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


by: Estevan Champlin Sr.


Estevan Champlin Sr.
GPA 3.66


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

Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 1 page Class Notes was uploaded by Estevan Champlin Sr. on Thursday October 22, 2015. The Class Notes belongs to MATH 122A at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 27 views. For similar materials see /class/226884/math-122a-university-of-california-santa-barbara in Mathematics (M) at University of California Santa Barbara.

Similar to MATH 122A at UCSB

Popular in Mathematics (M)




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: 10/22/15
Math 122B Complex Variables The CauchyGoursat Theorem CauchyGoursat Theorem If a function f is analytic at all points interior to and on a simple closed contour 0 ie f is analytic on some simply connected domain D containing 0 then f2 d2 0 0 Note If we assume that f is continuous and therefore the partial derivatives of u and v are continuous where f2 u7y iv7y7 this result follows immediately from Green7s theorem Letting R be the region enclosed by the curve 07 Cf2d2Auayivz7ydaidyAudxivdyi vdxudy AivzfaydAiAuzivydz40 since f is analytic use the Cauchy Riemann equations However7 the Cauchy Goursat theorem says we don7t need to assume that f is continuous only that it exists Theorem An extension of Cauchy Goursat ff is analytic in a simply connected domain D then Cf2d2 0 for every closed contour C lying in D Notes 0 Combining this theorem with Theorem 427 every function f that is analytic on a simply connected domain D must have an antiderivative on the domain D 0 Given two simple closed contours such that one can be continuous deformed into the other through a region where f is analytic7 the contour integrals of f over these two contours have the same value In other words7 f might not be analytic in some region R7 but if it is analytic outside of R7 then the value of the contour integrals off must be the same for all closed contours that enclose R 7 of course7 this value doesn7t have to be 0 since f is not analytic everywhere See the corollary below


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

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."

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!"

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

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.