- 11-188.8.131.52: Use the Nonlinear Finite-Difference method with h = 0.5 to approxim...
- 11-184.108.40.206: Use the Nonlinear Finite-Difference method with h = 0.25 to approxi...
- 11-220.127.116.11: Use the Nonlinear Finite-Difference Algorithm with TOL = 104 to app...
- 11-18.104.22.168: Use the Nonlinear Finite-Difference Algorithm with TOL = 104 to app...
- 11-22.214.171.124: Repeat Exercise 4(a) and 4(b) using extrapolation.
- 11-126.96.36.199: In Exercise 7 of Section 11.3, the deflection of a beam with suppor...
- 11-188.8.131.52: Show that the hypotheses listed at the beginning of the section ens...
Solutions for Chapter 11-4: Finite-Difference Methods for Nonlinear Problems
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
Composition of functions
(f ? g) (x) = f (g(x))
De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)
equation of a parabola
(x - h)2 = 4p(y - k) or (y - k)2 = 4p(x - h)
Sum of a finite number of terms.
The line through the focus and perpendicular to the directrix of a conic.
Reciprocal of the period of a sinusoid.
See Component form of a vector.
Connected subset of the real number line with at least two points, p. 4.
Line of symmetry
A line over which a graph is the mirror image of itself
Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.
A polynomial with exactly one term.
A distribution of data shaped like the normal curve.
Permutations of n objects taken r at a time
There are nPr = n!1n - r2! such permutations
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.
Quadratic equation in x
An equation that can be written in the form ax 2 + bx + c = 01a ? 02
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).
Zeros of a function that are rational numbers.
Re-expression of data
A transformation of a data set.
Reflection through the origin
x, y and (-x,-y) are reflections of each other through the origin.
Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n - 12d4,