 3.10.1: In 16, proceed as in Example 1 to find a particular solution yp(x) ...
 3.10.2: In 16, proceed as in Example 1 to find a particular solution yp(x) ...
 3.10.3: In 16, proceed as in Example 1 to find a particular solution yp(x) ...
 3.10.4: In 16, proceed as in Example 1 to find a particular solution yp(x) ...
 3.10.5: In 16, proceed as in Example 1 to find a particular solution yp(x) ...
 3.10.6: In 16, proceed as in Example 1 to find a particular solution yp(x) ...
 3.10.7: In 712, proceed as in Example 2 to find the general solution of the...
 3.10.8: In 712, proceed as in Example 2 to find the general solution of the...
 3.10.9: In 712, proceed as in Example 2 to find the general solution of the...
 3.10.10: In 712, proceed as in Example 2 to find the general solution of the...
 3.10.11: In 712, proceed as in Example 2 to find the general solution of the...
 3.10.12: In 712, proceed as in Example 2 to find the general solution of the...
 3.10.13: In 1318, proceed as in Example 3 to find the solution of the given ...
 3.10.14: In 1318, proceed as in Example 3 to find the solution of the given ...
 3.10.15: In 1318, proceed as in Example 3 to find the solution of the given ...
 3.10.16: In 1318, proceed as in Example 3 to find the solution of the given ...
 3.10.17: In 1318, proceed as in Example 3 to find the solution of the given ...
 3.10.18: In 1318, proceed as in Example 3 to find the solution of the given ...
 3.10.19: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.20: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.21: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.22: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.23: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.24: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.25: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.26: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.27: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.28: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.29: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.30: In 1930, proceed as in Example 5 to find a solution of the given in...
 3.10.31: In 3134, proceed as in Example 6 to find a solution of the initial...
 3.10.32: In 3134, proceed as in Example 6 to find a solution of the initial...
 3.10.33: In 3134, proceed as in Example 6 to find a solution of the initial...
 3.10.34: In 3134, proceed as in Example 6 to find a solution of the initial...
 3.10.35: In 35 and 36, (a) use (25) and (26) to find a solution of the bound...
 3.10.36: In 35 and 36, (a) use (25) and (26) to find a solution of the bound...
 3.10.37: In find a solution of the BVP when f(x) 1.
 3.10.38: In find a solution of the BVP when f(x) x.
 3.10.39: In 3944, proceed as in Examples 7 and 8 to find a solution of the g...
 3.10.40: In 3944, proceed as in Examples 7 and 8 to find a solution of the g...
 3.10.41: In 3944, proceed as in Examples 7 and 8 to find a solution of the g...
 3.10.42: In 3944, proceed as in Examples 7 and 8 to find a solution of the g...
 3.10.43: In 3944, proceed as in Examples 7 and 8 to find a solution of the g...
 3.10.44: In 3944, proceed as in Examples 7 and 8 to find a solution of the g...
 3.10.45: Suppose the solution of the boundaryvalue problem y0 Py9 Qy f(x), ...
 3.10.46: Use the result in to solve y0 y 1, y(0) 5, y(1) 10. 3.1
Solutions for Chapter 3.10: Greens Functions
Full solutions for Advanced Engineering Mathematics  6th Edition
ISBN: 9781284105902
Solutions for Chapter 3.10: Greens Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 6. Chapter 3.10: Greens Functions includes 46 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781284105902. Since 46 problems in chapter 3.10: Greens Functions have been answered, more than 39782 students have viewed full stepbystep solutions from this chapter.

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

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

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.