EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 26, Problem 11P
Develop a user-friendly program for the non-self-starting Heun method with a predictor modifier. Employ a fourth-order RK method to compute starter values. Test the program by duplicating Example 26.4.
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7.
Suppose that X is a set, that I is a nonempty set, and that for each i Є I that Yi
is a set. Suppose that I is a nonempty set. Prove the following:2
(a) If Y; CX for all i EI, then Uiel Yi C X.
¹See Table 4.8.1 in zyBooks.
Recall:
Nie X₁ = Vi Є I (x = X₁) and x = Uier X₁ = i Є I (x Є Xi).
(b) If XCY; for all i Є I, then X Ciel Yi.
(c) U(x)=xnUY.
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8.
For each of the following functions, determine whether or not it is (i) injective
and/or (ii) surjective. Justify why or why not.
(a) fiZZ defined by fi(n) = 2n.
(b) f2 RR defined by f2(x) = x² − 4x+7.
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(c) f3 Z {0, 1} defined by f3(n) = 0 if n is even and f3(n) = 1 if n is odd.
(d) f4 Z N defined by f4(n) = 2n if n > 0 and f4(n) = -2n-1 if n < 0.
Chapter 26 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 26 - Given dydx=200,000y+200,000exex (a) Estimate the...Ch. 26 - Given dydx=30(costy)+3sint If y(0)=1, use the...Ch. 26 - 26.3 Given
If, obtain a solution from using a...Ch. 26 - Solve the following initial-value problem over the...Ch. 26 - Repeat Prob. 26.4, but use the fourth-order Adams...Ch. 26 - Solve the following initial-value problem from...Ch. 26 - Solve the following initial-value problem from...Ch. 26 - Solve the following initial-value problem from...Ch. 26 - Develop a program for the implicit Euler method...Ch. 26 - 26.10 Develop a program for the implicit Euler...
Ch. 26 - Develop a user-friendly program for the...Ch. 26 - 26.12 Use the program developed in Prob. 26.11 to...Ch. 26 - 26.13 Consider the thin rod of length l moving in...Ch. 26 - Given the first-order ODE dxdt=700x1000etx(t=0)=4...Ch. 26 - 26.15 The following second-order ODE is...Ch. 26 - 26.16 Solve the following differential equation...
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