Programming Numerical Computing with. MATLAB for Scientists and Engineers

You will be able to Write simple MATLAB programs using if statement, Write simple MATLAB programs using for statement, Convert a for-loop based program into a matrix operation version. 2

Relational Operators Operators Results are logicals 3 < < <= > > >= == ~= a = 5 < 8 b = [1:2:8] > 3 c = [2:2:13] == [ 0:3:17 ] A = randint(3,4,10) A>5 A(A>5) = 5

Exercise 1: Hate 4 Generate a 5x6 matrix A with random integers between 0 and 10. If some elements of matrix A is 4, replace it with 0. If some elements of matrix A is odd, subtract 1 from the elements. 4 hate4.m

Logical Operators Operators Built-in Functions Examples 5 & & | | ~ ~ and(A,B) or(A,B) not(A) xor(A,B) all(A) any(A) find(A) find(A>d)

Conditional Statement: if 6 if condition if condition – else x<0 S1 x<0 S1 T F S2 T F n = input('Enter an integer: '); if mod(n,2) fprintf('%d is an odd integer.\n', n ); end n = input('Enter an integer: '); if mod(n,2) fprintf('%d is an odd integer.\n', n ); end S1 n = input('Enter an integer: '); if mod(n,2) fprintf('%d is an odd integer.\n', n ); else fprintf('%d is an even integer.\n', n ); end n = input('Enter an integer: '); if mod(n,2) fprintf('%d is an odd integer.\n', n ); else fprintf('%d is an even integer.\n', n ); end S1 S2

Exercise 2 Volume in a Water Tank Find the volume of the water tank below when the depth is h. 7 10m 8m 6m h m

Solution 2 Function m-file Commands 8 water_volume.m

if – elseif – else – end Nested If 9 F F F if S1 S2 T elseif S3 S4 T T if A x = a else if B x = b else if C x = c else x = d end if A x = a else if B x = b else if C x = c else x = d end if A x = a elseif B x = b elseif C x = c else x = d end if A x = a elseif B x = b elseif C x = c else x = d end

For Loops for n=a:b statements end 10 i=0; for t=0:0.1:100 i = i+1; x(i) = sin(2*pi*200*t); end i=0; for t=0:0.1:100 i = i+1; x(i) = sin(2*pi*200*t); end t=0:0.1:100; x = sin(2*pi*200*t); t=0:0.1:100; x = sin(2*pi*200*t); for n=1:5 for m=5:-1:1 a(n,m)=n^2 + m^2; end for n=1:5 for m=5:-1:1 a(n,m)=n^2 + m^2; end n=1:5; m=1:5; [nn,mm]=meshgrid(n,m); a=nn.^2 + mm.^2; n=1:5; m=1:5; [nn,mm]=meshgrid(n,m); a=nn.^2 + mm.^2;

Example Taylor series of sine function Write a function y= Tsin(x,n), which is the partial sum of n-terms. 11

Exercise 3 Taylor series of exp(x). Write a function y= Texp(x,n), which is the partial sum of n-terms. Use Texp() to plot exp(x), Texp(x,5), Texp(x,10), Texp(x,100). 12

Solution 3 Function m-file Commands and Screenshot 13 Texp.m

While Loops i=0;t=0; while t<=100 i = i+1; x(i) = sin(2*pi*200*t); t = t+0.1; end i=0;t=0; while t<=100 i = i+1; x(i) = sin(2*pi*200*t); t = t+0.1; end t=0:0.1:100; x = sin(2*pi*200*t); t=0:0.1:100; x = sin(2*pi*200*t); i=0; for t=0:0.1:100 i = i+1; x(i) = sin(2*pi*200*t); end i=0; for t=0:0.1:100 i = i+1; x(i) = sin(2*pi*200*t); end 14

Lotto Numbers disp('I generate Lotto numbers'); disp('Good Luck!'); B=[]; for i=1:5 L=0; while L ~= 6, fprintf('Try - %d \n ', i ); A=floor(rand(1,6)*45)+1; A=unique(A); L=length(A); end B(i,:) = A; pause(1); end B disp('I generate Lotto numbers'); disp('Good Luck!'); B=[]; for i=1:5 L=0; while L ~= 6, fprintf('Try - %d \n ', i ); A=floor(rand(1,6)*45)+1; A=unique(A); L=length(A); end B(i,:) = A; pause(1); end B 15

Branch apple=100; if apple < 5 disp('few'); elseif apple < 20 disp('a few'); else disp('a lot'); end apple=100; if apple < 5 disp('few'); elseif apple < 20 disp('a few'); else disp('a lot'); end mon = 10; switch mon case 1 month = 'January'; case 2 month = 'February'; otherwise month = 'Others'; end mon = 10; switch mon case 1 month = 'January'; case 2 month = 'February'; otherwise month = 'Others'; end 16

Branch x = 2.7; units = 'm'; switch units case {'inch', 'in'} y = x * 2.54; case {'feet', 'ft'} y = x * 2.54 * 12; case {'meter', 'm'} y = x * 100; case {'milimeter', 'mm'} y = x / 10; case {'centimeter', 'cm'} y = x; otherwise y = nan; end x = 2.7; units = 'm'; switch units case {'inch', 'in'} y = x * 2.54; case {'feet', 'ft'} y = x * 2.54 * 12; case {'meter', 'm'} y = x * 100; case {'milimeter', 'mm'} y = x / 10; case {'centimeter', 'cm'} y = x; otherwise y = nan; end Unlike C, no break! Unlike C, no break! 17