If M is an -dimensional manifold (or manifold-with-boundary) in R n, with the usual orientation, show that

Question:

If M is an -dimensional manifold (or manifold-with-boundary) in R n, with the usual orientation, show that ∫ fdx1 ^ . ^ dx n, as defined in this section, is the same as ∫ M f, as defined in Chapter 3.

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

Step by Step Answer:

Related Book For answer-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jan 12, 2010 12:45 AM

See More Questions

If M is an -dimensional manifold-with-boundary in Rn, define as the usual orientation of M x = Rnx (the orientation so defined is the usual orientation of M. If xЄM, show that the two...
If M is an oriented one-dimensional manifold in RN and c: [0, 1] M is orientation-preserving, show that
If M is an -dimensional manifold in Rn, with the usual orientation, show that dV = dx1^ . . . ^ dxn, so that the volume of M, as defined in this section, is the volume as defined in Chapter 3. (Note...
Tiffee Company identifies the following items for possible inclusion in the physical inventory. Indicate whether each item should be included or excluded from the inventory taking. (a) 900 units of...
What kinds of assets would you put in a $100,000 portfolio? What kind of tradeoff would you be willing to make between risk and return? How would you diversify?
A particle of mass 2.0 kg is moving in the xy-plane at a constant speed of 0.80 m/s in the +x-direction along the line y = 4 m. As the particle travels from x = -3 m to x +3 m, the magnitude of its...
Christopher Boling was seriously injured in 2008 when vapors escaping from a gas can ignited. He filed a products liability claim against the manufacturer. To fund the litigation, Boling entered into...
In order to meet holiday demand, Pennys Pie Shop requires a production line that is capable of producing 50 pecan pies per week, while operating only 40 hours per week. There are only 4 steps...
1 Problem 4 - A firm's optimal output choice (10 points) Consider a price taking firm, where the market price for the output is given by P. The firm's output choice is denote by Q. The firm has a...
Melissa Shallowford contributed a patent, accounts receivable, and $15,000 cash to a partnership. The patent had a book value of $6,000. However, the technology covered by the patent appeared to have...
a. Let : Rn Rn be self-adjoint with matrix A = (aij), so that aij = aji. If f (x) = = aij xixj, show that Dkf (x) = 2 j = 1 akjxj. By considering the maximum of on Sn-1 show that there is...
a. Show that Theorem 5-5 is false if M is not required to be compact. b. Show that Theorem 5-5 holds for noncom-pact M provided that w vanishes outside of a compact subset of M.
In preparation for a proposed bond sale, the city manager of the City of Appleton requested that you prepare a statement of legal debt margin and a schedule of direct and overlapping debt for the...
Norwegian Cruise Lines is offering cruise packages which include airfare and all meals as well as the cabin. What type of pricing are they using? Explain
In one of the great social media campaigns in Canadian business history, if social media metrics are any indication, WestJet emotionally engaged viewers during Christmas 2013 with a holiday YouTube...
A company conducted a focus group for an established brand to help the company adjust the marketing mix for the brand. The moderator asked the participants to say what came to mind ween they heard...
So Long Loadshedding? For the first time in history, the entire South Africa may be lit up. Eskom has never been able to provide power to 100% of the population. And while the state-owned enterprise...
PESTECH ( political, economic, social, technological, ecological, cultural, and historical) Research analysis of mango that would export product to Germany.
Consider a helium atom with one electron in the $n=1, l=0$ state, and another in the $n=2, l=0$ state. Calculate the energy of the ortho-helium state (the lowest energy state for these quantum...
Interview managers at three companies in your area about their use of ERP. How have their experiences been similar? What accounts for the similarities and differences?
Consider the system water(1) + MEK(2) at 299.85 K. The solubilities measured by Skrzec, A.E., Murphy, N.F., 1954. Ind. Eng. Chem., 46:2245, are x 1 = 0.927 and x 1 = 0.364. For a binary system,...
On January 1, 2020, Mr. Wild formed a corporation to provide services to clients. Information about the first year of operation follows: Jan. 1 Investors provided $1,500,000 in cash in exchange for...
What is the purpose of the statement of cash flows? What information does it provide? (b) Prepare the operating activities section of the statement of cash flows for the year ended December 31, 2018,...
The cash account for Brentwood Bike Co. at May 1 indicated a balance of $14,640. During May, the total cash deposited was $73,260 and checks written totaled $68,020. The bank statement indicated a...

If M is an -dimensional manifold (or manifold-with-boundary) in R n, with the usual orientation, show that

Question:

Step by Step Answer:

We can assume in the situation of Chapter 3 ...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Basic questions