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README.md

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-# 07_final_project
+# 07_final_project
+
+### Part A
+``` matlab
+function [w] = membrane_solution3(T,P) % Set up initial matrix
+    % T = given tension (microNewton/micrometer)
+    % P = given pressure (MPa)
+
+    od = ones(8,1);
+    od(3:3:end) = 0;
+    k = -4*diag(ones(9,1))+diag(ones(9-3,1),3)+diag(ones(9-3,1),-3)+diag(od,1)+diag(od,-1);
+
+    % Solve for unknown matrix, w
+    y = -(10/4)^2*(P/T)*ones(9,1); %output vector
+    w = k\y; %solves for w in microm
+
+    [x,y] = meshgrid(0:10/4:10,0:10/4:10);
+    z = zeros(size(x));
+    z(2:end-1,2:end-1) = reshape(w,[3 3]);
+    surf(x,y,z)
+end
+```
+
+### Part B
+``` matlab
+[w] = membrane_solution3(0.006,0.001);
+```
+
+![3x3 Interior Nodes](./figures/figure1.png)
+
+### Part C
+```matlab
+function [w] = membrane_solution(T,P,n)% Set up initial matrix
+    % T = given tension (microNewton/micrometer)
+    % P = given pressure (MPa)
+    % n = number of interior nodes
+
+    od = ones(n^2-1,1);
+    od(n:n:end) = 0;
+    k = -4*diag(ones(n^2,1))+diag(ones((n^2)-n,1),n)+diag(ones((n^2)-n,1),-n)+diag(od,1)+diag(od,-1);
+
+    % Solve for unknown matrix, w
+    y = -(10/(n+1))^2*(P/T)*ones(n^2,1); %output vector
+    w = k\y; %solves for w in microm
+
+    [x,y] = meshgrid(0:10/(n+1):10,0:10/(n+1):10);
+    z = zeros(size(x));
+    z(2:end-1,2:end-1) = reshape(w,[n n]);
+    surf(x,y,z)
+end
+```
+
+### Part D
+``` matlab
+[w] = membrane_solution(0.006,0.001,10)
+```
+
+![nxn Interior Nodes, n = 10](./figures/figure2.png)