A. A certain fluid is flowing with a constant speed V in a direction making an angle B with the positive x-axis. Find the complex potential for the fluid under consideration. Also determine the velocity and the stream functions.
Complex Variables Existence of a Function Show that the derivative of the following function does not exists at any point
Given that cos x=(e^jx + e^-jx)/2 and sin x=(e^jx - e^-jx)/2j Using ONLY this information, prove that: cosAsinB=1/2[sin(A+B)- sin(A-B)]. See the attached file.
Using the following data, obtained from an imaginary harness small manufacturing company, determine the correlation between the number of hours that an employee works and how many belts they produce: Hours Worked 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Belts Produced 2 3 3 4 5 6 6
Please show me how to solve the following : x^4 = 5 - 5i
What is the complex conjugate of 78.93iw^3+30.48iw^2+iw? How did you find it?
1) For each weighted voting system , find all dictators (d), veto power players( vp), and dummies (d) ( 7: 7,3,2,1) 2) For the weighted voting system ( 12: 6,4,3,1,1,) a) Find what percent of the total vote is the quota. b) In a Shapley-Shubik distribution system , how many sequential coalitions would be formed from thi
Find a conformal mapping from the unit disc Δ(0,1) = {z|z|<1} to D={z:|z|<1}[0,1]. Please see attached for diagram.
Use Cauchy's formula for the derivative to prove that if f is entire and |f(z)|≤ A|z|² + B|z| + C for all zεC, then f(z) = az² +bz + c Please see attached for full question.
Simplify the following (3+i )/2 + (1- i )/4.
Use the formal method, involving an infinite series of residues and illustrated in the examples. 7. F(s) = 1/(s cosh (s^½)) Please see attachment for full question.
The beta function is this function of two real variables... Make the substitution t=1/(x+1) and use the result obtained in the example in Sec. 77 to show that... Please see attachment for equations.
Please see the attachment for questions relating to residues and poles (polar numbers and Demoivre's Theorem). These problems are from complex variable class. Please specify the terms that you use if necessary and clearly explain each step of your solution.
Problem: Show that when ... Please see the attached file for the fully formatted problems.
Derive the expansions. Please see the attached file for the fully formatted problems.
Show that when z does not equal 0, a) e^2/z^2 = 1/z^2 + 1/z + 1/2! + z/3! + z^2/4! + ... (See attachment for other question)
Derive the Taylor Series representation ... (see attached)
This problems is from complex variable class. Please specify the terms that you use if necessary and clearly explain each step of your solution. Problem: Obtain the Taylor series ... (see attachment) for the function ... (see attachment)
Prove that ... (see attachment for equation).
Write z=re^i0, where 0<r<1, in the summation formula that was derived in the example in Sec. 52. Then, with the aid of the theorem in Sec. 52 show that... (See attachment for details)
Prove that f(x) has no multiple root over C ... (PLEASE SEE ATTACHMENT FOR FULL PROBLEM)
Show that phi is (infinite d,d) continuous where d is the standard metric... (See attachment for full question)
Let CN denote the boundary of the square formed by the lines... Please see the attached file for the fully formatted problems.
Please see the attached file for the fully formatted problems.
Please see the attached file for full problem description. --- 5. Write |exp (2z + i) | and | exp (iz2) | in terms of x and y. Then show that | exp (2z + i) + exp (iz2) | ≤ e2x + e-2xy. (exp means exponential function)
In each case, determine the singular points of the function and state why the function is analytic everywhere except at those points: (a) f (z) = (2z + 1) / [z (z^2 + 1)] (b) f (z) = (z^3 + i) / (z^2 - 3^z + 2) (c) f (z) = (z^2 + 1) / [(z + 2)(z^2 + 2z + 2)]
9. Let f denote the function whose values are _ f (z) = z^2 / z when z ≠ 0, f (z) = 0 when z = 0. Show that if z = 0, then ∆w/∆z = 1 at each nonzero point on the real and imaginary axes in the ∆z, or ∆x∆y, plane. Then show that ∆w/ͧ
7. Prove that dzn-1/ dz = nzn-1, for the derivative of zn remains valid when n is a negative integer (n = -1, -2, ???), provided that z≠0. (Suggestion: Write m = -n and use the formula for the derivative of a quotient of two functions). See the attached file.
3. Give a direct proof that f ΄(z) = -1 / z2 when f (z) = 1 / z (z ≠0). Use this definition to prove the problem. dw / dz = lim ∆w / ∆z ∆z→0
11. T (z) = (az + b) / (cz + d) (ad - bc ≠0) Show the following. (Please explain by using theorem.) (a) lim T (z) = ∞ if c = 0 z→∞ (b) lim T (z) = a / c and lim T (z) = ∞ if c ≠0. z→∞ z→-d/c