In many of the following problems, it will be essential to have a calculator or comp...

In many of the following problems, it will be essential to have a calculator or computer available. You may use a software package† or write a program for solving initial value problems using the improved Euler’s method algorithms on pages 127 and 128. (Remember, all trigonometric calculations are done in radians.)

Building Temperature. In Section 3.3 we modeled the temperature inside a building by the initial value problem

where M is the temperature outside the building, T is the temperature inside the building, H is the additional heating rate, U is the furnace heating or air conditioner cooling rate, K is a positive constant, and T0 is the initial temperature at time t0. In a typical model t0 = 0 (midnight) T0 = 65ºF H(t) =

The constant K is usually between ¼ and ½ , depending on such things as insulation. To study the effect of insulating this building, consider the typical building described above and use the improved Euler’s method subroutine with h = 2/3 to approximate the solution to (13) on the interval (1 day) for K = 0.2, 0.4, and 0.6.