 17.1.17.1.1: Verify all calculations in Example I.
 17.1.17.1.2: Why do the images of the curves /;;:1 = COIlsl and arg :: = COllst ...
 17.1.17.1.3: Doe, the mapping w = Z = x  iy preserve angles in size as well as ...
 17.1.17.1.4: Find and sketch or graph the image of the given curves under the gi...
 17.1.17.1.5: Find and sketch or graph the image of the given curves under the gi...
 17.1.17.1.6: Find and sketch or graph the image of the given curves under the gi...
 17.1.17.1.7: Find and sketch or graph the image of the given region under the gi...
 17.1.17.1.8: Find and sketch or graph the image of the given region under the gi...
 17.1.17.1.9: Find and sketch or graph the image of the given region under the gi...
 17.1.17.1.10: Find and sketch or graph the image of the given region under the gi...
 17.1.17.1.11: Find and sketch or graph the image of the given region under the gi...
 17.1.17.1.12: Find and sketch or graph the image of the given region under the gi...
 17.1.17.1.13: Find and sketch or graph the image of the given region under the gi...
 17.1.17.1.14: Find and sketch or graph the image of the given region under the gi...
 17.1.17.1.15: Find and sketch or graph the image of the given region under the gi...
 17.1.17.1.16: CAS EXPERI:\IENT. Orthogonal Nets. Graph the orthogonal net of the ...
 17.1.17.1.17: Find all points at which the following mappings are not conformal.
 17.1.17.1.18: Find all points at which the following mappings are not conformal.
 17.1.17.1.19: Find all points at which the following mappings are not conformal.
 17.1.17.1.20: Find all points at which the following mappings are not conformal.
 17.1.17.1.21: Find all points at which the following mappings are not conformal.
 17.1.17.1.22: Find all points at which the following mappings are not conformal.
 17.1.17.1.23: Find all points at which the following mappings are not conformal.
 17.1.17.1.24: Find the magnification ratio M. Describe what it tell, you about th...
 17.1.17.1.25: Find the magnification ratio M. Describe what it tell, you about th...
 17.1.17.1.26: Find the magnification ratio M. Describe what it tell, you about th...
 17.1.17.1.27: Find the magnification ratio M. Describe what it tell, you about th...
 17.1.17.1.28: Find the magnification ratio M. Describe what it tell, you about th...
 17.1.17.1.29: Magnification of Angles. Let f(:::) be analytic at ;:0' Suppose tha...
 17.1.17.1.30: Prove the statement in Prob. 29 for general k = I. 2, .... Hint. Us...
Solutions for Chapter 17.1: Geometry of Analytic Functions: Conformal Mapping
Full solutions for Advanced Engineering Mathematics  9th Edition
ISBN: 9780471488859
Solutions for Chapter 17.1: Geometry of Analytic Functions: Conformal Mapping
Get Full SolutionsThis textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 9. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9780471488859. This expansive textbook survival guide covers the following chapters and their solutions. Since 30 problems in chapter 17.1: Geometry of Analytic Functions: Conformal Mapping have been answered, more than 44185 students have viewed full stepbystep solutions from this chapter. Chapter 17.1: Geometry of Analytic Functions: Conformal Mapping includes 30 full stepbystep solutions.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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 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

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

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.

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.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

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.

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

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·

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

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