 5.6.1: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.2: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.3: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.4: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.5: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.6: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.7: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.8: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.9: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.10: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.11: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.12: In each of 1 through 12: (a) Find all the regular singular points o...
 5.6.13: In each of 13 through 17: (a) Show that x = 0 is a regular singular...
 5.6.14: In each of 13 through 17: (a) Show that x = 0 is a regular singular...
 5.6.15: In each of 13 through 17: (a) Show that x = 0 is a regular singular...
 5.6.16: In each of 13 through 17: (a) Show that x = 0 is a regular singular...
 5.6.17: In each of 13 through 17: (a) Show that x = 0 is a regular singular...
 5.6.18: (a) Show that (ln x)y + 1 2 y + y = 0 has a regular singular point ...
 5.6.19: In several problems in mathematical physics it is necessary to stud...
 5.6.20: Consider the differential equation x3 y + xy + y = 0, where and are...
 5.6.21: Consider the differential equation y + xs y + xt y = 0, (i) where =...
Solutions for Chapter 5.6: Series Solutions Near a Regular Singular Point, Part II
Full solutions for Elementary Differential Equations and Boundary Value Problems  9th Edition
ISBN: 9780470383346
Solutions for Chapter 5.6: Series Solutions Near a Regular Singular Point, Part II
Get Full SolutionsChapter 5.6: Series Solutions Near a Regular Singular Point, Part II includes 21 full stepbystep solutions. This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 9. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9780470383346. Since 21 problems in chapter 5.6: Series Solutions Near a Regular Singular Point, Part II have been answered, more than 13261 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.