Partial Differentiation
By Brad Rodgers (P1930) on Sunday,
October 15, 2000 - 12:19 am :
Does anyone know of a book to learn Partial Differentiation
from? This site's previous advice on books has been so good, I
thought I'd ask again. It appears that this will be necessary to
entirely understand relativity.
Thanks,
Brad
By Thomas Mooney (P3048) on Sunday,
October 15, 2000 - 12:39 am :
Yeah I do Brad. It's called Elementary applied partial
differential equations and it's by a guy called Richard Haberman.
Don't let the Elementary confuse you, this book is some serious
maths! but also theres another one called advanced Engineering
maths and it's by Denis G Zill and Michael R Cullen. It's da
bomb!. The latter is better.
By Sean Hartnoll (Sah40) on Sunday,
October 15, 2000 - 11:20 am :
Actually, I think Partial Differential Equations (PDEs) is
not what you want to know about, just partial differentiation. PDEs are fairly
advanced and you probably need to study ordinary (non-partial) differential
equations first. Partial differentiation is probably talked about in books
with titles like Advanced Calculus or Mathematical Methods.
The concept is not a difficult one. If you have a function, say
f(x,y,z)=x y2 z3 from a point in space (x,y,z) to a real number f(x,y,z)
then the partial derivatives with respect to x, y and z are just what
you get when you treat the other variables as constants, so
¶f/¶x=y2 z3
¶f/¶y=2x y z3
¶f/¶z=3x y2 z2
And that's it!
It has the important property that you can change the order (check this for the
example above)
¶/¶x(¶/¶y)f=¶/¶y(¶/ ¶x)f
And if x, y, z are functions of t, so
f(x(t),y(t),z(t)) then the total derivative of f is
df/dt=¶f/¶x dx/dt + ¶f/¶y dy/dt+¶f/ ¶z dz/dt
As an exercise, let x(t)=t, y(t)=t2, z(t)=t+1 and use this in the
pervious example for f to calculate the total derivative df/dt.
Sean