Assignment:
I hope you and your family are well.
I am currently taking a course in PDE's and would like a few things explained if possible.
• Consider a bar insulated on both sides with the ends held at some constant temperature (other than 0) my analysis gives, that as times goes to infinity, the temperature goes to 0 which is definitely not accurate and I don't know where my mistake is.
• How do I solve the same problem when the ends are at different temperatures?
• How do I solve the same problem if the ends are insulated?
Please show the analysis for each situation....I am using separation of variables and Fourier Series as the method of solution.