsolve to generate explicit or implicit solutions
of first-order equations. Errata: Despite the verbal assertion to the contrary, on the first line of the second screen, there is a missing right parenthesis. |
| Plots via Matlab | Professor Lipsman (video) shows how to use the Matlab commands
ezplot and plot to generate plots of
solutions to first-order equations. Errata: At one point in the video, Prof L incorrectly writes Math notation rather than MATLAB input; in particular, he writes: "x cubed minus three x squared plus 2x", when it should be "x^3 - 3*x^2 + 2*x". Finally, ezplot does not graph by default on the interval [-6,6], but actually on [-2pi, 2pi]. |
| Contour Plots via Matlab | Professor Lipsman (video) shows how to use the Matlab commands ezcontour and contour to generate contour plots of implicit solutions to first-order equations. |
| Direction Fields via Matlab | Professor Lipsman (video) shows how to use the Matlab command quiver to generate direction fields for first-order equations. |
| Phase-Line Protraits | Professor Lipsman (video) shows the relationship between the
direction field and the phase-line portrait of an
autonomous equation. Errata: In the first screen G'(y) is 1/f(y), not f(y). |
| Stability of Initial-Value Problems | Matlab m-file presentation prepared by Professor Lipsman that illustrates the stability of solutions to first-order initial-value problems. Download this m-file and run it with Matlab. |
| Stability of Initial-Value Problems | A published (pdf) file prepared from the above m-file. |