Math Methods 2

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W X O H A J C P X K Y I B D T Q V U J G C
N I I G O R H D K G M G P V K D B A Q P R
X N G T B J G S S S G P F Y A U B X O H J
Y M O D E U Y I Y T G I W D P D D A F V M
G Y E E K M S N B Q Y X E W K T T T U M C
I X T L P A I V F G L X G N B L F L F P B
B V P S F M M A C U I T O V F A P E O M X
D Y F Q V P N X G F A W L K S P C D N V K
K X A P M I H B R X W X O R Q L X F A I Q
S N P G F Q N O C F O O R X L A U N I E P
Y Y J F N A F Y D U F K V K O C X A C X J
U X R S X A C E U C E J T L K I Y I A U H
F G S R X H S I H U Y E L L B A F C L O K
R A H N W C W M V X F J D T N N W A P A K
E I X N J K U K N E C E F A Y U A L A Q B
V A X J J I K M S B S D X F R A X P L Y N
N O U J D F D Z X U X C C O N S T A N T J
B A D S C G W P G O U W I S M L P L H N E
M I S P J A V L J Q S C P N G O V D M K X
F U X I C A K T P A G W X X R O T R A H C
W S A E V L W K P N D B W V L K X I H U P

Clues

  • If F(x,y,z)=F(x,z) what is the EL equation? (8, 8)
  • State the alternative vanishing lemma (3)
  • State the Mean value property for harmonic functions (3)
  • What is a Green's function for the Dirichlet problem? (5, 4)
  • What is Poisson's equation? (9, 2, 1, 1)
  • What is the fundamental solution of Laplace's equation? (9, 1, 6, 1)
  • What is the Heat equation? (13, 1)
  • What is the shifted Newtonian potential? (5, 1, 3, 5, 1)
  • What is the solution of the Dirichlet problem? (3)
  • What is the solution to the Cauchy problem? (3)

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