- #1
Bryson
- 56
- 2
Hello, this is probably one of those shoot yourself in the foot type questions.
I am going through Landau & Lifshits CM for fun. On page 7 I do not understand this step:
[itex] L' = L(v'^2) = L(v^2 + 2 \vec{v} \cdot \vec{\epsilon} + \epsilon^2) [/itex]
where [itex] v' = v + \epsilon [/itex]. He then expands the expression in powers of [itex] \epsilon [/itex] (neglecting higher order terms) to get:
[itex] L(v'^2) = L(v^2) + \frac{\partial L}{\partial v^2} 2\vec{v} \cdot \vec{\epsilon} [/itex]
How did he arrive here? What expansion did he use? Taylor expansion?
Thanks for any help or comments!
I am going through Landau & Lifshits CM for fun. On page 7 I do not understand this step:
[itex] L' = L(v'^2) = L(v^2 + 2 \vec{v} \cdot \vec{\epsilon} + \epsilon^2) [/itex]
where [itex] v' = v + \epsilon [/itex]. He then expands the expression in powers of [itex] \epsilon [/itex] (neglecting higher order terms) to get:
[itex] L(v'^2) = L(v^2) + \frac{\partial L}{\partial v^2} 2\vec{v} \cdot \vec{\epsilon} [/itex]
How did he arrive here? What expansion did he use? Taylor expansion?
Thanks for any help or comments!