All Matches
Solution Library
Expert Answer
Textbooks
Search Textbook questions, tutors and Books
Oops, something went wrong!
Change your search query and then try again
Toggle navigation
FREE Trial
S
Books
FREE
Tutors
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Ask a Question
Search
Search
Sign In
Register
study help
mathematics
advanced engineering mathematics
Questions and Answers of
Advanced Engineering Mathematics
Evaluate the following integrals and show details of your work.
How would you find the image of x = Re z = 1 under w = iz, z2, ez, 1/z?
If w = f(z) is any transformation that has an inverse, prove the (trivial!) fact that f and its inverse have the same fixed points.
Expand the function in a Laurent series that converges for 0 < |Z| < R and determine the precise region of convergence. Show the details of your work.sin πz/z2
Determine the location and order of the zeros.z-2 sin2 πz
Find out whether w = z̅ preserves angles in size as well as in sense. Try to prove your result.
Find the branch points and the number of sheets of the Riemann surface.z2 + 3√4z + i
Find and sketch the image of the given region under w = ez.-∞ < x < ∞, 0 ≤ y ≤ 2π
Expand the function in a Laurent series that converges for 0 < |Z| < R and determine the precise region of convergence. Show the details of your work.1/z2 - z3
Find all the singularities in the finite plane and the corresponding residues. Show the details.8/1 + z2
Evaluate the following integrals and show the details of your work.
State the residue theorem and the idea of its proof from memory.
Derive the mapping in Example 2 from (2).
Expand the function in a Laurent series that converges for 0 < |Z| < R and determine the precise region of convergence. Show the details of your work.sinh 2z/z2
How did we evaluate real integrals by residue integration? How did we obtain the closed paths needed?
Determine the location and order of the zeros.z4 + (1 - 8i) z2 - 8i
Find and sketch or graph the images of the given curves under the given mapping.Curves as in Prob. 6, w = izData from Prob. 6Find and sketch or graph the images of the given curves under the given
Find the branch points and the number of sheets of the Riemann surface.n√z - z0
Find the inverse z = z(w). Check by solving z(w) for w.w = i/2z - 1
Find and sketch the image of the given region under w = ez.0 < x < 1, 0 < y < π
Expand the function in a Laurent series that converges for 0 < |Z| < R and determine the precise region of convergence. Show the details of your work.z3 cosh 1/z
Find all the singularities in the finite plane and the corresponding residues. Show the details.cot πz
What are improper integrals? Their principal value? Why did they occur in this chapter?
If your CAS can do conformal mapping, use it to solve Prob. 7. Then increase y beyond π, say, to 50π or 100π. State what you expected. See what you get as the image. Explain.Data from Prob. 7Find
What do you know about zeros of analytic functions? Give examples.
Determine the location and order of the zeros.sin 2z cos 2z
Find and sketch or graph the images of the given curves under the given mapping.Curves as in Prob. 6, w = z + 2 + iData from Prob. 6Find and sketch or graph the images of the given curves under the
Find the branch points and the number of sheets of the Riemann surface.√z3 + z
Find the inverse z = z(w). Check by solving z(w) for w.w = z - i/3iz + 4
Find the points at which w = sin z is not conformal.
Find the Laurent series that converges for 0 0|
Find all the singularities in the finite plane and the corresponding residues. Show the details.1/1 - ez
Evaluate the following integrals and show the details of your work.
What is the extended complex plane? The Riemann sphere R? Sketch z = 1 + i on R.
Find the LFT that maps the given three points onto the three given points in the respective order.1, i,-1 onto i, -1, -i
If f(z) is analytic and has a zero of order n at z = z0, show that f2(z) has a zero of order 2n at z0.
Sketch or graph the given region and its image under the given mapping.|z| ≤ 1/2, -π/8 < Arg z < π/8, w = z2
Find all points at which the mapping is not conformal. Give reason.A cubic polynomial
Evaluate (counterclockwise). Show the details.
Evaluate the following integrals and show details of your work.
Evaluate by the methods of this chapter. Show details.
Find all Taylor and Laurent series with center z0. Determine the precise regions of convergence. Show details.1/z2, z0 = i
Discuss e1/Z2 in a similar way as is discussed in Example 3 of the text.
Find all points at which the mapping is not conformal. Give reason.
Evaluate (counterclockwise). Show the details.
Evaluate by the methods of this chapter. Show details.
Find the Cauchy principal value (showing details):
Find all Taylor and Laurent series with center z0. Determine the precise regions of convergence. Show details.
Assuming that we let the image of the x-axis be the meridians 0° and 180°, describe and sketch (or graph) the images of the following regions on the Riemann sphere: (a) |z| > 100(b) The lower
Find all points at which the mapping is not conformal. Give reason.cosh z
Find and sketch or graph the image of the given region under w = sin z.0 < x < π/2, 0 < y < 2
Find the fixed points.w = (α + ib)z2
Find the Laurent series that converges for 0 0|
Find all the singularities in the finite plane and the corresponding residues. Show the details.ez/(z - πi)3
Evaluate the following integrals and show details of your work.
Integrate counterclockwise around C. Show the details.sin 3z/z2, C:|z| = π
Find the LFT that maps the given three points onto the three given points in the respective order.-1, 0, 1 onto -i, -1, i
Determine the location of the singularities, including those at infinity. For poles also state the order. Give reasons.
Sketch or graph the given region and its image under the given mapping.2 ≤ Im z ≤ 5, w = iz
Find and sketch or graph the image of the given region under w = sin z.0 < x < 2π, 1 < y < 3
Find the fixed points.w = 16z5
Find the Laurent series that converges for 0 0|
Evaluate the following integrals and show details of your work.
Integrate counterclockwise around C. Show the details.5z3/z2 + 4, C:|z| = 3
Find the LFT that maps the given three points onto the three given points in the respective order.0, 1, ∞ onto ∞, 1, 0
Determine the location of the singularities, including those at infinity. For poles also state the order. Give reasons.z exp (1/(z - 1 - i)2)
Sketch or graph the given region and its image under the given mapping.|z -1/2| ≤ 1/2, w = 1/z
Describe the mapping w = cosh z in terms of the mapping w = sin z and rotations and translations.
Find the fixed points.
Find the Laurent series that converges for 0 0|
Evaluate (counterclockwise). Show the details.
Evaluate the following integrals and show details of your work. .6 X - dx x6 +1
Integrate counterclockwise around C. Show the details.25z2/(z - 5)2, C:|z - 5| = 1
Find the LFT that maps the given three points onto the three given points in the respective order.1, i, 2 onto 0, -i - 1, -1/2
Find all points at which the mapping w = cosh 2πz is not conformal.
Determine the location of the singularities, including those at infinity. For poles also state the order. Give reasons.cot4 z
Sketch or graph the given region and its image under the given mapping.-Ln 2 ≤ x ≤ Ln 4, w = ez
Find an analytic function that maps the region R bounded by the positive x- and y-semi-axes and the hyperbola xy = π in the first quadrant onto the upper half-plane. Hint. First map R onto a
Find all LFTs with fixed point(s).z = 0
Write a program for obtaining Laurent series by the use of partial fractions. Using the program, verify the calculations in Example 5 of the text. Apply the program to two other functions of your
Evaluate (counterclockwise). Show the details.
Evaluate the following integrals and show details of your work.
Integrate counterclockwise around C. Show the details.cos z/zn, n = 0, 1, 2, · · ·, C:|z| = 1
Find an analytic function w = f(z) that maps the region 0 ≤ arg z ≤ π/4 onto the unit disk |w| ≤ 1.
Determine the location of the singularities, including those at infinity. For poles also state the order. Give reasons.1/(ez - e2x)
Sketch or graph the given region and its image under the given mapping.1 < |z| < 4, π/4 < θ ≤ 3π/4, w = Ln z
Find all LFTs with fixed point(s).z = ±i
Find all Taylor and Laurent series with center z0. Determine the precise regions of convergence. Show details.
Evaluate by the methods of this chapter. Show details.
Determine the location of the singularities, including those at infinity. For poles also state the order. Give reasons.e1/(z-1)/(ez - 1)
Find and sketch or graph the image of the given region under the mapping w = cos z.0 < x < π/2, 0 < y < 2 directly and from Prob. 11Data from Prob. 11Find and sketch or graph the image
Find all Taylor and Laurent series with center z0. Determine the precise regions of convergence. Show details.
Find and sketch or graph the image of the given region under the mapping w = cos z.π < x < 2π, y < 0
Find all Taylor and Laurent series with center z0. Determine the precise regions of convergence. Show details.
Show that w = Ln z-1/z+1 maps the upper half-plane onto the horizontal strip 0 ≤ Im w ≤ π as shown in the figure.
Find all Taylor and Laurent series with center z0. Determine the precise regions of convergence. Show details.
Evaluate (counterclockwise). Show the details.
Evaluate by the methods of this chapter. Show details.
Find the Cauchy principal value (showing details):
Find all points at which the mapping is not conformal. Give reason. sin πz
Showing 400 - 500
of 3884
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last