| № |
Condition |
free/or 0.5$ |
| m54121 | For each of the following matrices determine if it diagonalizable and, if so, find P and D with A = PDP−1.
a.
b.
c.
d. |
buy |
| m54169 | For the Adams-Bashforth and Adams-Moulton methods of order four,
a. Show that if f = 0, then
F(ti , h,wi+1, . . . ,wi+1−m) = 0.
b. Show that if f satisfies a Lipschitz condition with constant L, then a constant C exists with |
buy |
| m54176 | For the following initial-value problems, show that the given equation implicitly defines a solution. Approximate y(2) using Newton s method.
a. y = − y3 + y/((3y2 + 1)t) , 1≤ t ≤ 2, y(1) = 1; y3t + yt = 2
b. y = − (y cos t + 2tey)/(sin t + t2ey + 2) , 1≤ t ≤ 2, y(1) = 0; y sin t + t2ey + 2y = 1 |
buy |
| m54185 | For the given functions f (x), let x0 = 0, x1 = 0.6, and x2 = 0.9. Construct interpolation polynomials of degree at most one and at most two to approximate f (0.45), and find the absolute error.
a. f (x) = cos x
b. f (x) = √1 + x
c. f (x) = ln(x + 1)
d. f (x) = tan x |
buy |
| m54186 | For the given functions f (x), let x0 = 1, x1 = 1.25, and x2 = 1.6. Construct interpolation polynomials of degree at most one and at most two to approximate f (1.4), and find the absolute error.
a. f (x) = sin πx
b. f (x) = 3√(x - 1)
c. f (x) = log10(3x − 1)
d. f (x) = e2x - x |
buy |
| m54191 | For the matrices in Exercise 1 that have 3 linearly independent eigenvectors form the factorization A = PDP−1. |
buy |
| m54192 | For the matrices in Exercise 2 that have 3 linearly independent eigenvectors form the factorization A = PDP−1.
a.
b.
c.
d. |
buy |
| m54229 | Gauss-Jordan Method: This method is described as follows. Use the ith equation to eliminate not only xi from the equations Ei+1, Ei+2, . . . , En, as was done in the Gaussian elimination method, but also from E1, E2, . . . , Ei−1. Upon reducing [A, b] to: |
buy |
| m54240 | Given
Pn(x) = f [x0] + f [x0, x1](x − x0) + a2(x − x0)(x − x1)
+ a3(x − x0)(x − x1)(x − x2)+· · ·
+ an(x − x0)(x − x1) · · · (x − xn−1),
use Pn(x2) to show that a2 = f [x0, x1, x2]. |
buy |
| m54244 | Given the data:
a. Construct the least squares polynomial of degree 1, and compute the error.
b. Construct the least squares polynomial of degree 2, and compute the error.
c. Construct the least squares polynomial of degree 3, and compute the error.
d. Construct the least squares approximation of the form beax, and compute the error.
e. Construct the least squares approximation of the form bxa, and compute the error. |
buy |
| m54245 | Given the data
a. Use the singular value decomposition technique to determine the least squares polynomial of degree 1.
b. Use the singular value decomposition technique to determine the least squares polynomial of degree 2. |
buy |
| m54246 | Given the data
a. Use the singular value decomposition technique to determine the least squares polynomial of degree 2.
b. Use the singular value decomposition technique to determine the least squares polynomial of degree 3. |
buy |
| m54248 | Given the function f at the following values,
Approximate
Using all the appropriate quadrature formulas of this section |
buy |
| m54249 | Given the initial-value problem
y = 1/t2 - y/t − y2, 1≤ t ≤ 2, y(1) = −1, |
buy |
| m54250 | Given the initial-value problem
y = 1/t2 - y/t − y2, 1≤ t ≤ 2, y(1) = −1, |
buy |
| m54251 | Given the initial-value problem
y = 2/t y + t2et, 1≤ t ≤ 2, y(1) = 0, |
buy |
| m54252 | Given the initial-value problem
y = 2/t y + t2et, 1≤ t ≤ 2, y(1) = 0, |
buy |
| m54253 | Given the initial-value problem
y = −y + t + 1, 0 ≤ t ≤ 5, y(0) = 1, |
buy |
| m54254 | Given the linear system
2x1 − 6αx2 = 3,
3αx1 − x2 = 3/2 |
buy |
| m54255 | Given the linear system
x1 − x2 + αx3 = −2,
−x1 + 2x2 − αx3 = 3,
αx1 + x2 + x3 = 2 |
buy |