functional
action
Proof.
Remark.
Remark.
only
Proof.
system
catenoid
minimum
not
Lag-
rangian
action
continuous symmetry
Proof.
This subsection is covered by Lecture 1 of the IB Optimisation course.
strictly
Proofs for these conditions, where appropriate, are given in Lecture 1 of the IB Optimisation course.
Proof.
⋆
⋆
⋆
⋆
⋆
⋆⋆
⋆
⋆⋆
⋆
⋆⋆
⋆
⋆
Proof.
⋆
⋆
⋆
⋆
internal energy Helmholtz free energy
⋆
⋆
⋆
Hamiltonian
generalised momenta conjugate
momenta
trajectories
Proof.
