×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide

Solutions for Chapter 10.8: Laplaces Equation

Elementary Differential Equations and Boundary Value Problems | 11th Edition | ISBN: 9781119256007 | Authors: Boyce, Diprima, Meade

Full solutions for Elementary Differential Equations and Boundary Value Problems | 11th Edition

ISBN: 9781119256007

Elementary Differential Equations and Boundary Value Problems | 11th Edition | ISBN: 9781119256007 | Authors: Boyce, Diprima, Meade

Solutions for Chapter 10.8: Laplaces Equation

Solutions for Chapter 10.8
4 5 0 379 Reviews
24
5
Textbook: Elementary Differential Equations and Boundary Value Problems
Edition: 11
Author: Boyce, Diprima, Meade
ISBN: 9781119256007

Since 19 problems in chapter 10.8: Laplaces Equation have been answered, more than 12661 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 10.8: Laplaces Equation includes 19 full step-by-step solutions. This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 11. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9781119256007.

Key Math Terms and definitions covered in this textbook
  • Adjacency matrix of a graph.

    Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

  • Circulant matrix C.

    Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn - l . Cx = convolution c * x. Eigenvectors in F.

  • Cofactor Cij.

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

  • Condition number

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

  • Determinant IAI = det(A).

    Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

  • Elimination matrix = Elementary matrix Eij.

    The identity matrix with an extra -eij in the i, j entry (i #- j). Then Eij A subtracts eij times row j of A from row i.

  • Free columns of A.

    Columns without pivots; these are combinations of earlier columns.

  • Hankel matrix H.

    Constant along each antidiagonal; hij depends on i + j.

  • Hermitian matrix A H = AT = A.

    Complex analog a j i = aU of a symmetric matrix.

  • Indefinite matrix.

    A symmetric matrix with eigenvalues of both signs (+ and - ).

  • lA-II = 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.

  • Left inverse A+.

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

  • Multiplication Ax

    = Xl (column 1) + ... + xn(column n) = combination of columns.

  • Network.

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

  • 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.

  • Reflection matrix (Householder) Q = I -2uuT.

    Unit vector u is reflected to Qu = -u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q-1 = Q.

  • Right inverse A+.

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

  • Row space C (AT) = all combinations of rows of A.

    Column vectors by convention.

  • Singular matrix A.

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

×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide
×
Reset your password