- 15.1: Consider the boundary-value problem Approximate the solution of the...
- 15.2: Solve using mesh size . Use GaussSeidel iteration.
- 15.3: Consider the boundary-value problem (a) Note that the initial tempe...
Solutions for Chapter 15: NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS
Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined
See Geometric sequence.
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable
De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)
Divisor of a polynomial
See Division algorithm for polynomials.
Elements of a matrix
See Matrix element.
Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.
Inverse tangent function
The function y = tan-1 x
Real numbers that are not rational, p. 2.
The diagonal from the top left to the bottom right of a square matrix
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior
A set of n objects.
An arrangement of elements of a set, in which order is important.
See Polar coordinate system.
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u
Zeros of a function that are rational numbers.
Reflection through the origin
x, y and (-x,-y) are reflections of each other through the origin.
The points (0, y, z) in Cartesian space.