 5.2.1: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.2: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.3: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.4: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.5: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.6: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.7: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.8: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.9: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.10: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.11: In each of 1 through 11: a. Seek power series solutions of the give...
 5.2.12: In each of 12 through 14: a. Find the first five nonzero terms in t...
 5.2.13: In each of 12 through 14: a. Find the first five nonzero terms in t...
 5.2.14: In each of 12 through 14: a. Find the first five nonzero terms in t...
 5.2.15: a. By making the change of variable x 1 = t and assuming that y has...
 5.2.16: Prove equation (10).
 5.2.17: Show directly, using the ratio test, that the two series solutions ...
 5.2.18: The Hermite Equation. The equation y__ 2xy_ + y = 0, < x < , where ...
 5.2.19: Consider the initialvalue problem y_ =_1 y2, y(0) = 0. a. Show tha...
 5.2.20: In each of 20 through 23, plot several partial sums in a series sol...
 5.2.21: In each of 20 through 23, plot several partial sums in a series sol...
 5.2.22: In each of 20 through 23, plot several partial sums in a series sol...
 5.2.23: In each of 20 through 23, plot several partial sums in a series sol...
Solutions for Chapter 5.2: Series Solutions Near an Ordinary Point, Part I
Full solutions for Elementary Differential Equations and Boundary Value Problems  11th Edition
ISBN: 9781119256007
Solutions for Chapter 5.2: Series Solutions Near an Ordinary Point, Part I
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.2: Series Solutions Near an Ordinary Point, Part I includes 23 full stepbystep solutions. Since 23 problems in chapter 5.2: Series Solutions Near an Ordinary Point, Part I have been answered, more than 12655 students have viewed full stepbystep solutions from this chapter. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9781119256007. This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 11.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib IIĀ· Condition numbers measure the sensitivity of the output to change in the input.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

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.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Iterative method.
A sequence of steps intended to approach the desired solution.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.