- 11-22.214.171.124: The boundary-value problem y = 4(y x), 0 x 1, y(0) = 0, y(1) = 2 ha...
- 11-126.96.36.199: The boundary-value problem y = y + 2y + cos x, 0 x 2 , y(0) = 0.3, ...
- 11-188.8.131.52: Use the Linear Finite-Difference Algorithm to approximate the solut...
- 11-184.108.40.206: Although q(x) < 0 in the following boundary-value problems, unique ...
- 11-220.127.116.11: Use the Linear Finite-Difference Algorithm to approximate the solut...
- 11-18.104.22.168: Repeat Exercise 3(a) and (b) using the extrapolation discussed in E...
- 11-22.214.171.124: The lead example of this chapter concerned the deflection of a beam...
- 11-126.96.36.199: The deflection of a uniformly loaded, long rectangular plate under ...
- 11-188.8.131.52: Prove Theorem 11.3. [Hint: To use Theorem 6.29, first show that h 2...
- 11-184.108.40.206: Show that if y C6[a, b] and if w0, w1,... ,wN+1 satisfy Eq. (11.18)...
Solutions for Chapter 11-3: Finite-Difference Methods for Linear Problems
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.
a + b = b + a ab = ba
A sample that sacrifices randomness for convenience
See Cartesian coordinate system.
Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)
The gathering and processing of numerical information
Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis
A procedure for fitting an exponential function to a set of data.
See Component form of a vector.
The complex number.
Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible
Angle measure equal to 1/60 of a degree.
One-to-one rule of logarithms
x = y if and only if logb x = logb y.
Two vectors u and v with u x v = 0.
Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i
Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.
The function that associates points on the unit circle with points on the real number line
Zero factor property
If ab = 0 , then either a = 0 or b = 0.
Zero of a function
A value in the domain of a function that makes the function value zero.