You are looking for a bounded solution that oscillates in time, so set the above constant to be pure imaginary. Show that if A = iw, where w > 0, then T(t) = Coeiut and X(x) = C1e(1+i)= + C»e¯X1+i)¤ for some real number y > 0. What is y? Hint: you will need to calculate Viw/k. Refer to Section 17.2 of the textbook if you have forgotten how to find roots of complex numbers
You are looking for a bounded solution that oscillates in time, so set the above constant to be pure imaginary. Show that if A = iw, where w > 0, then T(t) = Coeiut and X(x) = C1e(1+i)= + C»e¯X1+i)¤ for some real number y > 0. What is y? Hint: you will need to calculate Viw/k. Refer to Section 17.2 of the textbook if you have forgotten how to find roots of complex numbers
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?
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Use separation of variables. Let u(x,t)=X(x)T(t) and show that kX′′(x)/X(x)=T′(t)/T(t)=λ, where λ is a constant.
Transcribed Image Text:You are looking for a bounded solution that oscillates in time, so set the above constant to be pure imaginary. Show that if A = iw, where
w > 0, then
T(t)
Coetut
and
X(x)
Cje^L+i)» + Cze¯
-(1+i)x
=
for some real number y > 0. What is y?
Hint: you will need to calculate Viw/k. Refer to Section 17.2 of the textbook if you have forgotten how to find roots of complex
numbers.
Transcribed Image Text:u(x, t) = X(x)T(t) = C3eiuste (1+i)x
The above solution is complex, but temperature is a real number. Find the real part of u(x, t) and verify that it also satisfies the heat
equation.
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