- 11-188.8.131.52: The boundary-value problem y = 4(y x), 0 x 1, y(0) = 0, y(1) = 2, h...
- 11-184.108.40.206: The boundary-value problem y = y + 2y + cos x, 0 x 2 , y(0) = 0.3, ...
- 11-220.127.116.11: Use the Linear Shooting method to approximate the solution to the f...
- 11-18.104.22.168: Although q(x) < 0 in the following boundary-value problems, unique ...
- 11-22.214.171.124: Use the Linear Shooting Algorithm to approximate the solution y = e...
- 11-126.96.36.199: Write the second-order initial-value problems (11.3) and (11.4) as ...
- 11-188.8.131.52: Let u represent the electrostatic potential between two concentric ...
- 11-184.108.40.206: Show that, under the hypothesis of Corollary 11.2, if y2 is the sol...
- 11-220.127.116.11: Consider the boundary-value problem y + y = 0, 0 x b, y(0) = 0, y(b...
- 11-18.104.22.168: Attempt to apply Exercise 9 to the boundary-value problem y y = 0, ...
Solutions for Chapter 11-1: The Linear Shooting Method
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
See Inverse cosecant function.
A logarithm with base 10.
Completing the square
A method of adding a constant to an expression in order to form a perfect square
The gathering and processing of numerical information
Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.
Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.
Inverse tangent function
The function y = tan-1 x
An equation written with logarithms instead of exponents
Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.
The number zero on a number line, or the point where the x- and y-axes cross in the Cartesian coordinate system, or the point where the x-, y-, and z-axes cross in Cartesian three-dimensional space
Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.
See Sequence of partial sums.
Quotient rule of logarithms
logb a R S b = logb R - logb S, R > 0, S > 0
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).
An expression that can be written as a ratio of two polynomials.
Any number that can be written as a decimal.
The difference y1 - (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.
A plot of all the ordered pairs of a two-variable data set on a coordinate plane.
Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.
Vertices of an ellipse
The points where the ellipse intersects its focal axis.