Show that log(x2 + y2) and x/x2 + y2 are harmonic functions, that is, solutions of the

Question:

Show that
log(x2 + y2) and x/x2 + y2
are harmonic functions, that is, solutions of the two-dimensional Laplace equation.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 09:02 AM

See More Questions

(Harmonic functions) Verify Theorem 1 for f = y2 x2 and the surface of the cylinder x2 + y2 < z < 5.
(a) Show that the function ex cos y is a solution to the two-dimensional Laplace equation. (b) Show that its quadratic Taylor polynomial at x = y = 0 is harmonic. (c) What about its degree 3 Taylor...
Show that (x2 + xy + x log y)3 is O(x6y3).
A simple beam AB of span length L = 24ft is subjected to two wheel loads acting at distance = 5 ft apart (see figure). Each wheel transmits a load P = 3.0 k, and the carriage may occupy any position...
1. What type of bailment is discussed in the video? 2. What were Vinnys duties with regard to the rug-cleaning machine? What standard of care should apply? 3. Did Vinny exercise the appropriate...
Name some advantages of indirect speech.
The data on January 1999 sanitation scores for 121 cruise ships, first presented in Exercise 2.58 (p. 74), are reproduced on page 225. Assess whether the sanitation scores are approximately normally...
Strategic analysis of operating income (continuation of 13-26). Refer to Exercise 13-26. 1. Calculate the operating income of Snyder Corporation in 2008 and 2009. 2. Calculate the growth,...
Morganton Company makes one product and it provided the following information to help prepare the master budget: a. The budgeted selling price per unit is $60. Budgeted unit sales for June July...
A scale is constructed using the 10-kg mass, the 2-kg pan P, and the pulley and cord arrangement. Cord BCA is 2 m long. If s = 0.75 m, determine the mass D in the pan. Neglect the size of thepulley....
Let S R be an open subset (i.e., a union of open intervals). True or false: ker D is a one-dimensional subspace of C1 (S).
The Fredholm Alternative of Theorem 5.55 first appeared in the study of what are now known as Fredholm integral equations: in which K(x, y) and f(x) are prescribed continuous functions. Explain how...
Determine the magnitude of the projected components of r1 along r=, and the projection of r2 alongr1. =9 m 120 30 e 60 450
n1 = 20, n2 = 25, S = 607, H1: 1 2. In Exercises 710, compute S, S, and the value of the test statistic z. Then find the P-value for the specified alternate hypothesis and values of n1, n2, and S.
To determine whether traffic levels differ between the morning and evening rush hours, a traffic engineer counted the number of cars passing through a certain intersection during five-minute periods...
Macon Timber Company established a $\$ 150$ petty cash fund on January 1, 2012. Required a. Is the establishment of the petty cash fund an asset source, use, or exchange transaction? b. Record the...
Following is a bank reconciliation for Holt's Sandwich Shop for May 31, 2012: Because of limited funds, Holt's employed only one accountant who was responsible for receiving cash, recording receipts...
For each of the following situations, fill in the blank with FIFO, LIFO, or weighted average. a. b. c. d. e. f. would produce the highest amount of net income in an inflationary environment. would...
Calculate the free energy change for this reaction at 25 C. Is the reaction spontaneous? C3H8(g) + 5O(g) 5 O(g) 3 CO(g) + 4HO(g) AHin = -2217 kJ; ASixn 101.1 J/K rxn
1. True or False. Pitfalls to consider in a statistical test include nonrandom samples, small sample size, and lack of causal links. 2. Because 25 percent of the students in my morning statistics...
Transistors have a life that is exponentially distributed with parameter . A random sample of n transistors is taken. What is the joint probability density function of the sample?
Suppose that X is uniformly distributed on the interval from 0 to 1. Consider a random sample of size 4 from X. What is the joint probability density function of the sample?
A procurement specialist has purchased 25 resistors from vendor 1 and 30 resistors from vendor 2. Let X1,1, X1,2, , X1,25 represent the vendor 1 observed resistances, which are assumed to be normally...
question 6 Timely Inc. produces luxury bags. The budgeted sales and production for the next three months are as follows july. august september Sales, in units 1,115. 1229. 1302 Production. in units...
On May 12 Zimmer Corporation placed in service equipment (seven-year property) with a basis of $220,000. This was Zimmer's only asset acquired during the year. Calculate the maximum depreciation...
Power Manufacturing has equipment that it purchased 7 years ago for $2,550,000. The equipment was used for a project that was intended to last for 9 years and was being depreciated over the life of...

Show that log(x2 + y2) and x/x2 + y2 are harmonic functions, that is, solutions of the

Question:

Step by Step Answer:

For u logx 2 y 2 we compute 2 ux 2 2y 2 2x 2 x 2 y ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions