Question: Problem 1. (max. 10 = 5+5 points) (a) When is a smooth one-form defined on the open set U1 = {(x, y) ( R2 :

Problem 1. (max. 10 = 5+5 points) (a) When is a

Problem 1. (max. 10 = 5+5 points) (a) When is a smooth one-form defined on the open set U1 = {(x, y) ( R2 : x > 0} called exact? Give the definition. (b) When is a smooth one-form defined on the open set U2 = {(x, y, z) ( R3 : z> x + y} called closed? Give the definition

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Solving Two-stage Robust Optimization Problems by A Constraint-and-Column Generation Method Bo Zeng Department of Industrial and Management Systems Engineering University of South Florida, Email:...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Lecture Notes DL MGT 5100 - Distribution Management Spring 2017 1.0. Day one, Monday, Monday, 9 Jan 17 1.1. Reading Assignments: Chapters 1 and 2 1.1.1. I intend to follow the book so as to provide a...

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

1. Calculate the sample size needed given these factors: one-tailed t-test with two independent groups of equal size small effect size (see Piasta, S.B., & Justice, L.M., 2010) alpha =.05 beta = .2...

3 COLLEGE ALGEBRA - TRIGONOMETRY Business and Finance (MAT115) This course will start with a review of basic algebra (factoring, solving linear equations, and equalities, etc.) and proceed to a study...

In this problem, you are to find the gravitational potential energy of the stick in Example 11-8 and a point mass m 0 that is on the x axis at x 0 . (a) Show that the potential energy of an element...

Lucia is a 69-year-old single individual who receives a taxable pension of $10,000 per year and Social Security benefits of $7,000. Lucia is considering the possibility of selling stock she has owned...

What does rel need to do to allow employees to mail their greatest possibie contebution to company productivity and compettiveness? manage both helenal and exhernal emeronmental factors Excus on the...

Write a C code for Bubble Sort Given an array of integers, sort the array in ascending order using the Bubble Sort algorithm above. Once sorted, print the following three lines: 1. Array is sorted in...

6. The circuit shown below is constructed using identical CMOS inverters. The channel width of the transistors is 14m. The channel length of the transistors is 1.2m. The equivalent resistances for...

Sun Microsystems, is a manufacturer of mid-size computers, which are primarily used by medium and small businesses. Sun Microsystemss product line currently consists of three models of mid-size...

Shirley bought a brand new car from Leyland Motors. The contract of sale contains the following exclusion clause: Leyland Motors does not make any guarantees whatsoever as to the quality or fitness...

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint. 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 4.4 4.0 5.2 3.0 4.8 Assume that the measurements are a...

Create a 200 word summary on the Juvenile Justice System than and today. Describe The Juvenile system and provide a generalizable definition. Highlight the issues in the Juvenile system and why this...

Because the workplace is the company's private property, the company could choose, if It wished, to allow employees to bring guns not only into the parking lot but also into the workplace itsett. !Ve...

Do you agree with the NRA that H companies ban guns from their parking lots, this restriction would take a wrecking ball to the Second Amendment or nul!Hy the right of people to have weapons for...

In your view, do employees have either a moral or a legal right to park cars wlth guns in them in the company parking lot? If so, what about Ille property rights and safety concerns of employeis? If...