 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 boundaryvalue p...
 11.4.8: (a) Find the eigenvalues and eigenfunctions of the boundaryvalue 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 SturmLiouville 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 SturmLiouville 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: SturmLiouville Problem
Full solutions for Differential Equations with BoundaryValue Problems  7th Edition
ISBN: 9780495108368
Solutions for Chapter 11.4: SturmLiouville Problem
Get Full SolutionsThis textbook survival guide was created for the textbook: Differential Equations with BoundaryValue Problems, edition: 7. Differential Equations with BoundaryValue Problems was written by and is associated to the ISBN: 9780495108368. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.4: SturmLiouville Problem includes 15 full stepbystep solutions. Since 15 problems in chapter 11.4: SturmLiouville Problem have been answered, more than 15958 students have viewed full stepbystep solutions from this chapter.

Combination
An arrangement of elements of a set, in which order is not important

Common ratio
See Geometric sequence.

Compounded monthly
See Compounded k times per year.

Conditional probability
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)

Directed distance
See Polar coordinates.

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Fivenumber summary
The minimum, first quartile, median, third quartile, and maximum of a data set.

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Identity function
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.

Logarithm
An expression of the form logb x (see Logarithmic function)

Logarithmic form
An equation written with logarithms instead of exponents

Measure of spread
A measure that tells how widely distributed data are.

Parallel lines
Two lines that are both vertical or have equal slopes.

Slant line
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.