
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Textbook Question
Chapter 5.4, Problem 2CP
Modify the MATLAB code for Adaptive Trapezoid Rule Quadrature to use Simpsons Rule instead, applying the criterion (5.42) with the 15 replaced by 10. Approximate the
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Chapter 5 Solutions
Numerical Analysis
Ch. 5.1 - Use the two-point forward-difference formula to...Ch. 5.1 - Use the three-point centered-difference formula to...Ch. 5.1 - Use the two-point forward-difference formula to...Ch. 5.1 - Carry out the steps of Exercise 3, using the...Ch. 5.1 - Use the three-point centered-difference formula...Ch. 5.1 - Use the three-point centered-difference formula...Ch. 5.1 - Develop a formula for a two-point...Ch. 5.1 - Prove the second-order formula for the first...Ch. 5.1 - Develop a second-order formula for the first...Ch. 5.1 - Find the error term and order formula for the...
Ch. 5.1 - Find a second-order formula for approximating by...Ch. 5.1 - (a) Compute the two-point forward-difference...Ch. 5.1 - Develop a second-order method for approximating ...Ch. 5.1 - Extrapolate the formula developed in Exercise...Ch. 5.1 - Develop a first-order method for approximating ...Ch. 5.1 - Apply extrapolation to the formula developed in...Ch. 5.1 - Develop a second-order method for approximating ...Ch. 5.1 - Find, an upper bound for the error of the machine...Ch. 5.1 - Prove the second-order formula for the third...Ch. 5.1 - Prove the second-order formula for the third...Ch. 5.1 - Prob. 21ECh. 5.1 - This exercise justifies the beam equations (2.33)...Ch. 5.1 - Use Taylor expansions to prove that (5.16) is a...Ch. 5.1 - Prob. 24ECh. 5.1 - Investigate the reason for the name extrapolation....Ch. 5.1 - Make a table of the error of the three-point...Ch. 5.1 - Make a table and plot of the error of the...Ch. 5.1 - Make a table and plot of the error of the...Ch. 5.1 - Prob. 4CPCh. 5.1 - Prob. 5CPCh. 5.2 - Apply the composite Trapezoid Rule with , , and 4...Ch. 5.2 - Apply the Composite Midpoint Rule with, , and 4...Ch. 5.2 - Apply the composite Simpson’s Rule with, 2, and 4...Ch. 5.2 - Apply the composite Simpson’s Rule with, 2, and 4...Ch. 5.2 - Apply the Composite Midpoint Rule with, 2, and 4...Ch. 5.2 - Apply the Composite Midpoint Rule with, 2, and 4...Ch. 5.2 - Prob. 7ECh. 5.2 - Apply the open Newton-Cotes Rule (5.28) to...Ch. 5.2 - Apply Simpson’s Rule approximation to, and show...Ch. 5.2 - Integrate Newton’s divided-difference...Ch. 5.2 - Find the degree of precision of the following...Ch. 5.2 - Prob. 12ECh. 5.2 - Develop a composite version of the rule (5.28),...Ch. 5.2 - Prove the Composite Midpoint Rule (5.27).
Ch. 5.2 - Find the degree of precision of the degree four...Ch. 5.2 - Use the fact that the error term of Boole’s Rule...Ch. 5.2 - Prob. 17ECh. 5.2 - Prob. 1CPCh. 5.2 - Prob. 2CPCh. 5.2 - Prob. 3CPCh. 5.2 - Prob. 4CPCh. 5.2 - Prob. 5CPCh. 5.2 - Prob. 6CPCh. 5.2 - Apply the Composite Midpoint Rule to the improper...Ch. 5.2 - The arc length of the curve defined by from to ...Ch. 5.2 - Prob. 9CPCh. 5.2 - Prob. 10CPCh. 5.3 - Apply Romberg Integration to find for the...Ch. 5.3 - Apply Romberg Integration to find for the...Ch. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prove formula (5.31).
Ch. 5.3 - Prove formula (5.35).
Ch. 5.3 - Use Romberg Integration approximation to...Ch. 5.3 - Use Romberg Integration to approximate the...Ch. 5.3 - (a) Test the order of the second column of Romberg...Ch. 5.4 - Apply Adaptive Quadrature by hand, using the...Ch. 5.4 - Apply Adaptive Quadrature by hand, using Simpson’s...Ch. 5.4 - Prob. 3ECh. 5.4 - Develop an Adaptive Quadrature method for rule...Ch. 5.4 - Use Adaptive Trapezoid Quadrature to approximate...Ch. 5.4 - Modify the MATLAB code for Adaptive Trapezoid Rule...Ch. 5.4 - Carry out the steps of Computer Problem 1 for...Ch. 5.4 - Carry out the steps of Computer Problem 1 for the...Ch. 5.4 - Carry out the steps of Computer Problem 1 for the...Ch. 5.4 - Use Adaptive Trapezoid Quadrature to approximate...Ch. 5.4 - Carry out the steps of Problem 6, using Adaptive...Ch. 5.4 - The probability within standard deviations of the...Ch. 5.4 - Write a MATLAB function called myerf.m that uses...Ch. 5.5 - Approximate the integrals, using Gaussian...Ch. 5.5 - Prob. 2ECh. 5.5 - Approximate the integrals in Exercise 1, using ...Ch. 5.5 - Change variables, using the substitution (5.46) to...Ch. 5.5 - Approximate the integrals in Exercise 4, using ...Ch. 5.5 - Approximate the integrals, using Gaussian...Ch. 5.5 - Prob. 7ECh. 5.5 - Find the Legendre polynomials up to degree 3 and...Ch. 5.5 - Prob. 9ECh. 5.5 - Verify the coefficients and in Table 5.1 for...Ch. 5.5 - Write a MATLAB function that uses Adaptive...Ch. 5.5 - Write a program that, for any input between 0 and...Ch. 5.5 - Equipartition the path of Figure 5.6 into ...Ch. 5.5 - Prob. 4SACh. 5.5 - Prob. 5SACh. 5.5 - Prob. 6SACh. 5.5 - Write a program that traverses the path according...
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- Q4: Discuss the stability critical point of the ODES x + sin(x) = 0 and draw phase portrait.arrow_forwardUsing Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates). HINT: Pay closeattention to both the 1’s and the 0’s of the function.arrow_forwardRecall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)arrow_forward
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