bachelor of science mathematics calculus

this is the notes of mathematics unit named calculation of variations in handwritten forms

1. UNIT-4
" (alculatian VauíaBfon
TCov]i
)
Fules fonctfon:-The necessaiy conditfon for I=
F(4) dx to be exthemum. is that
aseT If fn is Indeçendent a
By Eole, is Equa ton
dF =0
d oF=0 fs called Eoless equafon
do
n
Jtegating fDE =Consant,
By Eoless equatfon
F-9df = Cnstant
Case-T-1f fnis fndeperde
B Eoleys e quaton
JE-d aEA0
)JE_0 ie E=(ansta
Solve

2. Quu-find exhemurm thef hef
q dr
Rutting all waluet
dx 3
dtegzating

3. Qu' ind Exttemm c fh
Hexe Foncton(F) = 4 yy
=0
al valuel
ategating Ne get
Paga o.
Data