Homework Answers
Add Answer to:
Part 1: First, let's explore the Simpson's Rule formula itself: This formula has a very distincti...
1. Simpson's rule. Simpson's rule is a different formula for numerical integration of lºf (d.x which...
1. Simpson's rule. Simpson's rule is a different formula for numerical integration of lºf (d.x which is based on approximating f(2) with a piecewise quadratic function. We will now derive Simpson's rule and relate it to Romberg integration: a. Suppose that (2) is a quadratic polynomial so that q(-h) = f(-h), q0) = f(0) and q(h) = f(h). Prove that 92 f(-h) + 4f(0) + f(h)). -h b. Suppose that the interval [a, b] is divided by a = 20,...
Task 3 - Simpson's Rule (Maximum Mark 15) Find the equation the quadratic y = ax?...
Task 3 - Simpson's Rule (Maximum Mark 15) Find the equation the quadratic y = ax? + bx + c which passes through the points AC-h, Y.), B(0,y), and C(h.yc). Use your quadratic to find an expression for the area under the quadratic between the points A and C. Explaining carefully how your result can be used to prove the general formula for Simpson's Rule. Notes: . You will need to research independently to find the formula for Simpson's Rule....
Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the...
Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points A(Y) and (.ya) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: • This part of the assignment is testing that you can find the equation of a line and use this to derive other formulae. Marking Criteria...
HICULTUULUULULUI 2 Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line...
HICULTUULUULULUI 2 Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points 1 - ...) a | and B(x) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: . This part of the assignment is testing that you can find the equation of a line and use this...
MATLAB Create a function that provides a definite integration using Simpson's Rule Problem Summar This example demo...
MATLAB Create a function that provides a definite integration
using Simpson's Rule
Problem Summar This example demonstrates using instructor-provided and randomized inputs to assess a function problem. Custom numerical tolerances are used to assess the output. Simpson's Rule approximates the definite integral of a function f(x) on the interval a,a according to the following formula + f (ati) This approximation is in general more accurate than the trapezoidal rule, which itself is more accurate than the leftright-hand rules. The increased...
In this exercise we consider finding the first five coefficients in the series solution of the first order linear initial value problem (+3)y' 2y 0 subject to the initial condition y(0) 1. Si...
In this exercise we consider finding the first five coefficients in the series solution of the first order linear initial value problem (+3)y' 2y 0 subject to the initial condition y(0) 1. Since the equation has an ordinary point at z 0 it has a power series solution in the form We learned how to easily solve problems like this separation of variables but here we want to consider the power series method (1) Insert the formal power series into...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr whic...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
Short Answer Questions 1. A bumper sticker reads: “Remember: Pillage first, then burn.” How does the...
Short Answer Questions 1. A bumper sticker reads: “Remember: Pillage first, then burn.” How does the humor of this sticker illustrate the idea of maximization? 2. “Anything worth doing is worth doing well.” Comment from an economics point of view. 3. You have probably heard it said “The grass is always greener on the other side of the fence.” Presumably this means we always want things we don’t have. Indeed, the Hebrew 10th Commandment says “Do not covet (want) your...
Please do exercise 129: Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N...
Please do exercise 129:
Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N → N be the unique function that satisfies f(0) = 2 and f(next(n)) =r(f(n)) for all n E N. 102 1. Prove that f(3) = 8. 2. Prove that 2 <f(n) for all n E N. Exercise 129: Define r and f as in Exercise 128. Assume that x + y. Define r' = {(x,y),(y,x)}. Let g:N + {x,y} be the unique function that...
1. What is the outcome of this case? (Guilty, not guilty, acquitted, etc.) (2-3 sentences) 2....
1. What is the outcome of this case? (Guilty, not guilty, acquitted, etc.) (2-3 sentences) 2. What is the author's basis of dissent OR basis or support for upholding the opinion of the court? (1 full paragraph) 3. How does this judicial opinion (and general case) increase your understanding of what has been learned/discussed during this time period of the class and the events within it? Explain how this case is historically significant to what we have learned. (I full...
1. Simpson's rule. Simpson's rule is a different formula for numerical integration of lºf (d.x which is based on approximating f(2) with a piecewise quadratic function. We will now derive Simpson's rule and relate it to Romberg integration: a. Suppose that (2) is a quadratic polynomial so that q(-h) = f(-h), q0) = f(0) and q(h) = f(h). Prove that 92 f(-h) + 4f(0) + f(h)). -h b. Suppose that the interval [a, b] is divided by a = 20,...
Task 3 - Simpson's Rule (Maximum Mark 15) Find the equation the quadratic y = ax? + bx + c which passes through the points AC-h, Y.), B(0,y), and C(h.yc). Use your quadratic to find an expression for the area under the quadratic between the points A and C. Explaining carefully how your result can be used to prove the general formula for Simpson's Rule. Notes: . You will need to research independently to find the formula for Simpson's Rule....
Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points A(Y) and (.ya) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: • This part of the assignment is testing that you can find the equation of a line and use this to derive other formulae. Marking Criteria...
HICULTUULUULULUI 2 Task 2 - Trapezium Rule (Maximum Mark 10) Find the equation of the line through the points 1 - ...) a | and B(x) and find an expression for the area under this line between the points A and B. Explain carefully how your result can be used to prove the general formula for the Trapezium Rule. Notes: . This part of the assignment is testing that you can find the equation of a line and use this...
MATLAB Create a function that provides a definite integration
using Simpson's Rule
Problem Summar This example demonstrates using instructor-provided and randomized inputs to assess a function problem. Custom numerical tolerances are used to assess the output. Simpson's Rule approximates the definite integral of a function f(x) on the interval a,a according to the following formula + f (ati) This approximation is in general more accurate than the trapezoidal rule, which itself is more accurate than the leftright-hand rules. The increased...
In this exercise we consider finding the first five coefficients in the series solution of the first order linear initial value problem (+3)y' 2y 0 subject to the initial condition y(0) 1. Since the equation has an ordinary point at z 0 it has a power series solution in the form We learned how to easily solve problems like this separation of variables but here we want to consider the power series method (1) Insert the formal power series into...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
Please do exercise 129:
Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N → N be the unique function that satisfies f(0) = 2 and f(next(n)) =r(f(n)) for all n E N. 102 1. Prove that f(3) = 8. 2. Prove that 2 <f(n) for all n E N. Exercise 129: Define r and f as in Exercise 128. Assume that x + y. Define r' = {(x,y),(y,x)}. Let g:N + {x,y} be the unique function that...
Most questions answered within 3 hours.
-
Phosphorous + bromine = phosphorous tribromide. If 35.0 g of
bromine are reacted and 27.9 grams...
asked 1 hour ago -
Derive the long wavelength limit of the Planck energy density
distribution
asked 58 minutes ago -
Calculate the pH of each of the following solutions.
0.50 M HBr
3.1×10−4 M KOH
4.2×10−5...
asked 4 hours ago -
For the year ended December 31, Depot Max’s cost of merchandise
sold was $85,600. Inventory at the...
asked 4 hours ago -
Week 10 - Professional Memo Assignment
Professional Memo Assignment
Your mission for this week, should you...
asked 4 hours ago -
Write a Python program that stores the data for each
player on the team, and it...
asked 4 hours ago -
In
the last 3 months, mike never knows when he is going to get his
allowance...
asked 5 hours ago -
Is Ca(OH)2 a Bronsted base, Lewis base, or both? Why?
asked 5 hours ago -
1A- Why don’t voters complain about U.S. tariffs on imported
sugar?
Because sugar is only a...
asked 5 hours ago -
Cash Payback Period
Primera Banco is evaluating two capital investment proposals for
a drive-up ATM kiosk,...
asked 5 hours ago -
Create a button in Swift (Xcode) that will create a charge,
create a charge using Stripe's...
asked 5 hours ago -
The reaction rate of CO and NO2 in the reaction
CO(g) + NO2(g) → CO2(g) +...
asked 5 hours ago