### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Study Guide for Calc 3 MA 261

GPA 4.0

### View Full Document

## 54

## 0

## Popular in Calculus 3

## Popular in Mathematics (M)

This 6 page Study Guide was uploaded by Nikki Bee on Wednesday June 10, 2015. The Study Guide belongs to MA 261 at Purdue University taught by in Spring 2015. Since its upload, it has received 54 views. For similar materials see Calculus 3 in Mathematics (M) at Purdue University.

## Reviews for Study Guide for Calc 3

### 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: 06/10/15

MA 261 Fall 2012 Study Guide 3 You also need Study Guides 1 and 2 for the Final Exam Line integral of a function f 13 y 2 along C parameterized by 1 2 3375 y yt z 2t and a S t S b is C fw7y7z ds bfat ya 20 dt independent of orientation of C other properties and applications of line integrals of f Remarks a 0 fx y 2 ds is sometimes called the line integral of f with respect to arc length b emsmas bfltxlttgtylttgtzlttgtgtx39lttgtdt c Cfwyzdy bfltwlttgtylttgtzlttgtgty39lttgtdt d C mews bfltxlttgtylttgtzlttgtgtz39lttgtdt Line integral of vector eld F a y 2 along C parameterized by t and a S t S b is given by b F df Ff t m dt C 1 depends on orientation of C other properties and applications of line integrals of f Connection between line integral of vector elds and line integral of functions fFdFF Tds C C Where 39f is the unit tangent vector to the curve C If F013 3 Z PC7341 2 iUr 62013731 Zi R613 3 Z 12 then f df PwyzdwQwyzdyRwyzdz C C Work FquotdI quot C FUNDAMENTAL THEOREM OF CALCULUS FOR LINE INTEGRALS Vfdf f Fb f Fa c C rb 8Q8P 6 A vector eld 2 135 y i Qayjis conservative ie F Vf if E 8y how to determine a potential function f if Vf 8Q 8P 7 GREEN S THEOREM Pxy d3 Qxy dy 8 8 dA C boundary of D C D 33 y As a consequence of Green s Theorem one has 1 xdy ydxzf xdyz f ydxAreaD 2 C C C a 7 8 7 8 8 Del Operator 1 a yJ a f E 8 8 8 lFZV F cur x 833 ay 82 P Q R Properties of curl and divergence O 12 if FOE y Z PC7341 2 iUr 62013731 2 R613 3 127 then 8P 8Q 8R and leF VFa xa yg i If curl F 6 then F is a conservative vector eld ie7 Vf ii If curl F 6 then F is irrotational if div F 07 then F is incompressible 9 Parametric surface S Hum ltxuvyuvzuv Where u39v E D V D L L AK X Normal vector to surface S 2 Eu gtlt ECU tangent planes and normal lines to parametric surfaces 10 Surface area of a surface S 11 12 i AS Iquotu gtlt FvdA D ii If S is the graph of z ha y above D then AS 1 Sh3 332 8ho y2 dA D Remark dS lfu gtlt EU dA differential of surface area While dS 17 X EU dA The surface integral of f 13 y 2 over the surface S i fayzgtd8 flt uvgtlr ugtltmdA ii If S is the graph of z ha y above D then dS h aha 2 ME 2dA Ami2 Dfltxy xygtgt 1lt M lt ygt The surface integral of F over the surface S recall dS 171 X EU dA fSFd BFmmm fSF d AF dszf uxmm If S is the graph of z ha y above D With oriented upward and F P Q R then d D P Qg ZR M i Connection between surface integral of a vector eld and a function fgFdsS ds The above gives another way to compute S F ZS ii F dS dS 1 of F across the surface S s s n S 13 STOKES THEOREM F if curl d recall7 curlf V X C S n F dfquot circulation Of F around C C 14 THE DIVERGENCE THEOREMGAUSS THEOREM F d divf dV 5 E recall7 divf V n 34 15 Summary of Line Integrals and Surface Integrals LINE INTEGRALS SURFACE INTEGRALS CFtwherea t b S Fu39v Where u39v E D d8 l dt differential of arc length dS lfu gtlt EU dA differential of surface area d8 length of C 0 dS 2 surface area of S S C m y 2 ds mt lf tl dt independent of orientation of C fS 357972 ff u7v If x m dA independent of normal vector R r m dt ds a x a M fc df fab m m dt depends on orientation of C fS 39dng uw E u gtlt EU dA depends on normal vector LFdFLFTds The circulation of F around C fS dsSF dS The flux of F across S in direction 16 Integration Theorems b FUNDAMENTAL THEOREM OF CALCULUS F 3 d3 Fb Fa b FUNDAMENTAL THEOREM OF CALCULUS FOR LINE INTEGRALS V f df f E b f E a C a rb GREEN S THEOREM D STOKES THEOREM curlF d F df S C DIVERGENCE THEOREM divf dV 2 f F d E s n S 34

### 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!"

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

#### "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."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### 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.