Excel Definitions

Working with Data

• Example 5: Let A = [5 2 1 6; -1 0 4 -3]. Enter matrix A and find each of the following:
• sum(A)
• min(A)
• [mx, indx] = min(A)
• max(A)
• [Mx, indx] = max(A)
• length(A)
• mean(A)
• sum(A)/length(A)
• sum(A)/length(A(:,1))
• std(A)
• sort(A)

Working with Data

• Example 5: Use the following MATLAB commands to locate the minimum of the function y = 2 cos(2x) – 3 cos(x) on the interval [0, 2].
• x = linspace(0, 2*pi, 700);
• y = 2*cos(2*x)-3*cos(x);
• m = min(y)
• Plot this function and see if the “MATLAB solution” agrees with the graph.
• How else could we use MATLAB to solve this problem?

Working with Data

• Example 5 (cont.)
• One possible solution:
• Find where the derivative of y = 2 cos(2x) – 3 cos(x) is equal to zero and use fzero!
• plot(x, -4*sin(2*x)+3*sin(x))
• x1 = fzero('-4*sin(2*x)+3*sin(x)',[1 2])
• y1 = 2*cos(2*x1)-3*cos(x1)
• Each method yields a minimum of m = -2.5625.

Polynomials

• Recall that a polynomial is a function of the form p(x) = a0xn + a1xn-1 + … + an-1x + an where n is a non-negative integer and the ai are constants called coefficients. The degree of polynomial p(x) is n.
• In MATLAB, a polynomial can be represented as a row vector containing the coefficients.
• For example, the polynomial p(x) = x5+2x4-3x2+7x+12 is saved in MATLAB as
• p = [1 2 0 -3 7 12]
• Note that missing powers of x are included as 0’s in the vector.
• What polynomial would the vector r = [1 2 -3 7 12] represent in MATLAB?
• Answer: r(x) = x4 + 2x3 -3x2+7x+12.

Polynomials

• To evaluate a polynomial, we use “polyval”.
• Example 6: Try the following:
• p = [1 2 0 -3 7 12]
• polyval(p,3) %You should get 411.
• x = linspace(-2,2);
• y = polyval(p,x);
• plot(x,y)