New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Calculus IV

by: Felicita Lockman
Felicita Lockman
GPA 3.68

Michael Fairchild

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Michael Fairchild
Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Felicita Lockman on Sunday October 25, 2015. The Class Notes belongs to MATH 2242 at University of North Carolina - Charlotte taught by Michael Fairchild in Fall. Since its upload, it has received 25 views. For similar materials see /class/228910/math-2242-university-of-north-carolina-charlotte in Mathematics (M) at University of North Carolina - Charlotte.


Reviews for Calculus IV


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/25/15
Marsden 7215 Evalute the line integral 2zyz dm 22 dy zzy dz 0 where C is an oriented simple curve connecting 111 to 1 2 4 SOLUTION One hint is that the problem does not tell you what path to integrate along The wording of the problem seems to suggest that no matter what path you pick you get the same answer Question What kind of line integrals have this property Answer Line integrals of gradient elds see Theorem 73 on p440 Thus according to Theorem 73 if you can nd a scalar function 9 such that Vg Qxyz x22 y then 124 2xyzdx szzdy zzy dz Vg ds g124 7 g111 0 111 Its not hard to see that if gxyz xzyz then Vg 2syzx22x2y Thus the answer is 917274 9171718 1 7 This is probably the method the authors wanted you to use for this problem See note below for advice on how to nd such a function 9 Another solution is to explicitly parameterize a simple path connecting 111 to 124 A line segment connecting the two points is the simplest such path Using the techniques of chapter 1 we see that Ct 111 t013 11 t1 3t for 0 S t S 1 does the job Then c t 013 and using the formula f0 F ds Fct c t dt we get 1 2xyzdxz22dyz2ydz 28t6t213t1t013dt C 0 113t31tdt 1 6t4dt 0 I think the rst method is far superior since it does not require an explicit parameter ization or calculation of a messy integral But to use the rst method we need to nd a scalar eld 9 whose gradient is F What if you cant just see77 what 9 should be How do you systematically nd one In this case F Qxyz x22x2y The vector equation F Vg implies 69 69 69 2xzx22x2 iii lt y y Mawz The rst component of this equation says 2zyz Multiplying each side of this equa tion by dm and integrating with respect to m gives gxyz xzyz yz where our constant77 of integration is any function of y and 2 but not How do we nd yz 1 Well we have two other conditions to satsify namely 22 375 and y Using our temporary function gy z xzyz My 2 the rst of these implies 22 22 thus 37 0 so evidently b doesn7t depend on y after all That is b may only depend on 2 But doing the same trick for 2 that we did for y we nd that b doesn7t depend on 2 either Thus b is at most an honest to goodness constant like 3 or 7139 or H7 let7s call that constant a Thus we have gxyz xzyz a We may as well take 04 0 Why Because any choice for 04 doesn7t affect the relationship F Vg since 04 being a constant disappears when we take the derivatives involved in V9 IMPORTANT NOTE Its not always possible to nd a scalar function 9 whose gradient is F When you can F is called a gradient eld or a conservative eld It turns out that if V gtlt F 0 ie F is curl free then you can nd such a g and when V gtlt F 31 0 then you cant See the very important Theorem 87 on p551 You can check that V gtlt F 0 for this problem


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Janice Dongeun University of Washington

"I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.