{"id":5634,"date":"2025-05-21T20:21:31","date_gmt":"2025-05-21T16:51:31","guid":{"rendered":"https:\/\/projestaan.com\/mag\/?p=5634"},"modified":"2025-06-30T18:19:24","modified_gmt":"2025-06-30T14:49:24","slug":"matlab-application-civil-engineering","status":"publish","type":"post","link":"https:\/\/projestaan.com\/mag\/matlab-application-civil-engineering\/","title":{"rendered":"\u06a9\u0627\u0631\u0628\u0631\u062f \u0646\u0631\u0645\u200c\u0627\u0641\u0632\u0627\u0631 \u0645\u062a\u0644\u0628 \u062f\u0631 \u0645\u0647\u0646\u062f\u0633\u06cc \u0639\u0645\u0631\u0627\u0646 | \u0647\u0645\u0631\u0627\u0647 \u0628\u0627 6 \u0645\u062b\u0627\u0644"},"content":{"rendered":"\t\t
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\u0645\u062a\u0644\u0628 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0632\u0628\u0627\u0646 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u0633\u0637\u062d \u0628\u0627\u0644\u0627 \u0648 \u0645\u062d\u06cc\u0637 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0639\u062f\u062f\u06cc\u060c \u0627\u0628\u0632\u0627\u0631\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0645\u0641\u06cc\u062f \u0628\u0631\u0627\u06cc \u0645\u0647\u0646\u062f\u0633\u0627\u0646 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0646\u0631\u0645\u200c\u0627\u0641\u0632\u0627\u0631 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0642\u062f\u0631\u062a \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0628\u0627\u0644\u0627\u060c \u0642\u0627\u0628\u0644\u06cc\u062a \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647\u060c \u0648 \u062a\u0648\u0627\u0646\u0627\u06cc\u06cc \u0634\u0628\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u0633\u0627\u0626\u0644 \u0645\u0647\u0646\u062f\u0633\u06cc\u060c \u0628\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc \u0636\u0631\u0648\u0631\u06cc \u062f\u0631 \u0645\u0647\u0646\u062f\u0633\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a \u00a0\u06a9\u0647 \u062f\u0631 \u0631\u0634\u062a\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0645\u0647\u0646\u062f\u0633\u06cc\u060c \u0627\u0632 \u062c\u0645\u0644\u0647 \u0645\u0647\u0646\u062f\u0633\u06cc \u0639\u0645\u0631\u0627\u0646\u060c \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u06af\u0633\u062a\u0631\u062f\u0647\u200c\u0627\u06cc \u062f\u0627\u0631\u062f. \u0627\u0632 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u0645\u062a\u0644\u0628 \u062f\u0631 \u0631\u0634\u062a\u0647 \u0645\u0647\u0646\u062f\u0633\u06cc \u0639\u0645\u0631\u0627\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u062a\u062d\u0644\u06cc\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u0642\u0627\u0628\u200c\u0647\u0627\u06cc \u0633\u0627\u0632\u0647\u200c\u0627\u06cc (Frame Analysis) \u0627\u0634\u0627\u0631\u0647 \u06a9\u0631\u062f \u06a9\u0647 \u0627\u0632 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062a\u062f\u0627\u0648\u0644 \u062f\u0631 \u0645\u0647\u0646\u062f\u0633\u06cc \u0633\u0627\u0632\u0647 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u062a\u062d\u0644\u06cc\u0644 \u0646\u06cc\u0631\u0648\u0647\u0627\u06cc \u062f\u0627\u062e\u0644\u06cc \u0648 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06a9\u0627\u0646\u200c\u0647\u0627 \u062f\u0631 \u0642\u0627\u0628\u200c\u0647\u0627\u06cc \u062f\u0648\u0628\u0639\u062f\u06cc \u0648 \u0633\u0647\u200c\u0628\u0639\u062f\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u062a\u062d\u0644\u06cc\u0644 \u062a\u06cc\u0631\u0647\u0627\u06cc \u062a\u062d\u062a \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc (Beam Analysis) \u0646\u06cc\u0632 \u062f\u0631 \u0645\u0647\u0646\u062f\u0633\u06cc \u0639\u0645\u0631\u0627\u0646\u060c \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0645\u0647\u0645\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062a\u062d\u0644\u06cc\u0644 \u0631\u0641\u062a\u0627\u0631 \u062a\u06cc\u0631\u0647\u0627\u06cc \u0633\u0627\u062f\u0647 \u06cc\u0627 \u0645\u0631\u06a9\u0628 \u062a\u062d\u062a \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0642\u0627\u0628\u0644\u06cc\u062a \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u062f\u0631 \u0645\u062a\u0644\u0628 \u062f\u0627\u0631\u062f. \u0634\u0628\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u062c\u0631\u06cc\u0627\u0646 \u0622\u0628 \u062f\u0631 \u06a9\u0627\u0646\u0627\u0644 \u0628\u0627\u0632 (Open Channel Flow) \u0646\u06cc\u0632 \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0645\u0647\u0645 \u062f\u0631 \u0645\u0647\u0646\u062f\u0633\u06cc \u0647\u06cc\u062f\u0631\u0648\u0644\u06cc\u06a9 \u0648 \u0645\u0647\u0646\u062f\u0633\u06cc \u0639\u0645\u0631\u0627\u0646 \u0627\u0633\u062a. \u062a\u062d\u0644\u06cc\u0644 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0634\u06cc\u0628\u200c\u0647\u0627 (Slope Stability Analysis) \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0645\u0647\u0646\u062f\u0633\u06cc \u0698\u0626\u0648\u062a\u06a9\u0646\u06cc\u06a9 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0645\u0646\u0638\u0648\u0631 \u062c\u0644\u0648\u06af\u06cc\u0631\u06cc \u0627\u0632 \u0644\u063a\u0632\u0634 \u0632\u0645\u06cc\u0646 \u06cc\u0627 \u0645\u0635\u0627\u0644\u062d \u0633\u0627\u062e\u062a\u0645\u0627\u0646\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0637\u0631\u0627\u062d\u06cc \u062f\u0627\u0644 \u0628\u062a\u0648\u0646\u06cc \u062a\u062d\u062a \u0628\u0627\u0631 \u0645\u062a\u0645\u0631\u06a9\u0632 \u0648 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u062f\u0631 \u0645\u0647\u0646\u062f\u0633\u06cc \u0633\u0627\u0632\u0647\u060c \u0646\u06cc\u0632 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u062f\u0631 \u0646\u0631\u0645 \u0627\u0641\u0632\u0627\u0631 \u0645\u062a\u0644\u0628 \u0634\u0628\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u0634\u0648\u062f. \u062a\u062d\u0644\u06cc\u0644 \u062a\u0646\u0634 \u0648 \u06a9\u0631\u0646\u0634 \u062f\u0631 \u0633\u062a\u0648\u0646 \u0628\u062a\u0648\u0646\u06cc\u060c \u0645\u062d\u0627\u0633\u0628\u0647 \u0639\u0645\u0642 \u0628\u062d\u0631\u0627\u0646\u06cc \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0633\u0631\u0631\u06cc\u0632\u060c \u0634\u0628\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u062f\u0631 \u062f\u06cc\u0648\u0627\u0631\u0647\u0627\u06cc \u0633\u0627\u062e\u062a\u0645\u0627\u0646\u06cc\u060c \u062a\u062d\u0644\u06cc\u0644 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06a9\u0627\u0646 \u067e\u0644 \u062a\u062d\u062a \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc \u062a\u0631\u0627\u0641\u06cc\u06a9\u06cc \u0648 \u0637\u0631\u0627\u062d\u06cc \u0633\u06cc\u0633\u062a\u0645 \u0632\u0647\u06a9\u0634\u06cc \u0628\u0631\u0627\u06cc \u0633\u0627\u0632\u0647\u200c\u0647\u0627\u06cc \u0647\u06cc\u062f\u0631\u0648\u0644\u06cc\u06a9\u06cc \u0646\u06cc\u0632 \u0642\u0627\u0628\u0644\u06cc\u062a \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u062f\u0631 \u0646\u0631\u0645 \u0627\u0641\u0632\u0627\u0631 \u0645\u062a\u0644\u0628 \u062f\u0627\u0631\u0646\u062f.<\/span><\/p>

\u0647\u0645\u0686\u0646\u06cc\u0646 \u062a\u062d\u0644\u06cc\u0644 \u0646\u0641\u0648\u0630 \u0622\u0628 \u062f\u0631 \u062e\u0627\u06a9 (Seepage Analysis in Soil) \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644 \u0645\u0647\u0645 \u062f\u0631 \u0645\u0647\u0646\u062f\u0633\u06cc \u0698\u0626\u0648\u062a\u06a9\u0646\u06cc\u06a9 \u0648 \u0645\u062d\u06cc\u0637\u200c\u0632\u06cc\u0633\u062a \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u0628\u0647 \u0628\u0631\u0631\u0633\u06cc \u062c\u0631\u06cc\u0627\u0646 \u0622\u0628 \u062f\u0631 \u062e\u0627\u06a9 \u0648 \u062a\u0623\u062b\u06cc\u0631 \u0622\u0646 \u0628\u0631 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0633\u0627\u0632\u0647\u200c\u0647\u0627\u060c \u062a\u062d\u0644\u06cc\u0644 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0634\u06cc\u0628\u200c\u0647\u0627\u060c \u0648 \u0637\u0631\u0627\u062d\u06cc \u0633\u0627\u0632\u0647\u200c\u0647\u0627\u06cc \u0647\u06cc\u062f\u0631\u0648\u0644\u06cc\u06a9\u06cc \u0645\u0631\u0628\u0648\u0637 \u0645\u06cc\u200c\u0634\u0648\u062f. \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u062f\u0644\u200c\u0647\u0627\u06cc \u067e\u0627\u06cc\u0647 \u0628\u0631\u0627\u06cc \u062a\u062d\u0644\u06cc\u0644 \u0646\u0641\u0648\u0630 \u0622\u0628\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0627\u0631\u0633\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u06cc\u0627\u0646 \u0645\u06cc\u200c\u06a9\u0646\u062f \u062c\u0631\u06cc\u0627\u0646 \u0622\u0628 \u062f\u0631 \u062e\u0627\u06a9 \u0645\u062a\u0646\u0627\u0633\u0628 \u0628\u0627 \u06af\u0631\u0627\u062f\u06cc\u0627\u0646 \u0647\u06cc\u062f\u0631\u0648\u0644\u06cc\u06a9\u06cc \u0648 \u0646\u0641\u0648\u0630\u067e\u0630\u06cc\u0631\u06cc \u062e\u0627\u06a9 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0646\u0631\u0645\u200c\u0627\u0641\u0632\u0627\u0631 \u0645\u062a\u0644\u0628 \u0634\u0628\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>

\u0645\u0648\u0633\u0633\u0647 \u067e\u0631\u0648\u0698\u0633\u062a\u0627\u0646 \u0622\u0645\u0627\u062f\u0647 \u062e\u062f\u0645\u0627\u062a \u0631\u0633\u0627\u0646\u06cc \u0628\u0647 \u062f\u0627\u0646\u0634\u062c\u0648\u06cc\u0627\u0646 \u0639\u0632\u06cc\u0632 \u0631\u0634\u062a\u0647 \u0645\u0647\u0646\u062f\u0633\u06cc \u0639\u0645\u0631\u0627\u0646 \u062f\u0631 \u062a\u0645\u0627\u0645\u06cc \u0645\u0642\u0627\u0637\u0639 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u067e\u0631\u0648\u0698\u0647 \u0645\u062a\u0644\u0628<\/a> \u0645\u06cc \u0628\u0627\u0634\u062f.<\/span><\/p>

\u0645\u062b\u0627\u0644 1: \u062a\u062d\u0644\u06cc\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u0642\u0627\u0628\u200c\u0647\u0627 (Frame Analysis)<\/span><\/h2>

clc; clear;close all<\/span><\/p>

% \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0647\u200c\u0647\u0627 \u0648 \u0627\u0639\u0636\u0627\u06cc \u0642\u0627\u0628<\/span><\/p>

n_nodes = 3;<\/span><\/p>

n_elements = 2;<\/span><\/p>

% \u0645\u062e\u062a\u0635\u0627\u062a \u06af\u0631\u0647\u200c\u0647\u0627<\/span><\/p>

nodes = [0, 0; 3, 0; 6, 0];<\/span><\/p>

% \u0645\u0634\u062e\u0635\u0627\u062a \u0627\u0639\u0636\u0627 (\u0637\u0648\u0644\u060c \u0645\u062f\u0648\u0644 \u0627\u0644\u0627\u0633\u062a\u06cc\u0633\u06cc\u062a\u0647 \u0648 \u0633\u0637\u062d \u0645\u0642\u0637\u0639)<\/span><\/p>

E = 210e9;\u00a0 % \u0645\u062f\u0648\u0644 \u0627\u0644\u0627\u0633\u062a\u06cc\u0633\u06cc\u062a\u0647 (\u067e\u0627\u0633\u06a9\u0627\u0644)<\/span><\/p>

A = 0.02;\u00a0\u00a0 % \u0633\u0637\u062d \u0645\u0642\u0637\u0639 (\u0645\u062a\u0631 \u0645\u0631\u0628\u0639)<\/span><\/p>

% \u062a\u0639\u0631\u06cc\u0641 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u062e\u062a\u06cc<\/span><\/p>

K = zeros(2*n_nodes);<\/span><\/p>

% \u06a9\u062f \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u062e\u062a\u06cc \u0628\u0631\u0627\u06cc \u0647\u0631 \u0639\u0636\u0648<\/span><\/p>

for i = 1:n_elements<\/span><\/p>

\u00a0\u00a0\u00a0 % \u0645\u062d\u0627\u0633\u0628\u0647 \u0637\u0648\u0644 \u0639\u0636\u0648<\/span><\/p>

\u00a0\u00a0\u00a0 node1 = nodes(i, :);<\/span><\/p>

\u00a0\u00a0\u00a0 node2 = nodes(i+1, :);<\/span><\/p>

\u00a0\u00a0\u00a0 L = norm(node2 – node1);<\/span><\/p>

\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0% \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u062e\u062a\u06cc \u0639\u0636\u0648<\/span><\/p>

\u00a0\u00a0\u00a0 k = E*A\/L * [1 -1; -1 1];<\/span><\/p>

\u00a0\u00a0\u00a0<\/span><\/p>

\u00a0\u00a0\u00a0 % \u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f\u0646 \u0628\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u062e\u062a\u06cc \u06a9\u0644\u06cc<\/span><\/p>

\u00a0\u00a0\u00a0 K(i:i+1, i:i+1) = K(i:i+1, i:i+1) + k;<\/span><\/p>

end<\/span><\/p>

% \u0646\u0645\u0627\u06cc\u0634 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u062e\u062a\u06cc \u0646\u0647\u0627\u06cc\u06cc<\/span><\/p>

disp(K);<\/span><\/p>

\u062e\u0631\u0648\u062c\u06cc:<\/span><\/h2>

\u00a0\u00a0 1.0e+09 *<\/span><\/p>

\u00a0\u00a0\u00a0 1.4000\u00a0\u00a0 -1.4000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a00\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0<\/span><\/p>

\u00a0\u00a0 -1.4000\u00a0\u00a0\u00a0 2.8000\u00a0\u00a0 -1.4000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0<\/span><\/p>

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0 -1.4000\u00a0\u00a0\u00a0 1.4000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0<\/span><\/p>

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a00\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0<\/span><\/p>

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a00\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0<\/span><\/p>

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a00\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0<\/span><\/p>

\u062a\u0648\u0636\u06cc\u062d- \u0645\u0631\u062d\u0644\u0647 \u0628\u0646\u062f\u06cc \u06a9\u062f \u0628\u0647 \u0634\u0631\u062d \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/span><\/p>

  1. \u0627\u0628\u062a\u062f\u0627 \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0647\u200c\u0647\u0627 \u0648 \u0627\u0639\u0636\u0627 \u0645\u0634\u062e\u0635 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/li>
  2. \u0645\u062e\u062a\u0635\u0627\u062a \u06af\u0631\u0647\u200c\u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/li>
  3. \u0645\u062f\u0648\u0644 \u0627\u0644\u0627\u0633\u062a\u06cc\u0633\u06cc\u062a\u0647 (E) \u0648 \u0633\u0637\u062d \u0645\u0642\u0637\u0639 (A) \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/span><\/li>
  4. \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u062e\u062a\u06cc \u06a9\u0644 \u0642\u0627\u0628 \u0628\u0647 \u0635\u0648\u0631\u062a \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0635\u0641\u0631 \u0622\u063a\u0627\u0632 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/li>
  5. \u0637\u0648\u0644 \u0647\u0631 \u0639\u0636\u0648 \u0642\u0627\u0628 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0641\u0627\u0635\u0644\u0647 \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u06af\u0631\u0647\u200c\u0647\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0648 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u062e\u062a\u06cc \u0647\u0631 \u0639\u0636\u0648 \u062a\u0639\u06cc\u06cc\u0646 \u0648 \u0628\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u06a9\u0644\u06cc \u0627\u0636\u0627\u0641\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/li><\/ol>

    \u0645\u062b\u0627\u0644 2: \u062a\u062d\u0644\u06cc\u0644 \u062a\u06cc\u0631\u0647\u0627\u06cc \u062a\u062d\u062a \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc (Beam Analysis)<\/span><\/h2>

    clc; clear;close all<\/span><\/p>

    % \u0637\u0648\u0644 \u062a\u06cc\u0631 \u0648 \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc<\/span><\/p>

    L = 5;\u00a0 % \u0645\u062a\u0631<\/span><\/p>

    q = 10;\u00a0 % \u06a9\u06cc\u0644\u0648 \u0646\u06cc\u0648\u062a\u0648\u0646 \u0628\u0631 \u0645\u062a\u0631<\/span><\/p>

    % \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0631\u0634 \u0648 \u0644\u0646\u06af\u0631<\/span><\/p>

    x = linspace(0, L, 100);<\/span><\/p>

    V = q * (L – x);\u00a0 % \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0631\u0634<\/span><\/p>

    M = q * x .* (L – x) \/ 2;\u00a0 % \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0646\u06af\u0631<\/span><\/p>

    % \u0631\u0633\u0645 \u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u0631\u0634 \u0648 \u0644\u0646\u06af\u0631<\/span><\/p>

    figure;<\/span><\/p>

    subplot(2,1,1);<\/span><\/p>

    plot(x, V);<\/span><\/p>

    title(‘\u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u0631\u0634’);<\/span><\/p>

    xlabel(‘\u0645\u06a9\u0627\u0646 (\u0645\u062a\u0631)’);<\/span><\/p>

    ylabel(‘\u0646\u06cc\u0631\u0648 (\u06a9\u06cc\u0644\u0648 \u0646\u06cc\u0648\u062a\u0648\u0646)’);<\/span><\/p>

    subplot(2,1,2);<\/span><\/p>

    plot(x, M);<\/span><\/p>

    title(‘\u0646\u0645\u0648\u062f\u0627\u0631 \u0644\u0646\u06af\u0631’);<\/span><\/p>

    xlabel(‘\u0645\u06a9\u0627\u0646 (\u0645\u062a\u0631)’);<\/span><\/p>

    ylabel(‘\u0644\u0646\u06af\u0631 (\u06a9\u06cc\u0644\u0648 \u0646\u06cc\u0648\u062a\u0648\u0646-\u0645\u062a\u0631)’);<\/span><\/p>

    \u062e\u0631\u0648\u062c\u06cc:<\/span><\/h3>
    \"\u062a\u062d\u0644\u06cc\u0644
    \u0645\u062b\u0627\u0644 \u062a\u062d\u0644\u06cc\u0644 \u062a\u06cc\u0631\u0647\u0627\u06cc \u062a\u062d\u062a \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc<\/span><\/figcaption><\/figure>

    \u00a0\u00a0\u00a0 \u00a0<\/span>\u062a\u0648\u0636\u06cc\u062d:<\/span><\/p>

    1. \u0637\u0648\u0644 \u062a\u06cc\u0631 (L) \u0648 \u0645\u0642\u062f\u0627\u0631 \u0628\u0627\u0631\u06af\u0630\u0627\u0631\u06cc \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a (q) \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/span><\/li>
    2. \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0631\u0634 \u0648 \u0644\u0646\u06af\u0631 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0631\u0648\u0627\u0628\u0637 \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u062a\u06cc\u0631\u0647\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/span><\/li>
    3. \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062f\u0633\u062a\u0648\u0631plot \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0628\u0631\u0634 \u0648 \u0644\u0646\u06af\u0631 \u0631\u0633\u0645 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/span><\/li><\/ol>

      \u0645\u062b\u0627\u0644 3: \u0634\u0628\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u062c\u0631\u06cc\u0627\u0646 \u0622\u0628 \u062f\u0631 \u06a9\u0627\u0646\u0627\u0644 \u0628\u0627\u0632 (Open Channel Flow)<\/span><\/h2>

      clc; clear;close all<\/span><\/p>

      % \u0645\u0634\u062e\u0635\u0627\u062a \u06a9\u0627\u0646\u0627\u0644<\/span><\/p>

      b = 5;\u00a0 % \u0639\u0631\u0636 \u06a9\u0627\u0646\u0627\u0644 (\u0645\u062a\u0631)<\/span><\/p>

      h = 2;\u00a0 % \u0639\u0645\u0642 \u0622\u0628 (\u0645\u062a\u0631)<\/span><\/p>

      g = 9.81;\u00a0 % \u0634\u062a\u0627\u0628 \u06af\u0631\u0627\u0646\u0634 (\u0645\u062a\u0631 \u0628\u0631 \u062b\u0627\u0646\u06cc\u0647 \u0645\u0631\u0628\u0639)<\/span><\/p>

      % \u0645\u062d\u0627\u0633\u0628\u0647 \u0639\u062f\u062f \u0641\u0631\u0648\u062f<\/span><\/p>

      Fr = sqrt(g * h) \/ (h * b);<\/span><\/p>

      % \u0646\u0645\u0627\u06cc\u0634 \u0646\u062a\u06cc\u062c\u0647<\/span><\/p>

      if Fr < 1<\/span><\/p>

      \u00a0\u00a0\u00a0 disp(‘\u062c\u0631\u06cc\u0627\u0646 \u0632\u06cc\u0631 \u0628\u062d\u0631\u0627\u0646\u06cc \u0627\u0633\u062a.’);<\/span><\/p>

      else<\/span><\/p>

      \u00a0\u00a0\u00a0 disp(‘\u062c\u0631\u06cc\u0627\u0646 \u0641\u0648\u0642 \u0628\u062d\u0631\u0627\u0646\u06cc \u0627\u0633\u062a.’);<\/span><\/p>

      end<\/span><\/p>

      \u062e\u0631\u0648\u062c\u06cc:<\/span><\/h3>

      \u062c\u0631\u06cc\u0627\u0646 \u0632\u06cc\u0631 \u0628\u062d\u0631\u0627\u0646\u06cc \u0627\u0633\u062a.<\/span><\/p>

      \u062a\u0648\u0636\u06cc\u062d:<\/span><\/p>

      1. \u0639\u0631\u0636 \u0648 \u0639\u0645\u0642 \u06a9\u0627\u0646\u0627\u0644 \u0648 \u0634\u062a\u0627\u0628 \u06af\u0631\u0627\u0646\u0634 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/span><\/li>
      2. \u0639\u062f\u062f \u0641\u0631\u0648\u062f (Fr) \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u062a\u0627 \u0646\u0648\u0639 \u062c\u0631\u06cc\u0627\u0646 (\u0632\u06cc\u0631 \u0628\u062d\u0631\u0627\u0646\u06cc \u06cc\u0627 \u0641\u0648\u0642 \u0628\u062d\u0631\u0627\u0646\u06cc) \u062a\u0639\u06cc\u06cc\u0646 \u0634\u0648\u062f.<\/span><\/li>
      3. \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0634\u0631\u0637 if \u0646\u0648\u0639 \u062c\u0631\u06cc\u0627\u0646 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/li><\/ol>

        \u0645\u062b\u0627\u0644 4: \u062a\u062d\u0644\u06cc\u0644 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0634\u06cc\u0628\u200c\u0647\u0627 (Slope Stability Analysis)<\/span><\/h2>

        clc; clear;close all<\/span><\/p>

        % \u0632\u0627\u0648\u06cc\u0647 \u0634\u06cc\u0628 \u0648 \u0636\u0631\u06cc\u0628 \u0627\u0635\u0637\u06a9\u0627\u06a9<\/span><\/p>

        theta = 30;\u00a0 % \u062f\u0631\u062c\u0647<\/span><\/p>

        phi = 35;\u00a0 % \u0636\u0631\u06cc\u0628 \u0627\u0635\u0637\u06a9\u0627\u06a9<\/span><\/p>

        % \u0645\u062d\u0627\u0633\u0628\u0647 \u0636\u0631\u06cc\u0628 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646<\/span><\/p>

        FS = tan(deg2rad(phi)) \/ tan(deg2rad(theta));<\/span><\/p>

        % \u0646\u0645\u0627\u06cc\u0634 \u0646\u062a\u06cc\u062c\u0647<\/span><\/p>

        disp([‘\u0636\u0631\u06cc\u0628 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646: ‘, num2str(FS)]);<\/span><\/p>

        \u062e\u0631\u0648\u062c\u06cc:<\/span><\/h3>

        \u0636\u0631\u06cc\u0628 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646: 1.2128<\/span><\/p>

        \u062a\u0648\u0636\u06cc\u062d:<\/span><\/p>

        1. \u0632\u0627\u0648\u06cc\u0647 \u0634\u06cc\u0628 (theta) \u0648 \u0636\u0631\u06cc\u0628 \u0627\u0635\u0637\u06a9\u0627\u06a9 \u062f\u0627\u062e\u0644\u06cc (phi) \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/span><\/li>
        2. \u0636\u0631\u06cc\u0628 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0634\u06cc\u0628 (FS) \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0648 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/li><\/ol>

          \u0645\u062b\u0627\u0644 5: \u0637\u0631\u0627\u062d\u06cc \u062f\u0627\u0644 \u0628\u062a\u0646\u06cc \u062a\u062d\u062a \u0628\u0627\u0631 \u0645\u062a\u0645\u0631\u06a9\u0632<\/span><\/h2>

          clc; clear;close all<\/span><\/p>

          % \u0645\u0634\u062e\u0635\u0627\u062a \u062f\u0627\u0644 \u0628\u062a\u0646\u06cc<\/span><\/p>

          b = 2;\u00a0 % \u0639\u0631\u0636 \u062f\u0627\u0644 (\u0645\u062a\u0631)<\/span><\/p>

          h = 0.15;\u00a0 % \u0636\u062e\u0627\u0645\u062a \u062f\u0627\u0644 (\u0645\u062a\u0631)<\/span><\/p>

          P = 5000;\u00a0 % \u0628\u0627\u0631 \u0645\u062a\u0645\u0631\u06a9\u0632 (\u0646\u06cc\u0648\u062a\u0648\u0646)<\/span><\/p>

          % \u0645\u062d\u0627\u0633\u0628\u0647 \u062a\u0646\u0634 \u062e\u0645\u0634\u06cc<\/span><\/p>

          M = P * b \/ 8;<\/span><\/p>

          sigma = M \/ (b * h^2 \/ 6);<\/span><\/p>

          % \u0646\u0645\u0627\u06cc\u0634 \u0646\u062a\u06cc\u062c\u0647<\/span><\/p>

          disp([‘\u062a\u0646\u0634 \u062e\u0645\u0634\u06cc: ‘, num2str(sigma), ‘ \u067e\u0627\u0633\u06a9\u0627\u0644’]);<\/span><\/p>

          \u062e\u0631\u0648\u062c\u06cc:<\/span><\/h3>

          \u062a\u0646\u0634 \u062e\u0645\u0634\u06cc: 166666.6667 \u067e\u0627\u0633\u06a9\u0627\u0644<\/span><\/p>

          \u062a\u0648\u0636\u06cc\u062d:<\/span><\/p>

          1. \u0645\u0634\u062e\u0635\u0627\u062a \u062f\u0627\u0644 \u0628\u062a\u0646\u06cc \u0648 \u0628\u0627\u0631 \u0645\u062a\u0645\u0631\u06a9\u0632 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/span><\/li>
          2. \u062a\u0646\u0634 \u062e\u0645\u0634\u06cc \u062f\u0631 \u062f\u0627\u0644 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0648 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/li><\/ol>

            \u0645\u062b\u0627\u0644 6: \u062a\u062d\u0644\u06cc\u0644 \u0646\u0641\u0648\u0630 \u0622\u0628 \u062f\u0631 \u062e\u0627\u06a9 (Seepage Analysis in Soil)<\/span><\/h2>

            clc; clear;close all<\/span><\/p>

            % \u067e\u0627\u0631\u0627\u0645\u062a\u0631\u0647\u0627\u06cc \u0648\u0631\u0648\u062f\u06cc<\/span><\/p>

            k = 1e-6; % \u0636\u0631\u06cc\u0628 \u0646\u0641\u0648\u0630\u067e\u0630\u06cc\u0631\u06cc \u062e\u0627\u06a9 (\u0645\u062a\u0631 \u0628\u0631 \u062b\u0627\u0646\u06cc\u0647)<\/span><\/p>

            h1 = 10; % \u0627\u0631\u062a\u0641\u0627\u0639 \u0622\u0628 \u062f\u0631 \u0628\u0627\u0644\u0627\u062f\u0633\u062a (\u0645\u062a\u0631)<\/span><\/p>

            h2 = 3; % \u0627\u0631\u062a\u0641\u0627\u0639 \u0622\u0628 \u062f\u0631 \u067e\u0627\u06cc\u06cc\u0646 \u062f\u0633\u062a (\u0645\u062a\u0631)<\/span><\/p>

            L = 20; % \u0637\u0648\u0644 \u062e\u0627\u06a9\u200c\u0631\u06cc\u0632 (\u0645\u062a\u0631)<\/span><\/p>

            % \u0645\u062d\u0627\u0633\u0628\u0647 \u062c\u0631\u06cc\u0627\u0646 \u0646\u0641\u0648\u0630<\/span><\/p>

            Q = k * (h1 – h2) \/ L;<\/span><\/p>

            % \u0646\u0645\u0627\u06cc\u0634 \u0646\u062a\u06cc\u062c\u0647<\/span><\/p>

            disp([‘\u062f\u0628\u06cc \u0646\u0641\u0648\u0630 \u0622\u0628: ‘, num2str(Q), ‘ \u0645\u062a\u0631 \u0645\u06a9\u0639\u0628 \u0628\u0631 \u062b\u0627\u0646\u06cc\u0647’]);<\/span><\/p>

            \u062e\u0631\u0648\u062c\u06cc:<\/span><\/h3>

            \u062f\u0628\u06cc \u0646\u0641\u0648\u0630 \u0622\u0628: 3.5e-07 \u0645\u062a\u0631 \u0645\u06a9\u0639\u0628 \u0628\u0631 \u062b\u0627\u0646\u06cc\u0647<\/span><\/p>

            \u062a\u0648\u0636\u06cc\u062d:<\/span><\/p>

            1. \u062a\u0639\u0631\u06cc\u0641 \u067e\u0627\u0631\u0627\u0645\u062a\u0631\u0647\u0627:<\/span><\/li><\/ol>

              k = 1e-6\u00a0 \u00a0\u0627\u06cc\u0646 \u062e\u0637 \u0636\u0631\u06cc\u0628 \u0646\u0641\u0648\u0630\u067e\u0630\u06cc\u0631\u06cc \u062e\u0627\u06a9 \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0633\u0631\u0639\u062a \u0646\u0641\u0648\u0630 \u0622\u0628 \u062f\u0631 \u062e\u0627\u06a9 \u0627\u0633\u062a. \u0648\u0627\u062d\u062f \u0622\u0646 \u0645\u062a\u0631 \u0628\u0631 \u062b\u0627\u0646\u06cc\u0647 \u0627\u0633\u062a.<\/span><\/p>

              h1 = 10 \u00a0\u0627\u0631\u062a\u0641\u0627\u0639 \u0622\u0628 \u062f\u0631 \u0628\u0627\u0644\u0627\u062f\u0633\u062a \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0633\u0637\u062d \u0622\u0628 \u062f\u0631 \u0633\u0645\u062a \u0628\u0627\u0644\u0627\u06cc \u062e\u0627\u06a9\u200c\u0631\u06cc\u0632 \u0627\u0633\u062a.<\/span><\/p>

              h2 = 3 \u00a0\u0627\u0631\u062a\u0641\u0627\u0639 \u0622\u0628 \u062f\u0631 \u067e\u0627\u06cc\u06cc\u0646 \u062f\u0633\u062a \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0633\u0637\u062d \u0622\u0628 \u062f\u0631 \u0633\u0645\u062a \u067e\u0627\u06cc\u06cc\u0646\u06cc \u062e\u0627\u06a9\u200c\u0631\u06cc\u0632 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/span><\/p>

              L = 20 \u00a0\u0637\u0648\u0644 \u062e\u0627\u06a9\u200c\u0631\u06cc\u0632 \u0631\u0627 \u0645\u0634\u062e\u0635 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0641\u0627\u0635\u0644\u0647 \u0628\u06cc\u0646 \u062f\u0648 \u0646\u0642\u0637\u0647 (\u0628\u0627\u0644\u0627\u062f\u0633\u062a \u0648 \u067e\u0627\u06cc\u06cc\u0646 \u062f\u0633\u062a) \u0627\u0633\u062a.<\/span><\/p>

              1. \u0645\u062d\u0627\u0633\u0628\u0647 \u062c\u0631\u06cc\u0627\u0646 \u0646\u0641\u0648\u0630:<\/span><\/li><\/ol>

                Q = k * (h1 – h2) \/ L \u00a0\u062f\u0631 \u0627\u06cc\u0646 \u062e\u0637\u060c \u062f\u0628\u06cc \u0646\u0641\u0648\u0630 \u0622\u0628 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0631 \u0627\u0633\u0627\u0633 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0627\u0631\u0633\u06cc\u060c \u062c\u0631\u06cc\u0627\u0646 \u0622\u0628 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u062e\u0627\u06a9 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f:<\/span><\/p>

                (h1 – h2) \u00a0\u0627\u06cc\u0646 \u0639\u0628\u0627\u0631\u062a \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0627\u062e\u062a\u0644\u0627\u0641 \u0627\u0631\u062a\u0641\u0627\u0639 \u0622\u0628 \u062f\u0631 \u0628\u0627\u0644\u0627\u062f\u0633\u062a \u0648 \u067e\u0627\u06cc\u06cc\u0646 \u062f\u0633\u062a \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06af\u0631\u0627\u062f\u06cc\u0627\u0646 \u0647\u06cc\u062f\u0631\u0648\u0644\u06cc\u06a9\u06cc \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>

                k\u00a0 \u00a0\u0636\u0631\u06cc\u0628 \u0646\u0641\u0648\u0630\u067e\u0630\u06cc\u0631\u06cc \u062e\u0627\u06a9 \u0627\u0633\u062a \u06a9\u0647 \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0642\u0627\u0628\u0644\u06cc\u062a \u062e\u0627\u06a9 \u062f\u0631 \u0639\u0628\u0648\u0631 \u0622\u0628 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>

                L\u00a0 \u00a0\u0637\u0648\u0644 \u062e\u0627\u06a9\u200c\u0631\u06cc\u0632 \u0627\u0633\u062a \u06a9\u0647 \u062c\u0631\u06cc\u0627\u0646 \u0622\u0628 \u0627\u0632 \u0622\u0646 \u0639\u0628\u0648\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0628\u0627 \u062a\u0642\u0633\u06cc\u0645 \u0628\u0631 \u0637\u0648\u0644\u060c \u062f\u0628\u06cc \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f.<\/span><\/p>

                \u0627\u06af\u0631 \u0639\u0644\u0627\u0642\u0647 \u0645\u0646\u062f \u0628\u0647 \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0646\u0631\u0645 \u0627\u0641\u0632\u0627\u0631 \u0645\u062a\u0644\u0628 \u0647\u0633\u062a\u06cc\u062f\u060c \u0645\u0637\u0627\u0644\u0639\u0647 \u0645\u0637\u0627\u0644\u0628 \u0632\u06cc\u0631 \u0628\u0647 \u0634\u0645\u0627 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0645\u06cc \u0634\u0648\u062f:<\/span><\/p>

                1. \u0631\u0627\u0647\u0646\u0645\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062f\u0633\u062a\u0648\u0631<\/a><\/li>
                2. logspace \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/li>
                3. \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0633\u062a\u0648\u0631axis \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/li>
                4. \u062f\u0633\u062a\u0648\u0631 sqrt \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/li>
                5. \u062f\u0633\u062a\u0648\u0631 conj \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/li>
                6. \u0622\u0631\u0627\u06cc\u0647 \u0633\u0644\u0648\u0644\u06cc \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/li>
                7. \u0641\u0627\u06a9\u062a\u0648\u0631\u06cc\u0644 \u062f\u0631 \u0645\u062a\u0644\u0628<\/a><\/li>
                8. \u06a9\u0627\u0631\u0628\u0631\u062f \u0647\u0627\u06cc \u0646\u0631\u0645 \u0627\u0641\u0632\u0627\u0631 \u0645\u062a\u0644\u0628<\/a><\/li>
                9. \u06a9\u0627\u0631\u0628\u0631\u062f \u0645\u062a\u0644\u0628 \u062f\u0631 \u0645\u062f\u06cc\u0631\u06cc\u062a<\/a><\/li>
                10. \u06a9\u0627\u0631\u0628\u0631\u062f \u0645\u062a\u0644\u0628 \u062f\u0631 \u0645\u0647\u0646\u062f\u0633\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9<\/a><\/li>
                11. \u00a0<\/li><\/ol>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

                  \u0645\u062a\u0644\u0628 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0632\u0628\u0627\u0646 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u0633\u0637\u062d \u0628\u0627\u0644\u0627 \u0648 \u0645\u062d\u06cc\u0637 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0639\u062f\u062f\u06cc\u060c \u0627\u0628\u0632\u0627\u0631\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0645\u0641\u06cc\u062f \u0628\u0631\u0627\u06cc \u0645\u0647\u0646\u062f\u0633\u0627\u0646 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0646\u0631\u0645\u200c\u0627\u0641\u0632\u0627\u0631 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0642\u062f\u0631\u062a \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0628\u0627\u0644\u0627\u060c \u0642\u0627\u0628\u0644\u06cc\u062a \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647\u060c \u0648 \u062a\u0648\u0627\u0646\u0627\u06cc\u06cc \u0634\u0628\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u0633\u0627\u0626\u0644 \u0645\u0647\u0646\u062f\u0633\u06cc\u060c \u0628\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc \u0636\u0631\u0648\u0631\u06cc \u062f\u0631 \u0645\u0647\u0646\u062f\u0633\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a \u00a0\u06a9\u0647 \u062f\u0631 \u0631\u0634\u062a\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0645\u0647\u0646\u062f\u0633\u06cc\u060c \u0627\u0632 \u062c\u0645\u0644\u0647 \u0645\u0647\u0646\u062f\u0633\u06cc \u0639\u0645\u0631\u0627\u0646\u060c \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u06af\u0633\u062a\u0631\u062f\u0647\u200c\u0627\u06cc […]<\/p>\n","protected":false},"author":6,"featured_media":5713,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rank_math_lock_modified_date":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5634","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matlab-training"],"views":686,"_links":{"self":[{"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/posts\/5634","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/comments?post=5634"}],"version-history":[{"count":20,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/posts\/5634\/revisions"}],"predecessor-version":[{"id":6149,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/posts\/5634\/revisions\/6149"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/media\/5713"}],"wp:attachment":[{"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/media?parent=5634"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/categories?post=5634"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projestaan.com\/mag\/wp-json\/wp\/v2\/tags?post=5634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}