Find the general solution u(t, z) of the heat equation aurkau, , u(t,0)

= 0,

u(t, L) =

0,

where kand L are positive constants. Do not just state theorems from the lectures: you must show all your work in here.

clock

step-by-step explanation:

8 2/3 is the answer

step-by-step explanation: just use a calculator

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

the 3rd on is correct

step-by-step explanation: