Matlab Programming for Engineering Analysis

a=[1,2,4]; b=[3,2,-1]; c=[-1,0,4]; A=[a;b;c]; d=[a,b,c]; B=A'; % If A is complex, A' produces complex conjugate transpose; A.' would be % just transpose % Array addressing a2=a(2); %a(:) % represents all elements of vector a %a(2:5) % represents 2nd to 5th element A23=A(2,3); % A(:,3) %denotes all elements in the 3rd column of the matrix A % A(3,:) % all elements is second raw d=A(:); %creates a vector from columns of A % A(3;:)=[] % deletes a third raw % A(1,5)=3 changes matrix by adding two vanishing columns, with A_15=3 % A(:,2)=[] % removes the second column % if linear indexing is used with a matrix to delete an element, % the matrix will be reshaped into a vector mat=[7 9 8;4 6 5]; mat= 7 9 8 4 6 5 mat(3)=[] mat = 7 4 6 8 5 xmax=max(A); % max element in each column of A [x,y]=max(A); % vector x is max and vector y is the index of A corresponding to x % similar for function min(A) % C=max(A,B) makes C from larger of A and B matrix elements % length(A); larger of two dimensions of matrix A % sum(A) sums the elements of each column % sort(A) sorts each column is ascending order % sort(A,'descend'); % size(A); returns dimensions [m,n] of a matrix A % numel(A); returm the number of elements in matrix %A(end,1); last element in first column %A(2,end); last element in second row rand(3) % generates a random 3x3 matrix rand(2,3) % (2x3) matrix round(rand(2,3)*10) % random integer matrix %%%% mat=[2:4;3:5]; mat(1,2)=11 mat= 2 11 4 3 4 5 mat(2,:)=5:7 % entire 2nd row changed mat(:,4)=[9 2]'; % adding a fourth column to the matrix % Multidimensional arrays A=[1,2,3;-2,3,0]; A(:,:,2)=[2,1,3;-3,2,6]; % 2 to add page (layer) 2 % alternatively %define matrices A and B and use function cat to define 3-dimensional array %C=cat(3,A,B); %C(2,1,2) would be B_21 and C(2,1,1) would be A_21 %Array operations B=3*A; %element by element multiplication x=[1,2,3]; y=[3,2,1]; z=x.*y; a=x*y'; b=x'*y; % for matrices A and B %C=A.*B; %generates C with C_ij=A_ijB_ij % D=A./B+A.^3; %Vectorized functions z=exp(y).*sin(x).*(cos(x)).^2; %where x and y are vector arrays t=[0:0.001:0.5]; y=exp(-8*t).*sin(9*t+pi/2); % Matrix multiplication C=A*B; %Example: Max height in projectile motion for varios v and theta %h=v^2sin^2\theta/(2g) g=9.81; %units of m/s^2 v=[10:2:20]; %in units of m/s; v is (1x6) theta=[50:10:80]; % in degrees ; theta is (1x4) h=(v'.^2)*(sind(theta).^2)/(2*g); %v' is 6x1, theta is (1x4) and h is (6x4) table=[0,theta;v',h]; %Special matrices eye(n); %creates an nxn identity matrix eye(size(A)); % I of the size(A) ones(n) % nxn matrix of ones ones(m,n) % mxn matrix of ones zeros(n) % nxn matrix of zeros zeros(m,n) % mxn matrix of zeros %Examples of above %Plot f(x)= 10, 0<=x<=2 % 0, 2< x <5 % -3, 5<=x<=7 x1=[0:0.01:2]; f1=10*ones(size(x1)); x2=[2.01:0.01:4.99]; f2=zeros(size(x2)); x3=[5:0.01:7]; f3=-3*ones(size(x3)); x=[x1,x2,x3]; f=[f1,f2,f3]; plot(x,f),xlabel( 'x' ),ylabel( 'y' ) %Solving Ax=b (System of linear alg. equations) A=[6,12,4;7,-2,3;2,8,-9]; B=[70;5;64]; %write b as column vector, i.e. matrix (3x1) x=A\B %matrix division

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