100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Lecture notes Mathematics II (MATH2011A) - Calculus_Chapter_4 R350,00
Add to cart
Quickly navigate to
Preview
  2.  
  3. University Of The Witwatersrand (wits)
  4.  
  5. Mathematics II (MATH2011A)

Class notes

Lecture notes Mathematics II (MATH2011A) - Calculus_Chapter_4
 45 views  0 purchase

This document clearly describes, with detailed notes and examples, how to evaluate/solve the following: ~ Path Integrals in Scalar Fields ~ Path Integrals in Vector Fields ~ Double and Repeated Integrals ~ Enclosed Volumes ~ Change of variables in Double Integrals ~ Green's Theorem - Corolla...

[Show more]

Preview 1 out of 41  pages

Document information

  • February 14, 2022
  • 41
  • 2021/2022
  • Class notes
  • Mensah folly-gbetoula/sameerah jamal
  • All classes

Subjects

Written for

All documents for this subject (22)

Seller

avatar-seller
Akshay101

Reviews received

Content preview

CHAPTER 4 8 ECTOR INTEGRATION :


PATH INTEGRALS IN SCALAR FIELDS :


9- SCALAR FIELD IS 0
2 THE PATH TALK ABOUT IS LABELLED [
.




3 THE ARC LENGTH IS DENOTED BY S .




4




INTEGRAL OVER C OF ¢ W R -1
- .
.
5 !

f. ¢cx,y ds

ONE INTERPRETATION OF WHAT THIS REPRESENTS IS :


↳ AND IF IT IS A TWO
VARIABLE FUNCTION
AS WELL !




( 3D)




}
"" " """" """" " "" "


> C IS THE PATHWAY
>
¢ IS THE HEIGHT OF
" "
SO CALLED FENCE


% TO CALCULATE THIS
THE AREA OF

FENCE , WE WOULD CALCULATE THE
PATH INTEGRAL to


•
WE DO NOT WANT TO WORK WITH S -
ARC LENGTH AS THE VARIABLE
% WE PARAMETERISE TO CHANGE VARIABLES :




SUPPOSE TOOK dt :



£"

J }
ds dt REMEMBER IN "" N " " ER ^^ " C "

=
☐ ( r (f) dt
To to MUST REPRESENT THE INITIAL

POINT OF C AND t1 THE END
£0 POINT OF C.
PARAMETER /SEE
VECTOR n




fyot
DEPENDENT ON t T
" t T



µ
IF VARIABLE AS ARC LENGTH

dr
( r(É)
= 1 To USE + VE SIGN !
dt However .
tr ARCÉÉNGTHT
If 0 IF VARIABLE t As

!
•
N§ %USEVESlGNf
IT IS EASY TO SEE IF S 1ST I -
LOOK
AT THE DIRECTION OF THE CURVE /
THE DIRECTION OF INTEGRATION
!

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying this summary from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller Akshay101. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy this summary for R350,00. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

53022 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy summaries for 14 years now

Start selling
R350,00
  • (0)
Add to cart
Added