Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
what is the power series form for quadratic terms?(in two variable calculus)
 one year ago
 one year ago
what is the power series form for quadratic terms?(in two variable calculus)
 one year ago
 one year ago

This Question is Open

ac7qzBest ResponseYou've already chosen the best response.0
A power series is done pretty much the same as single variable, but you have to take all the variables into account. So in the linear term, you replace df/dx with di f/ di x + di f/di y. (I'm saying "di" in place of the curly d for partial derivatives because the equation editor doesn't seem to support partials.) To get the second derivative term you have to take the partial with respect to both variables of the original partials. So replace d^2 f/dx^2 with (di^2 f/di x^2 + di^2 f/di y^2 + 2 di^2 f/ di x di y). Third derivative is harder, and with more than two variables it gets really bad really quick, especially with trig functions or exponentials. So they often lump the second or third derivative terms together behind a capital script "O", meaning "on the order of", and then give the most significant power of the most significant variable, as in "O x^4", then prove that that is insignificant compared to the terms already listed, and ignore it. I first ran across this in an MIT paper on wave propagation in a taut string. That led directly to my review of calculus on OCW...
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.