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Abelian integrals by George Kempf

By George Kempf

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The fact that different solids expand at different rates makes some interesting engineering problems in structures built from different materials. The first question is: What does the 'coefficient of expansion' mean? The units are actually (units of length expansion) per (units of length to start) per (units of temperature). The length units cancel. 0307 in This isn't very much, but how much would a house expand in volume? 35 Let's say the interior of the house is a rectangular solid 40 feet long, 30 feet wide, and 8 feet high.

Show that the derivative of g[t] is: dg d(asi — bi dt d{(s-±)i) = adt It ~ J — si = a"i \ \ s This equation is hard to analyze, but we can use the invariant from Chapter 2, s -\-i c a constant Log[si = k1 with the computer to find the crossing points of the curves s _|_ i 1 Log[s] = k c & s2 - si 2 1 s + ~z ^ = 0 c c or crossing points of the curves 5+ i Logfs] = k & c s—i= c Discuss various cases of the value of c and the initial values of s and i. 7: Intersection of the Critical Equation and Invariant We can also modify the SIRsolver program to plot the expressions for f'\t) and g'[t] in various special cases.

We use a potential outbreak of strep throat on campus as a test case for our model. 1. Basic Assumptions We will make the following basic assumptions: (1) SIS: Individuals all fit into one of the following two categories: : Susceptible: those who can catch the disease : Infected: those who can spread the disease *Note: There are no removeds who are immune and cannot spread the disease. (2) The population is large but fixed in size and confined to a well-defined region. We imagine the population to be in a large public university during the semester when relatively little outside travel takes place.

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