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.