Page 1 of 8 123 ... LastLast
Results 1 to 25 of 197
Like Tree91Likes

Thread: MATH2111 Higher Several Variable Calculus

  1. #1
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    MATH2111 Higher Several Variable Calculus

    Is there a higher dimensional implicit differentiation hax (sorry I'm doing maths whilst being a bit hyper) to get me a shortcut for this question



    Or should I just chain rule it because z = +'ve sqrt(...)

    Last edited by dan964; 8 Jun 2017 at 12:05 AM.

  2. #2
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    Is there a higher dimensional implicit differentiation hax (sorry I'm doing maths whilst being a bit hyper) to get me a shortcut for this question



    Or should I just chain rule it because z = +'ve sqrt(...)

    Last edited by InteGrand; 19 May 2016 at 11:16 PM.
    leehuan likes this.

  3. #3
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus





    leehuan and dan964 like this.

  4. #4
    Cole World Nailgun's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Posts
    2,218
    Rep Power
    4

    Re: Multivariable Calculus

    I was kind of hoping InteGrand would use the word 'hax' ahahah
    Veni, Vidi, Vici

  5. #5
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Last edited by InteGrand; 19 May 2016 at 11:29 PM.

  6. #6
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by InteGrand View Post
    Oh wow that is nifty.
    ______________________________________________
    Feeling somewhat ashamed that I don't know how to do this


  7. #7
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    Oh wow that is nifty.
    ______________________________________________
    Feeling somewhat ashamed that I don't know how to do this









    Last edited by InteGrand; 19 May 2016 at 11:43 PM.
    leehuan and dan964 like this.

  8. #8
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    Ahh, ok problem - my course doesn't actually teach the total derivative itself... How would I derive it?

  9. #9
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by InteGrand View Post
    We were probably on our way to it now that I think about it... Thus far he's only mentioned that there's multiple chain rules but not exactly what they are yet...

    Edit: Ok yep looking at the lecture slides it seems like they were to come. Ahh thanks though

  10. #10
    Taking a break! dan964's Avatar
    Join Date
    Jun 2014
    HSC
    2014
    Uni Grad
    2018
    Gender
    Male
    Location
    South of here
    Posts
    2,752
    Rep Power
    4

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    We were probably on our way to it now that I think about it... Thus far he's only mentioned that there's multiple chain rules but not exactly what they are yet...

    Edit: Ok yep looking at the lecture slides it seems like they were to come. Ahh thanks though
    Aah, the good old chain rule. I have a whole subject of Multivariable calculus this session (UOW for the win). And basically the chain rule reduces down in some measure to matrix multiplication which is pretty cool.

  11. #11
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by dan964 View Post
    Aah, the good old chain rule. I have a whole subject of Multivariable calculus this session (UOW for the win). And basically the chain rule reduces down in some measure to matrix multiplication which is pretty cool.
    Saw it in my lecture slides as well, but again to come. Being taught it today.

  12. #12
    Supreme Member seanieg89's Avatar
    Join Date
    Aug 2006
    HSC
    2007
    Gender
    Male
    Posts
    2,679
    Rep Power
    10

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    Thus far he's only mentioned that there's multiple chain rules but not exactly what they are yet...
    Perhaps in some notations it will seem that way, but they can be unified remarkably well once one learns to think of the derivative of a function f at a point p as nothing more than a linear map between the vector space of tangents at p and the vector space of tangents at f(p) (pretty much the most flexible and abstract way to think of the classical derivative).

    What it then boils down to is that if we have two smooth functions and , then is smooth and .
    leehuan likes this.

  13. #13
    Supreme Member seanieg89's Avatar
    Join Date
    Aug 2006
    HSC
    2007
    Gender
    Male
    Posts
    2,679
    Rep Power
    10

    Re: Multivariable Calculus

    (Where, X,Y,Z are open subsets of arbitrary dimension Euclidean spaces, or more generally of curves/surfaces/manifolds.)

    Sidebar: Spivak has a less well known book "Calculus on Manifolds", that is amazing for learning multivariable calculus. From introducing partial derivatives and Riemann integration to differential forms and the modern version of Stokes theorem. It is quite compact and terse though and considerably less accessible than his "Calculus".
    Last edited by seanieg89; 20 May 2016 at 1:34 PM.

  14. #14
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    Re: Multivariable Calculus

    Getting stuck on how to incorporate the 0.02 correctly



    Progress so far:


    Last edited by leehuan; 22 May 2016 at 4:13 PM.

  15. #15
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    Getting stuck on how to incorporate the 0.02 correctly



    Progress so far:




    leehuan likes this.

  16. #16
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    Re: Multivariable Calculus

    This thread may be packed with questions...cause my book doesn't give answers to almost anything. Sorry!



    I did something like this and I'm not sure if I can break it down any further


  17. #17
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    This thread may be packed with questions...cause my book doesn't give answers to almost anything. Sorry!



    I did something like this and I'm not sure if I can break it down any further

    leehuan likes this.

  18. #18
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by InteGrand View Post
    Hmm, makes sense but I'm having a dumb. What is the difference between f1(u,v) and f2(u.v)?

  19. #19
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    Hmm, makes sense but I'm having a dumb. What is the difference between f1(u,v) and f2(u.v)?

  20. #20
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    Re: Multivariable Calculus

    Ah ok so you basically do leave it as is I see. So is this right...?






  21. #21
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    Ah ok so you basically do leave it as is I see. So is this right...?





    Yeah that's correct.

  22. #22
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    Re: Multivariable Calculus

    Cool. Ok this one is twisting with me but here's my attempt






  23. #23
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    Cool. Ok this one is twisting with me but here's my attempt





    leehuan likes this.

  24. #24
    Ancient Orator
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    5,971
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by leehuan View Post
    Cool. Ok this one is twisting with me but here's my attempt







    leehuan likes this.

  25. #25
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,800
    Rep Power
    6

    Re: Multivariable Calculus

    Quote Originally Posted by InteGrand View Post


    Yep sweet, was about to post that.
    __________________________

    Last question of this bundle:







    There might be an accidental typo

Page 1 of 8 123 ... LastLast

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •