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CYBR 150
∂2u /∂x2+∂2u /∂y2 = 0
u(x, y) =Aπ ∞X n=01B eC D
Analyse all three cases of a separation constants (λ <, =, > 0). Coeffiffifficients A, B, C and D (D is a trigonometric expression) have to be calculated and highlighted in your assignment. Full marks are awarded for a complete step by step proof.
iii. Take T the temperature from part a) to be equal to the last two fifigures of your student Monash ID number (if ID XXXXXX31, take T=31; ID XXXXXX09, take T=9; ID XXXXX1100, take T=10).
And take a = 1. In MATLAB, on the same graph plot the partial sum up to the 50th harmonic of u(x, y) for 10 relevant values y = 0, 0.01, 0.02, …… and continuing with any y of your own choice.
Label and ADD a legend to the graph and publish the graph of your solution, and attach it to the assignment.
iii. For what value y does the temperature drop to 10% of the initial temperature for 0 < x < a?
TOTAL=4+18+10+1+2[neat]=35 marks