Second order Taylor approximation

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SUMMARY

The discussion centers on the derivation of the first line in the second order Taylor approximation, specifically regarding the terms ct=yt-gt. The user expresses confusion over additional terms encountered during their attempt to apply a three-variable Taylor approximation, particularly the terms involving (gt-g)(chit-chi). Clarification is sought on the assumptions that allow certain terms, such as u_{G}(G_{t}-G) and u_{\zeta}(\zeta_{t}-\zeta), to be disregarded in the formula. The conversation highlights the importance of understanding the conditions under which these terms can be considered negligible.

PREREQUISITES
  • Understanding of Taylor series expansions, specifically second order approximations.
  • Familiarity with multivariable calculus concepts.
  • Knowledge of the variables involved, such as u_{G}, G_{t}, and \zeta_{t}.
  • Basic proficiency in mathematical notation and terminology used in calculus.
NEXT STEPS
  • Study the derivation of second order Taylor approximations in multivariable calculus.
  • Research the conditions under which certain terms can be neglected in Taylor expansions.
  • Explore examples of Taylor approximations applied to real-world problems.
  • Learn about the implications of assumptions made in mathematical derivations.
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Students and professionals in mathematics, particularly those studying calculus and its applications in fields such as physics and engineering, will benefit from this discussion.

tanvi nautiyal
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Hello,
Can someone explain this to me? In the above case ct=yt-gt
I tried to solve it as a three variable taylor approximation but got a few extra terms that weren't included in the above. So I am a little confused now.
I only need to understand how the first line was derived because I get additional terms with (gt-g)(chit-chi)..https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-xap1/v/t35.0-12/13570139_10210195219259688_119153535_o.png?oh=5a83810acd11160ed4bf6a19de37d6ec&oe=57781CBB&__gda__=1467485097_6da652cc9db77ba174ecad977bc59004
 
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In fact in the Taylor expansion you have also the terms ##u_{G}(G_{t}-G)## and ##u_{\zeta}(\zeta_{t}-\zeta)## but in the formula doesn't appear, I think there are some assumptions that permit to put zero these terms ...

PS. ##\zeta## is not chi that is ##\chi##
 
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Likes   Reactions: Simon Bridge
Hey tanyi nautiyal.

Can you please re-attach the image so we can have a look at it?
 

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