 17.17.1.106: How did we define the angle of imersection of two oriented curves, ...
 17.17.1.107: At what points is a mapping w = f(::) by an analytic function not c...
 17.17.1.108: What happens to angles at::o under a mapping w = f(:) if J' (Zo) = ...
 17.17.1.109: What do "surjective." "injective." and "'bijective" mean?
 17.17.1.110: What mapping gave the 10ukowski airfoil?
 17.17.1.111: What are linear fractional transformations (LFTs)? Why are they imp...
 17.17.1.112: Why did we require that ad  be * 0 for a LFT?
 17.17.1.113: What are fixed points of a mapping? Give examples.
 17.17.1.114: Can you remember mapping properties of II = sin::.? cos:? e Z ?
 17.17.1.115: What is a Riemann surface? Why was it imroduced? Explain the simple...
 17.17.1.116: Find and sketch the image of the given curve or region under 1V = Z...
 17.17.1.117: Find and sketch the image of the given curve or region under 1V = Z...
 17.17.1.118: Find and sketch the image of the given curve or region under 1V = Z...
 17.17.1.119: Find and sketch the image of the given curve or region under 1V = Z...
 17.17.1.120: Find and sketch the image of the given curve or region under 1V = Z...
 17.17.1.121: Find and sketch the image of the given curve or region under 1V = Z...
 17.17.1.122: Find and sketch the image of the gi ven curve or region under w = I...
 17.17.1.123: Find and sketch the image of the gi ven curve or region under w = I...
 17.17.1.124: Find and sketch the image of the gi ven curve or region under w = I...
 17.17.1.125: Find and sketch the image of the gi ven curve or region under w = I...
 17.17.1.126: Find and sketch the image of the gi ven curve or region under w = I...
 17.17.1.127: Find and sketch the image of the gi ven curve or region under w = I...
 17.17.1.128: Where is the mapping by the given function not conformal? (Give rea...
 17.17.1.129: Where is the mapping by the given function not conformal? (Give rea...
 17.17.1.130: Where is the mapping by the given function not conformal? (Give rea...
 17.17.1.131: Where is the mapping by the given function not conformal? (Give rea...
 17.17.1.132: Where is the mapping by the given function not conformal? (Give rea...
 17.17.1.133: Where is the mapping by the given function not conformal? (Give rea...
 17.17.1.134: Find the LFT that maps 0, 1, 2 onto 0, i, 2i, respectively
 17.17.1.135: Find the LFT that maps1. 1, 2 onto O. 2, 312, respectively
 17.17.1.136: Find the LFT that maps1, 1, i onto I, I, i, respectively
 17.17.1.137: Find the LFT that maps1, I, i onto 1  i, 2, 0, respectively
 17.17.1.138: Find the LFT that maps0, GO. 2 onto O. 1. "". respectively
 17.17.1.139: Find the LFT that mapsO. i, 2i onto 0, x, 2i
 17.17.1.140: Fixed Points. Find all fixed points of
 17.17.1.141: Fixed Points. Find all fixed points of
 17.17.1.142: Fixed Points. Find all fixed points of
 17.17.1.143: Fixed Points. Find all fixed points of
 17.17.1.144: Fixed Points. Find all fixed points of
 17.17.1.145: Fixed Points. Find all fixed points of
 17.17.1.146: Find an analytic function II' = .f(z) that maps:The infinite strip ...
 17.17.1.147: Find an analytic function II' = .f(z) that maps: The intelior of th...
 17.17.1.148: Find an analytic function II' = .f(z) that maps:The region x > 0, Y...
 17.17.1.149: Find an analytic function II' = .f(z) that maps:The semidisk Izl <...
 17.17.1.150: Find an analytic function II' = .f(z) that maps:The sector 0 < arg ...
Solutions for Chapter 17: Conformal Mapping
Full solutions for Advanced Engineering Mathematics  9th Edition
ISBN: 9780471488859
Solutions for Chapter 17: Conformal Mapping
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9780471488859. Chapter 17: Conformal Mapping includes 45 full stepbystep solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 9. Since 45 problems in chapter 17: Conformal Mapping have been answered, more than 44454 students have viewed full stepbystep solutions from this chapter.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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

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

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

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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

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

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

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·