Numerical Methods

The extension, y, of a material with an applied force, F, is given by y = e^Fx1x10-3 a) Calculate the work done if the force increases from 100N to 500N using: i) An analytical integration technique ii) A numerical integration technique [Note: the work done is given by the area under the curve] b) Compare the two answers c) Using a computer spreadsheet increase the number of values used for your numerical method d) Analyse any affect the size of numerical step has on the result.

A mass of 5 kg oscillates at the end of a spring. Let s(t) be the displacement of the mass from equilibrium position at time t. Assuming that the mass is located at the origin at t = 0 and has velocity v(t) = sin(t) + 1/T+1, find displacement s(t).

Calculate cond(A) for A=\left[\begin{array}{ll} 1 & c \\ c & 1 \end{array}\right], \quad|c| \neq 1 When does A become ill-conditioned? what does this day about the linear system Ax = b?How is cond(A) related to det A?

Consider the linear equation Y^{\prime}(x)=\lambda Y(x)+(1-\lambda) \cos (x)-(1+\lambda) \sin (x), q u a d Y(0)=1 The true solution is Y (x) = sin(x)+cos(x). Solve this problem using Euler's method with several values of A and h, for 0 < x < 10. Comment on the results. a) = -1: h = 0.5.0. 25. 0.125. )\= 1; h = 0.5, 0.25, 0.125 \ = -5; h = 0.5, 0.25, 0.125, 0.0625II 1) A = 5; h = 0.0625

39. If your car gets 32 miles per gallon, how much does it cost you to drive 30 miles when gasoline costs $2.55 per gallon?

14) A community college student interviews everyone in a statistics class to determine the percentage of students that own a car.

In Probs. 33-36 find the transform. In Probs. 37-45 find the inverse transform. Show the details of your work. \text { 35. } 0.5 e^{-4.5 t} \sin 2 \pi t

Use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class. 15) Phone Calls (per day)

An internet research company surveyed 85 online shoppers, each of whom made one purchase today. The company recorded the type of purchase each shopper made. Here is a summary. Three shoppers from the survey are selected at random, one at a time without replacement. What is the probability that none of the three shoppers purchased electronics?

In order to make a pumpkin pie I need 5 pumpkins.If p is the number of pies I want to make and P(p)is the number of pumpkins I need. A reasonable function for this is a. P(p) =10pb. P(p)=5p+1c. P(p) =6pd. P(p)=5p