- 4-126.96.36.199: Approximate the following integrals using Gaussian quadrature with ...
- 4-188.8.131.52: Repeat Exercise 1 with n = 3.
- 4-184.108.40.206: Repeat Exercise 1 with n = 4.
- 4-220.127.116.11: Repeat Exercise 1 with n = 5.
- 4-18.104.22.168: Determine constants a, b, c, and d that will produce a quadrature f...
- 4-22.214.171.124: Determine constants a, b, c, and d that will produce a quadrature f...
- 4-126.96.36.199: Verify the entries for the values of n = 2 and 3 in Table 4.11 by f...
- 4-188.8.131.52: Show that the formula Q(P) = n i=1 ci P(xi) cannot have degree of p...
Solutions for Chapter 4-7: Gaussian Quadrature
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
Basic logistic function
The function ƒ(x) = 1 / 1 + e-x
An interval that includes its endpoints
The probability of an event A given that an event B has already occurred
The factor Ae-a in an equation such as y = Ae-at cos bt
Difference of functions
(ƒ - g)(x) = ƒ(x) - g(x)
See Polar coordinates.
Elements of a matrix
See Matrix element.
equation of a hyperbola
(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1
equation of a parabola
(x - h)2 = 4p(y - k) or (y - k)2 = 4p(x - h)
A function whose domain is the first n positive integers for some fixed integer n.
The line through the focus and perpendicular to the directrix of a conic.
A distribution of data shaped like the normal curve.
See Periodic function.
Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.
Real part of a complex number
See Complex number.
Reflection across the y-axis
x, y and (-x,y) are reflections of each other across the y-axis.
If a polynomial f(x) is divided by x - c , the remainder is ƒ(c)
Semiperimeter of a triangle
One-half of the sum of the lengths of the sides of a triangle.
A matrix whose number of rows equals the number of columns.
A letter that represents an unspecified number.