**Notes/Resources**
- Pre-requisite quiz Some of this might be used in the first discussion. It will
*not* be collected and *will not be graded!* If you can't solve the questions, or don't understand what's being asked,
it is *your* responsibility to refresh your memory and ask for help. In particular you *must* know
how to work with matrices before we get to chapter 3!
- Slope Fields
- Existence/Uniqueness
- General/singular solutions example (pdf)
- The Reservoir Problem (pdf)
- Population models (mostly for interest + beyond the scope of the class - know the logistic equation and basic birth/death rate concepts)
- Mechanical Vibrations Summary: do questions open-book. To get the (not very exciting) animations to work, download to your desktop and open in Adobe Reader --- other pdf viewers might not animate.
- Non-homogeneous equation with repeated roots
- Damped Vibrations Summary: also open-book
- The Brine Tanks problem
- Linear Systems and their vector fields
- Non-linear Systems some overlap with section 8 in the text
- Predator-Prey Models Only the first two pages are examinable, but you might need the rest to answer all the homework questions...
- Chaos in non-linear systems. Entirely non-examinable and just for fun but leads to lots of new ideas...
- Translation in Laplace transforms: a step-function force applied to a spring.
- Convolution: solving a problem using Laplace transforms versus an elementary method.