Math 210, Spring 2013 Lab #4 Solutions LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic= Q#1 Specify the function as an expression, proceed... 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OK, I hadn't realized this wouldn't show much. Let's look at it with y cropped a bit. 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Q#2 straightforward use of the sum, eval and limit commands QyQ+SSNTbkc2Ii1JJHN1bUdGJTYkLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJCokSSJpR0YlIiIjISIiL0YxOyIiIUkibkdGJSIiIg== LUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtSSRleHBHRiQ2IywkKiRJImlHRiciIiMhIiIvRi47IiIhSSJuR0Yn QyQtSSZldmFsZkclKnByb3RlY3RlZEc2Iy1JJWV2YWxHRiU2JEkjU25HNiIvSSJuR0YrIiImIiIi JCIrLic9alEiISIq LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMtSSZsaW1pdEc2IjYkSSNTbkdGKC9JIm5HRihJKWluZmluaXR5R0Yk JCIrLSc9alEiISIq Notice that something is slightly fishy above in the last digit... but this is what Maple returns Q#3 Enter the RHS function and determine the Euler iterative map QyQ+SSJmRzYiZio2I0kidUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJDkkIiIlISIiIiIiRjFGJUYlRiVGMQ== Zio2I0kidUc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJDkkIiIlISIiIiIiRi5GJUYlRiU= QyY+SSJORzYiIiNdIiIiPkkia0dGJSNGJyIjREYn IiNd IyIiIiIjRA== 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Q#4 Enter f QyQ+SSJmRzYiZio2I0kidUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiM5JEYlRiVGJSIiIg== Zio2I0kidUc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiM5JEYlRiVGJQ== Write the commands in one line so it is easier to cut and paste for other N Qy4+SSJORzYiIiM1IiIiPkkia0dGJS1JJmV2YWxmRyUqcHJvdGVjdGVkRzYjKiRGJCEiIkYnPkkkZXVtR0YlZio2I0kidUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUYrNiMsJjkkRicqJkYpRictSSJmR0YlNiNGO0YnRidGJUYlRiVGJz5GNEYnRic/KEkiakdGJUYnRidGJEkldHJ1ZUdGLD5GNC1GMUYzRi9GNEYn IiM1 JCIrKysrKzUhIzU= Zio2I0kidUc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMsJjkkIiIiKiZJImtHRiVGLy1JImZHRiU2I0YuRi9GL0YlRiVGJQ== IiIi JCIiIkkpaW5maW5pdHlHJSpwcm90ZWN0ZWRH Already for N=10 we have exceeded the size of allowable floating point numbers. We studied this problem analytically and found that the solution did not exist at time 1 (there was a singularity between t=0 and t=1) so we can't expect Euler's method to converge to a solution that does not exist.