- 13.1: Find the steady-state temperature u(r, u) in a circular plate of ra...
- 13.2: Find the steady-state temperature in the circular plate in if
- 13.3: Find the steady-state temperature u(r, u) in a semicircular plate o...
- 13.4: Find the steady-state temperature u(r, u) in the semicircular plate...
- 13.5: Find the steady-state temperature u(r, u) in the plate shown in Fig...
- 13.6: Find the steady-state temperature u(r, u) in the infinite plate sho...
- 13.7: Suppose heat is lost from the flat surfaces of a very thin circular...
- 13.8: Suppose xk is a positive zero of J0. Show that a solution of the bo...
- 13.9: Find the steady-state temperature u(r, z) in the cylinder in Figure...
- 13.10: Solve the boundary-value problem
- 13.11: Find the steady-state temperature u(r, u) in a sphere of unit radiu...
- 13.12: Solve the boundary-value problem [Hint: Proceed as in 9 and 10 in E...
- 13.13: The function u(x) Y0(aa)J0(ax) J0(aa)Y0(ax), a 0 is a solution of t...
- 13.14: Use the results of to solve the following boundary-value problem fo...
- 13.15: Discuss how to solve with the boundary conditions given in Figure 1...
Solutions for Chapter 13: BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS
Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once
a + b = b + a ab = ba
Complements or complementary angles
Two angles of positive measure whose sum is 90°
Variable representing the range value of a function (usually y)
A number that is associated with a square matrix
Using the science of statistics to make inferences about the parameters in a population from a sample.
Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the left-hand endpoint of each subinterval
An arrangement of elements of a set, in which order is important.
A procedure for fitting a curve y = a . x b to a set of data.
See Division algorithm for polynomials.
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.
Reciprocal of a real number
See Multiplicative inverse of a real number.
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the x-axis, and a perpendicular dropped from a point on the terminal side to the x-axis. The angle in a reference triangle at the origin is the reference angle
Reflexive property of equality
a = a
Ratio change in y/change in x
A matrix whose number of rows equals the number of columns.