answer key involves matlab:

43. Many applications require us to know the temperature distribution in an object. For example, this information is important for controlling the material properties, such as hardness, when cooling an object formed from molten metal. In a heat-transfer course, the following description of the temperature distribution in a flat, rectangular metal plate is often derived. The temperature is held constant at T1 on three sides and at T2 on the fourth side (see ! Figure P43 ). The temperature T(x,y ) as a function of the xy coordinates shown is given by T(x,y)=(T2T1)w(x,y)+T1 where w(x,y)=2noddn2sin(Lnx)sinh(nW/L)sinh(ny/L) Use the following data: T1=70F,T2=200F, and W=L=2ft. a. The terms in the preceding series become smaller in magnitude as n increases. Write a MATLAB program to verify this fact for n=1,,19 for the center of the plate (x=y=1). 4.43. (a) We do not include the term 2 because it appears in every term, and thus does not affect the relative magnitudes of the terms. Set x=y=1 and W=L=2 in the series. The script file is n=[1,3,5,7,9,11,13,15,17,19]; term = abs ((2,)sin(npi/2)(sinh(npi/2)/sinh(npi))); format short disp (term' /term(1)) The results showing the ratios of the magnitudes of each term relative to that of the first term are 1.0000e+000 1.5026e002 3.8963e004 1.2027e005 4.0423e007 1.4292e008 5.2260e010 1.9573e011 7.4630e013 2.8856e014 Thus the magnitude of the second term is 1.5026102 times smaller than the first term, and so on