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Assignment_LinearEquationsmlx.mlx

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+% -----------------------------------------
+% HW1
+% LiXin
+% 2022/2/18
+% -----------------------------------------
+clear all; close all; clc
+
+%% Problem 1
+
+% 1
+r=0.15; % interest rate
+L=50000; % loan amount
+N=[0.5:1/12:20]; % number of years
+PN=(r*L*(1+r/12).^(12*N))./(12*((1+r/12).^(12*N)-1)) % monthly payment
+
+% 2
+plot(N, PN) % plot the monthly payment and the number of years
+
+% 3
+text(10,1000,"LiXin")
+
+%% Problem 2
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+% a
+A=[20 4 2 6; 6 37 2 3;8 5 9 9] % create the matrix
+% b
+x1=A(1,:) % assign the first row of A to a vector called x1
+% c
+y=A([end-1 end],:) % assign the last 2 rows of A to an array called y
+% d
+B=A(:,2:2:size(A,2)) % assign the even-numbered columns of A to an array called B
+% e
+C=A' % assign the transpose of A to C
+% f
+reciprocal = 1./A % compute the reciprocal of each element of A
+% g
+A(3, 2)=100 % change the number in column 2, row 3 of A to 100
+
+%% Problem 3
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+% a
+figure % create an empty figure
+
+% b
+t=0:0.01:2*pi; % create a vector contains numbers range from 0 to 2*pi
+y=sin(4*t).*cos(2*t); % calculate the result of the function according to the scope
+ax1=subplot(1,2,1);
+plot(t,y) % normal plot
+ax2=subplot(1,2,2);
+polarplot(t,y) % polar plot
+
+% c
+legend(ax1,'y^k_{max}=sin(4t)cos(2t)') % put legend on the first subgraph
+
+% d
+grid(ax1, 'on') % grid on the first subgraph
+
+% e
+text(0,0,'Lixin') % text on the second subgraph
+
+%% Problem 4
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+% a
+num=input('Enter a number: ');
+
+% b
+num_cm=num * 2.54; % convert to cm
+fprintf('%.2f inches is %.2f cm\n', num, num_cm)
+
+% c
+num_mm=num_cm * 10; % the number converted to mm
+formatSpec='%.2f';
+str = [num2str(num, formatSpec), ' is also ', num2str(num_mm, formatSpec), 'mm'];
+disp(str)
+
+%% Problem 5 
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+Nr = logspace(4,8,100); % Reynolds number
+for De = [20 100 1000 1000 100000] % D/epsilon
+    f = 0.25./(log(1/(3.7*De)+5.74./Nr.^0.9)/log(10)).^2;
+    loglog(Nr, f)
+    hold on
+end
+grid on
+grid minor
+Nr=[1e2:0.2e4];
+f = 64./Nr;
+plot(Nr, f) % plot f = 64 / Nr
+title('Moody''s Diagram')
+ylabel('Friction Factor')
+xlabel('Reynolds Number N_R')
+legend('D/\epsilon = 20', 'D/\epsilon = 100', 'D/\epsilon = 1000', 'D/\epsilon = 10000', 'D/\epsilon = 100000','Laminar flow',...
+'Location','southwest')
+text(1e7,0.08,'Lixin') % print my name
+xlim([0.8e3 1e8])
+ylim([0.8e-2 1e-1])% adjust axis limits
+
+%% Problem 6
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+[x, y]=meshgrid(-2:0.1:2);
+f=50*y.^2.*exp(-x.^2-0.5*y.^2);
+C=x.*y;
+surf(x,y,f,C)
+xlabel('x');
+ylabel('y');
+zlabel('f(x,y) = 50y^2e^{-x^2-0.5y^2}');
+title('My Plot Title')
+
+

Assignment_LinearEquationsmlx.pdf

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+% -----------------------------------------
+% HW1
+% LiXin
+% 2022/2/18
+% -----------------------------------------
+clear all; close all; clc
+
+%% Problem 1
+
+% 1
+r=0.15; % interest rate
+L=50000; % loan amount
+N=[0.5:1/12:20]; % number of years
+PN=(r*L*(1+r/12).^(12*N))./(12*((1+r/12).^(12*N)-1)) % monthly payment
+
+% 2
+plot(N, PN) % plot the monthly payment and the number of years
+
+% 3
+text(10,1000,"LiXin")
+
+%% Problem 2
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+% a
+A=[20 4 2 6; 6 37 2 3;8 5 9 9] % create the matrix
+% b
+x1=A(1,:) % assign the first row of A to a vector called x1
+% c
+y=A([end-1 end],:) % assign the last 2 rows of A to an array called y
+% d
+B=A(:,2:2:size(A,2)) % assign the even-numbered columns of A to an array called B
+% e
+C=A' % assign the transpose of A to C
+% f
+reciprocal = 1./A % compute the reciprocal of each element of A
+% g
+A(3, 2)=100 % change the number in column 2, row 3 of A to 100
+
+%% Problem 3
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+% a
+figure % create an empty figure
+
+% b
+t=0:0.01:2*pi; % create a vector contains numbers range from 0 to 2*pi
+y=sin(4*t).*cos(2*t); % calculate the result of the function according to the scope
+ax1=subplot(1,2,1);
+plot(t,y) % normal plot
+ax2=subplot(1,2,2);
+polarplot(t,y) % polar plot
+
+% c
+legend(ax1,'y^k_{max}=sin(4t)cos(2t)') % put legend on the first subgraph
+
+% d
+grid(ax1, 'on') % grid on the first subgraph
+
+% e
+text(0,0,'Lixin') % text on the second subgraph
+
+%% Problem 4
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+% a
+num=input('Enter a number: ');
+
+% b
+num_cm=num * 2.54; % convert to cm
+fprintf('%.2f inches is %.2f cm\n', num, num_cm)
+
+% c
+num_mm=num_cm * 10; % the number converted to mm
+formatSpec='%.2f';
+str = [num2str(num, formatSpec), ' is also ', num2str(num_mm, formatSpec), 'mm'];
+disp(str)
+
+%% Problem 5 
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+Nr = logspace(4,8,100); % Reynolds number
+for De = [20 100 1000 1000 100000] % D/epsilon
+    f = 0.25./(log(1/(3.7*De)+5.74./Nr.^0.9)/log(10)).^2;
+    loglog(Nr, f)
+    hold on
+end
+grid on
+grid minor
+Nr=[1e2:0.2e4];
+f = 64./Nr;
+plot(Nr, f) % plot f = 64 / Nr
+title('Moody''s Diagram')
+ylabel('Friction Factor')
+xlabel('Reynolds Number N_R')
+legend('D/\epsilon = 20', 'D/\epsilon = 100', 'D/\epsilon = 1000', 'D/\epsilon = 10000', 'D/\epsilon = 100000','Laminar flow',...
+'Location','southwest')
+text(1e7,0.08,'Lixin') % print my name
+xlim([0.8e3 1e8])
+ylim([0.8e-2 1e-1])% adjust axis limits
+
+%% Problem 6
+clear all; close all; clc % erase all the workspace data, command window output, and close all figures
+[x, y]=meshgrid(-2:0.1:2);
+f=50*y.^2.*exp(-x.^2-0.5*y.^2);
+C=x.*y;
+surf(x,y,f,C)
+xlabel('x');
+ylabel('y');
+zlabel('f(x,y) = 50y^2e^{-x^2-0.5y^2}');
+title('My Plot Title')
+
+

Assignment_NumericalIntegration.mlx

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+%% Problem 1
+Name = "LiXin"
+
+%% Problem 2
+ans = 15 / (8 * 10)
+
+%% Problem 3
+a = 6
+
+%% Problem 4
+c = a * 2
+
+%% Problem 5
+w = [18 12 1; 4 8 1]
+
+%% Problem 6
+ans = w.^3
+
+%% Variables and Arrays
+% Problem 1
+M12 = zeros(5, 6);
+M12 = M12 + 12
+% Problem 2
+% a
+A = rand(randi(9)+1, randi(9)+1)
+% b
+rows = size(A, 1);
+columns = size(A, 2);
+% c
+w = A(rows, columns - 1);
+% Problem 3
+% a
+clc
+% b
+% LiXin HW1, Problem 3
+% c
+y = [ 2 3 4; 5 6 7];
+% d
+ra = y + 16;
+% e
+x = y;
+rd = sqrt(exp(x))
+

Assignment_NumericalIntegration.pdf

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+% -----------------------------------------
+% HW1
+% LiXin
+% 2022/2/28
+% -----------------------------------------
+close all; clear all; clc;
+
+%% Input for Problem 1~5
+
+% Problem 1
+M = [1 2; 3 4];
+even_index(M)
+
+% Problem 2
+v = [1 2 3 4];
+flip_it(v)
+
+% Problem 3
+N = magic(5);
+n = 2;
+top_right(N, n);
+
+% Problem 4
+A = magic(5);
+peri_sum(A)
+
+% Problem 5
+cal(pi/2)
+
+%% Problem 6
+h = 2;
+v = sqrt(2 * 9.8 *h);
+for i = 1:8 % rebound 8 times
+    v = 0.85 * v;
+end
+h = v*v/(2*9.8)
+
+%% Problem 7
+n=1;
+T=300;
+R=0.08206;
+a=1.39;
+b=0.039;    
+V=linspace(0.08,6,100);
+P1=n*R*T./V;
+P2=n*R*T./(V-n*b)-n*n*a./V.^2;
+plot(V,P1)
+hold on
+plot(V,P2)
+
+%% Problem 8
+
+% a
+x = 10 * rand(ceil(10*rand)+2,1)
+% b
+mysum=0;
+for i = 1:size(x,1)
+    mysum = mysum + x(i,1);
+end
+mysum
+% c
+if mysum == sum(x)
+    disp('Congratulations!! you did it right')
+    load handel;
+    sound(y, Fs)
+else
+    fprintf('Sorry, %.2f ~= %.2f. Please try again.\n', mysum, sum(x))
+end
+% d
+x = 10 * rand(ceil(10*rand)+2,1);
+mysum=0;
+i = 1;
+while i <= size(x,1)
+    mysum = mysum + x(i,1);
+    i = i + 1;
+end
+mysum
+if mysum == sum(x)
+    disp('Congratulations!! you did it right')
+    load handel;
+    sound(y, Fs)
+else
+    fprintf('Sorry, %.2f ~= %.2f. Please try again.\n', mysum, sum(x))
+end
+    
+
+%% Problem 1
+% returns a matrix that contains only those elements of M that are in
+% even rows and columns
+function res = even_index(M) % M as a matrix
+    res = M(2:2:end, 2:2:end);
+end
+
+%% Problem 2
+% returns the opposite order of v
+function w = flip_it(v) % row vector v, row vector w
+    for i = size(v,2) : -1 : 1
+        w(1,size(v,2) - i + 1) = v(1,i);
+    end
+end
+
+%% Problem 3
+% returns the n-by-n square subarray of N located at the top right corner
+% of N
+function M = top_right(N, n) % a matrix N, a scalar non-negative integer n
+    M = N(1:n, end-n+1:end)
+end
+
+%% Problem 4
+% add together the elements that are in the first and last rows and columns
+function my_sum = peri_sum(A)
+    my_sum = 0;
+    my_sum = my_sum + sum(A(:,1)) + sum(A(:,end)) + sum(A(1,:)) + sum(A(end,:));
+    my_sum = my_sum - A(1,1) - A(1,end) - A(end, end) - A(end,1);
+end
+
+%% Problem 5
+% power series for sin(x), 5 terms are needed, when i exceeds 20, the loop 
+% terminates
+function sin_x = cal(x)
+sin_x = 0;
+    for i = [1:2:20]
+        sin_x = sin_x + (-1)^floor(i/2)*x^i/factorial(i);
+        sin(x)-sin_x
+    end
+end