Problem 3 (hand-calculation): Consider the functiong() 1 +e. Show that, for any initial guess zo ...
Problem 3 (hand-calculation): Given f(x) = In (5-z) for x E [0,2], apply Taylor's theorem with zo = 1 in the following (a) Find the lowest-order Taylor polynomial approximation that is accurate to within (b) Find the actual errors at x = 0, 1 and 2. exercises. 10-3 Take a photo of your work. Include all pages in a single photo named problem3.jpg. Set the following in your homework script: figure(3); imshow (imread('problem3.jpg'); p3 = 'See figure 3'. Problem 3...
Problem 3 (hand-calculation): Consider a two-dimensional function: f(x, y)- sin(x)cos() where x and y are in radi ans (a) Evaluate a f/oz, f / ду, and /(8z0) at x = y = 1 analytically. (b) Evaluate af/az. Э//ду, and Эг f/0гду) at x = y = 1 numerically using 2nd-order central difference formula with a grid spacing h -0.1. Take a photo of your work. Include all pages in a single photo named problem3.jpg. Set the following in your homework...
Problem 2 (hand-calculation): Consider the function f(x) tabulated in table 1. Apply improved trapezoid rule to estimate the integral, If) J ) dz, by using the following number of subintervals, n (a) n-3. Use grid points at i0, 4, 8 and 12 (b) n- 6. Use grid points at i0, 2,4, 6, 8, 10 and 12 (c) n = 12, Use all grid points For each part, compute the integral, T(f) and the corresponding absolute error Er(f), and the error...
node index, i 2 3 0 depth, z (m) 12 32 -52 -72 92 -130 -180 -230 -280 -330 temperature, T (C) 15.3 15.29 15.28 15.27 15.26 15.22 15.14 14.19 13.31 12.9 Table 1: Temperature of seawater in the upper ocean surface layer Problem 4 (hand-calculation): Consider the seawater temperature data in table 1 to estimate the ternperature at depth z = 150 m. Use Newton polynomials with the following nodes (a) Nodes i = 3 and 4. (b) Nodes...
Problem 4 (hand-calculation): Consider the constant-pressure specific heat of air at high temperature presented in ta- ble 4, where T is the temperature and Cp is the specific heat. Determine a least squares quadratic polynomial approximation for this set of data. The quadratic polynomial has the following form: Cp = a + bT+cT. where the coefficients a, b and c are to be determined using the least squares method. Hint Follow the derivation of linear regression discussed in class. You...