Numerical Methods

3. Buckling of Column: Under a uniform load, small deflections y of a simply supported beam are given by where L = 10 feet is the length of the beam, EI = 1900 is modulus of elasticity times moment of inertia, and q = -0.6 is load distribution. The beam extends from z = 0 to z = L. The goal is to find y at every 0.02 foot using the Direct Method and plot y(z) versus I. (a) Using centered-differencing, formulate the finite difference approximation. To illustrate your work, use 5 grid points (2 of them are on the boundaries, y = 0 and y = L). Write down finite-difference approximations for the interior points, for a general uniform grid spacing of Ar. Then write your algebraic equations in the matrix-vector form with unknown vector on the left hand side and all known quantities on the right hand side. (b) Using a computer program for N + 1 total points, solve the above equation using the direct method with the grid spacing of 0.02 foot. Plot y(z) versus z. Compare your solution with the Exact Solution (clearly label your graphs).

In Probs. 33-36 find the transform. In Probs. 37-45 findthe inverse transform. Show the details of your work. \text { 43. } \frac{2 s-1}{s^{2}-6 s+18}

3 The drawing shows three octagons. a. Is octagon B a scale drawing of octagon A? Explain. b. Is octagon C a scale drawing of octagon A? Explain.

31-40: USCS-Metric Conversions. Convert the following quantities to the indicated units.Where necessary, round to the nearest tenth. 31. 13 liters to quarts

Determine whether the data set is a population or a sample. 1) The age of each employee at a local grocery store

The graph of the function f over the interval [1, 7]is shown. Using values from the graph, find trapezoidal rule estimates for the integral f(x) dx by using theindicated number of subintervals. (a) n = 3 9 = u (q)

25) 2-POINT QUESTION. Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores for a physics class had a mean of 69 with a standard deviation of 3.7. Suppose a student gets a 76 on the history test and a 100 on the physics test. a) Calculate the z-score for each test. Use the symbols Zh for the history test and Zp for the physics test. Show your work. b) On which test did the student perform better? Explain your reason.

66. You purchase fresh strawberries in Mexico for 28 pesos per kilogram. 'What is the price in U.S. dollars per pound? (1 kg=2.205 lb)

To solve the ordinary differential equation 3 \frac{d y}{d x}+x y^{2}=\sin (x), y(0)=5 by the Runge-Kutta 2nd order method, you need to rewrite the equation as

1. Using linear stability analysis, identify any restrictions on the step size for a stable solution.