Calculus/Math Help

Advertisement

Expert: - 2/5/2012


Question
Hi Sir,

  Suppose u(x,t) = f(x+at) + g(x-at), where a is constant and f & g
are twice differentiable functions of 1 variable.

I found partial d2u/ partial dt2 = a^2[ f '' (x+at) + g'' (x-at)]. f'' and g'' refers to 2nd derivative of f & g wrt variable x or t?


Cheers

Answer
It is with respect to t; in this case you are partial differentiating wrt t and treating x as the constant all the way. 1st round of partial differentiation flushes out the constant a and -a from the separate original functions f and g respectively; a second round flushes out a*a=a^2  and (-a)*(-a)=a^2 from f' and g' respectively.

Hope this helps. Peace.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Frederick Koh

Expertise

I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.

Experience

3 years helping out in a singaporean youth forum: http://forums.sgclub.com/math_help/ (under the moniker whitecorp) You can also visit my main maths website http://www.whitegroupmaths.com where I have designed "question locker" vaults to store tons of fully worked math problems. Peace.

Organizations
IEEE(Institute of Electrical and Electronics Engineers )

Education/Credentials
Former straight As A level student from HCJC (aka HCI); scored distinctions in both C and Further Mathematics B Eng (Hons) From The National University Of Singapore (NUS)

©2012 About.com, a part of The New York Times Company. All rights reserved.