- 11.4.1: In 1 and 2 find the eigenfunctions and the equation that defines th...
- 11.4.2: In 1 and 2 find the eigenfunctions and the equation that defines th...
- 11.4.3: Consider y ly 0 subject to y(0) 0, y(L) 0. Show that the eigenfunct...
- 11.4.4: Consider y ly 0 subject to the periodic boundary conditions y(L) y(...
- 11.4.5: Find the square norm of each eigenfunction in 1.
- 11.4.6: Show that for the eigenfunctions in Example 2, 'sin a .
- 11.4.7: (a) Find the eigenvalues and eigenfunctions of the boundary-value p...
- 11.4.8: (a) Find the eigenvalues and eigenfunctions of the boundary-value p...
- 11.4.9: Laguerres differential equation xy (1 x)y ny 0, n 0, 1, 2, . . . ha...
- 11.4.10: Hermites differential equation y 2xy 2ny 0, n 0, 1, 2, . . . has po...
- 11.4.11: Consider the regular Sturm-Liouville problem: . (a) Find the eigenv...
- 11.4.12: (a) Find the eigenfunctions and the equation that defines the eigen...
- 11.4.13: Consider the special case of the regular Sturm-Liouville problem on...
- 11.4.14: (a) Give an orthogonality relation for the SturmLiouville problem i...
- 11.4.15: (a) Give an orthogonality relation for the SturmLiouville problem i...
Solutions for Chapter 11.4: Sturm-Liouville Problem
Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition
An arrangement of elements of a set, in which order is not important
See Geometric sequence.
See Compounded k times per year.
The probability of an event A given that an event B has already occurred
Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S
De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)
Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)
See Polar coordinates.
Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.
The minimum, first quartile, median, third quartile, and maximum of a data set.
The area of ¢ABC with semiperimeter s is given by 2s1s - a21s - b21s - c2.
The function ƒ(x) = x.
Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.
Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.
An expression of the form logb x (see Logarithmic function)
An equation written with logarithms instead of exponents
Measure of spread
A measure that tells how widely distributed data are.
Two lines that are both vertical or have equal slopes.
A line that is neither horizontal nor vertical
Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.