@@uclamodelingclass3003 I was a Physics student in university and haven't got back to it in years. I didn't think I could understand this video but after I finished I realized I wish I had professor, teachers, mentors like you back in the day! Because you explained complicated subject so understandable that amazed me. So much respect❤
May I pose a question? From a units perspective, when we look at the rate of change in worm population, the units should be population/time. It appears that the parameter r has units = 1/t but the negative term has no units. Should the negative term also have some rate constant with units 1/t in order that those two terms may be added together?
Jack, good question. The whole issue of units in differential equations is very important, and very poorly understood. (See David Rowland's paper "Student difficulties with units in differential equations in modelling contexts". It's excellent). So yes, the units must always work out! We must always subtract oranges from oranges. So the first question is what are the units of X? Is it "animals", or is it "animal fraction". Then the units of X' are the units of X divided by time. Now, for the right hand side, both of those terms have to be in the same units as X'. The way this is set up, it's really fractions, so X is dimensionless, r = 1/time, and the predation term has a multiplicative parameter 1, whose units are 1/time. Hope this helps Alan
I cannot express how much I enjoyed watching this simply and deeply explained modeling of this outbreak system professor.
thank you so-o much!!
Thanks so much 😊
@@uclamodelingclass3003 I was a Physics student in university and haven't got back to it in years. I didn't think I could understand this video but after I finished I realized I wish I had professor, teachers, mentors like you back in the day! Because you explained complicated subject so understandable that amazed me. So much respect❤
Thank you for explaining this! I was confused about this in Strogatz book, enjoyed the explanation of the hysteresis
Thank you so much! Your wonderful explanation made my concepts clear.
thank you!
Thank you so much for this video!
Amazing explainaition , thank you so much sir!
May I pose a question? From a units perspective, when we look at the rate of change in worm population, the units should be population/time. It appears that the parameter r has units = 1/t but the negative term has no units. Should the negative term also have some rate constant with units 1/t in order that those two terms may be added together?
Jack, good question. The whole issue of units in differential equations is very important, and very poorly understood. (See David Rowland's paper "Student difficulties with units in differential equations in modelling contexts". It's excellent). So yes, the units must always work out! We must always subtract oranges from oranges. So the first question is what are the units of X? Is it "animals", or is it "animal fraction". Then the units of X' are the units of X divided by time. Now, for the right hand side, both of those terms have to be in the same units as X'. The way this is set up, it's really fractions, so X is dimensionless, r = 1/time, and the predation term has a multiplicative parameter 1, whose units are 1/time.
Hope this helps
Alan
That was very helpful! Thank you for your time, Alan!