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MATH 442: Mathematical Modeling Lecturer: Dr. Jean Marie Linhart http://www.math.tamu.edu/~jmlinhart/m442 Getting started with Matlab Matlab is short for MATrix LABoratory. Matlab makes it easy to work with matrices. Matlab assumes if you add (+) or multiply (*), you mean matrix addition or multiplication. This is practice and explanation; it is not handed in. 1. Enter the following into Matlab to create a row vector a = [1 2 3] 2. Enter the following into Matlab to create a column vector b = [1; 2; 3] 3. You can also create a column vector using the matrix transpose operation, which you get with a single quote. Try it: b = [1 2 3]’] or b = a’ 4. Generalize from the rules above to enter the following matrix into matlab: 1 −2 c= 1 1 5. What happens if you end a line in Matlab with a semi-colon? What is the difference between x = [1 0 1] and x = [1 0 1]; 6. With the variables as defined above, try the two multiplications a*b and b*a Why do these give different answers? What is happening here? 1 Now try a*a Did that work? How about a.*a Now, answer the question: what is the difference between * and .*? The description we use for .* is elementwise multiplication. Likewise ./ is elementwise division. Addition and subtraction are always elementwise! 7. Functions work elementwise. exp(c) is the exponential function ex and it works elementwise on c. log(c) takes the natural log or the entries of c. If you want the base-10 logarithm use log10(c). 8. Ways of creating a vector of evenly spaced values: t = 0:0.1:10; t = linspace(0,10,100) t = linspace(0,10,101) Which of these are equivalent and can you figure out why? Use the semicolon to end the line if you don’t want to see all those values echoed out! Making this work for trigonometry: t = 0:4*pi/100:4*pi t = linspace(0, 4*pi,100 9. Try x = exp(t); x = sin(t); x = cos(t); Notice that the following does not work. Why not? How do you fix it? (Hint: elementwise!) x = sin(t)*cos(t); 10. To make a simple plot, we can simply use the plot(t, x) command. 11. Generally, for class, you need to make multiple plots with titles, axis labels and legends. Try: x = exp(t); figure(2) plot(t, x, ’k--’, ’LineWidth’, 2) title(’x= exp(t)’) xlabel(’t’) ylabel(’x’) 2 Here is a more complicated figure which plots cosine, sine, and a dotted line at zero. This figure includes labels, titles and a legend, with the font increased on the labels and title. t = linspace(0,3*pi, 100); x = cos(t); y = sin(t); z = zeros(size(t)); figure(3) plot(t, x, ’k--’, ’LineWidth’, 2) hold on; plot(t, y, ’k’, ’LineWidth’, 2) plot(t, z, ’:k’) title(’Sine and Cosine’,’FontSize’, 24) xlabel(’t’, ’FontSize’, 20) ylabel(’x’, ’FontSize’, 20)) legend(’cos(t)’, ’sin(t)’) 12. Matlab has for loops and if statements like any other programming language. If I wanted to collect the first 4 odd numbers into a column called odd: odd = zeros(4,1) for i = 1:4 2*i - 1; end odd If I want Matlab to count from 1 to 10, printing out even numbers and replacing odd numbers with *, I might try the following, which uses the floor() function, which takes the largest integer less than the one you put in. There are many other ways to do this. for i = 1:10 if (i/2 - floor(i/2) > 0) fprintf(’*, ’) else fprintf(’%d, ’, i) end fprintf(’\n’) 3