Samp;Z Ch 4 Difference EquationsS amp；Z CH 4的差分方程.docxVIP

IdeasDo this chapter in conjunction with system dynamics models? Two sessions. Then do Schelling with exercises?AssignmentRead chapter. Write up responses to example problems on page 49.Rhetorical TasksSimple examples.NotationThe MathEquilibriumStocks and FlowsConcepts and VocabularyNotation, subscripts, equilibrium, period, stable/unstable, first order/second order, etc., nonlinear, iteration, rule of 72, limit as n goes to infinity, 45 degree line, critical mass, LectureConsider the following sequence of numbers1 1 2 3 5 8 …Three dots = ellipsis = and so onLets refer to each of these as an sequence member.And so lets call the first one sequence member 1 and so onSequence Member 11Sequence Member 21Sequence Member 32But I tire of writing out sequence member so Im going to abbreviate it ss43s55s68But now I want to offer some typographical signal that the s is an abbreviation and the digit is a part of a numbering system. And so I write the digits as a subscript.s713s821s934Obviously, the index can be any number, but I dont want to have to write out millions of terms of the sequence. So, by convention, I write the subscript generically as I: , i = 1,2,3,…We will frequently use I in this style to stand for any old element of the sequence while we use the subscript n to refer to a particular element.In particular, if I wanted to say that one element was equal to the one before it times 2, I could writeLets talk about your bank account. Suppose you are getting 2% interest each year. Lets say your initial deposit is p0 (p stands for principal). How much will we have in the bank after the first year?orand=Examples4.1A totalitarian country that prohibits migration has a birth rate b and a death rate d. How does the population change from one year to the next?Let Pi be the population in year i. Then4.2There are no births in a Shaker community, only R recruits per year. The death rate is d. What is the difference equation that describes this situation?Let Pi be the