### Create a StudySoup account

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

Already have a StudySoup account? Login here

# CALCULUS IV MATH 241

Penn

GPA 3.56

### View Full Document

## 9

## 0

## Popular in Course

## Popular in Mathematics (M)

This 4 page Class Notes was uploaded by Claudine Friesen on Monday September 28, 2015. The Class Notes belongs to MATH 241 at University of Pennsylvania taught by N. Rimmer in Fall. Since its upload, it has received 9 views. For similar materials see /class/215395/math-241-university-of-pennsylvania in Mathematics (M) at University of Pennsylvania.

## Popular in Mathematics (M)

## Reviews for CALCULUS IV

### 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: 09/28/15

Section 181 Contour Integrals F3 WWW Wm Let s go back to Section Parametric Curve xffvygf A B B C B 2 A B A A a Smooth b Piecewise id Simplc c Closed curve smooth cune closed bul nol curve simple Orientation of the curve m h zt lz C r r llm 3u qu Malhz lrkimmer SQ 131 Contour Integrals C parametric curve in the complex plane defined by x xt y y t a S t S b t real Now let zt xt iyta S t S b define C If C is piecewise srnooth we will now call it a An integral off z on C is called a The general If C is simple and To reinforce the positive symbol is closed we use orientation we use To evaluate the countour integral Intheformulaforfz IfZdZ replace z by C then dz for continuous f and smooth C m Math 241 Rimmer Evaluate 131 Contour Integrals Izzdz where C is de ned by z t 2 3t 2it 2 St S 2 C fzz2 SO fzt 1 3t2it3 Z1 dzz tdt dz Izzdz j f ztz tdt FE Math 241 Rimmer Evaluate 131 Contour Integrals x2 2 sz Where C is left half of the ellipse 7 L C 36 4 1 fromz 2 2i to z 2 2i 2 2 We need to parametrize C L L 1 36 4 Orientation S I S mt Math 241 Rimmer 131mm Odds and ends from Section 181 WW8 Complex functions can be thought of as Consider f z as a at the point z fz in yivxa y representation for the path of a particle in the flow gt rt 2 has vector T r t x t iy t that must coincide With the function fxtiyt 960 ytivxta yt dx dy 3 t and t 3 and 2 x y dt dt the solutions xt and y I are called the of the ow mg Math241 Rimmer Flnd the streamlines of the flow assomated W1thf z lZ 181 Cum mm f Z fz u u andv fiiiiT 3 3 l 7 d dt x A z z Q 3 Sep of Var Q dx r A the streamlines are centered at the origin v v v v mg 131 C m me Ll Continuing to View the complex function as a flow quot 39 V s we can now calculate and C positively oriented simple closed curve The around C measures the tendency of the ow to rotate C The 7 7 across C is the difference between the rate at which uid enters and the rate at which fluid leaves the region bounded by C PEI Math 2A1 7 Kim a y 181 Conmnr ln39eyals Boundin Theorem f iii on a if curve C 2 and L length of C for all z on C

### 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

#### "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!"

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "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!"

#### "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."

### Refund Policy

#### STUDYSOUP CANCELLATION 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 support@studysoup.com

#### STUDYSOUP REFUND POLICY

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: support@studysoup.com

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 support@studysoup.com

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.