.7 Lgrge. ( + = f, ) = f (,, ) = + + + = + + =, f (,, ) = + + A + B + C = 0, > > > 0 A + B + C = L (,, λ) = λ( + ) L = λ = 0 L = λ = 0 λ = ( + ) = 0, = =, + = 4, f m f(, ) = = 4 L (,,, λ) = + λ( + + ) L = λ= 0 L = λ = 0 L = λ = 0 λ = ( + + ) = 0, 6
= = + + = (,, ) = ± (,, ) ± (,, ) ± fm = f(,, ) = f mi = f(,, ) = L (,,, λµ, ) = + + λ ( + + ) µ ( A+ B+ C) L = λ µ A= 0 L = B 0 λ µ = L = λ µ C = 0 Lλ = ( + + ) = 0 Lµ = ( A+ B+ C) = 0 + + = + + λ = 0 ( L L L) λ A B C AL BL CL µ A B C + + = + + ( + + = ) 0 6
A B C A B C µ = + + = + + A + B + C L A AB AC = λ 0, = L AB B BC = + 0, λ = L AC BC C = + λ 0 = λ ( A B C λ + + + ) λ+ ( A + B + C ) = 0 λ 0 f A B C A λ + ( + + ) λ + ( B + C + ) = 0. p,, S S = p( p )( p )( p ) L(,,, λ) = p( p )( p )( p ) λ( + + p) L = p( p )( p ) + λ = 0, L = p( p )( p ) + λ = 0, L = p( p )( p ) + λ = 0, 6
p = p = p = = = p p 9. r hπ rh= S rh r = π + π Lrh (,, λ) = πrh+ πr λ( πrh ) Lr = πh+ 4πr πrhλ = 0 Lh = πr πr λ = 0 h= rπ rh= r = h 4 π = π π 4 π 4. = + + + = d(,, ) d = + + L (,,, λµ, ) = + + λ ( + ) µ ( + + ) 64
L = λ µ = 0, L = λ µ = 0, L = + λ µ = 0, ( )( ) = λ = 0 λ λ = 0 µ = = = = + + + = ( ) = ± = = d = 9 5 d = 9 5 d = 9 5 m + mi 5. + = (, ), 0 S = ( ) L (,, λ) = ( ) λ( + ) L = λ, L = 6 λ, λ 6 + =0 + = 0 ( (0,), ) ( =, ) (0,) 0 6. (,, ) S = (, ) = (, ) S = 9 Sm = 9 A + B + C + D = 0 65
(,, ) (,, ) d(,, ) d = ( ) + ( ) + ( ) L (,,, λ) = d(,, ) λ( A+ B+ C+ D) L = ( ) Aλ = 0, L = ( ) Bλ = 0, L = ( ) Cλ = 0, = + λ A = + λb = + λc A + B + C + D = 0 λ A+ B+ C+ D = A + B + C d λa λb λc = + + ( A + B + C + D) = = A + B + C (,, ) A + B + C + D = 0 d A + B + C + D = A + B + C A + = 7. + B + C = 0 A, B, C, (,, ) d L (,,, λµ, ) = + + λ ( + ) µ ( A+ B+ C) 66
λ L = µ A= 0, L = λ B 0 µ =, L = µ C = 0, Lλ = ( + ) = 0, Lµ = ( A+ B+ C) = 0, ( ) L + L + L = + + λ = 0 C A+ B C λ µ = = L λ A AB = + 0 + =, C C L AB λ B = + 0 + =, C C 0 λ A λ B A B + + = 0 4 C C C λ + λ λ A B 0 = λ + C λ λ S = π λ λ λλ = ( A + B + C ) C 67
4 π S A B C = + + C 4 8. = ( + ) + = 0 0 = = 4 4 + + 4 4 4 L(,, λ) = ( + ) λ( + ) L = λ = 0, L = λ = 0, Lλ = ( + ) =0, 4 4 = ( + ) {(, ) + =, 0, 0} (0, ),(,0) 6 4 fmi f(, ) = = 9. > 0, > 0, > 0 f (0, ) f(,0) f(, ) 6 4 4 4 4 + 4 + = = 6 f (,, ) = l + l + l 4 4 = = > = + + = 6R,, + + 08 6 L (,,, λ) = l+ l + l λ( + + 6 R) 6 68
L L L = λ = 0, = λ = 0, = λ = 0, λ = = = + + = 6R = R = R = R 6 + + l ( 6 R ) l l l l[ R ( R )( R ) ] = 6 + + 6 6 ( ) fm = f( R, R, R) = l 6 R = = = + + 08 6 6 0 f (,, ) = ( > 0, > 0, > 0) + + =,,, u, v, w u v w u + v + w + + + + L (,,, λ) = l+ l + l λ( + + ) 69
L L λ L λ = λ = = = = = 0, 0, 0, + + λ = = = + + = = λ = = = + + + + + + = l + l + l = l( ) l ( ) + + + + ( + + ) u v = = u + v + w u + v + w + + w u v w = + + + + = u v w u v w = = u+ v+ w u+ v+ w u+ v+ w u+ v+ w + + ( ) ( + + ) + + u v w u + v + w + + + + 70
, + = ( ) + = + = ( ) + = g= (, ) (, 0) ( ) + + = g =, Lgrge mi L (,, λ) = ( ) + λ( + ) λ L = ( ) = 0, λ λ L = = ( ) = 0, Lλ = + = 0, = 0 = + = + =, 4 ( ), gmi = ( ) + = λ = g = ( ) + = = mi ( ) + = 0 < 4 = (0,) + = 4 ( ) + = S π 7
λ = = g mi = λ =, 4 = + 4 f (, ) = π = + l (,, λ) = π 4 λ( ) l = π λ( ) = 0, = = l π λ( ) 0, 4 λ =, = + S π 6 = = = π π < 6 = = + = ( ) + = ABC f (, ) = 0 g (, ) = 0 ) h(, = 0 ABC ABC BC A f (, ) = 0 = () f (, ) = 0 ( ) ABC d d ( ) = 0 f (, ) = 0 A BC A BC f (, ) = 0, g(, ) = 0 h(, ) = 0 7
,,, f (,,, ) = = = f (,,, ) {(,,, ) + + + < } f (,,, ) + + + = L(,,,, λ) = f(,,, ) λ ( + + + ) L = λ = 0, =,, = = 0, =,, λ + + + = λ =± = f (,,, ) = = =± ± = = f m = f mi = = = 7
4 ij i j ( ij = ji ) i, j= (,,, ) R = = L (,,,, λ) = λ ( + + + ) ij i j i, j= L = 0,,,, ii λ = = i= Lλ = ( + + + ) = 0, = 0 L = i i λ = i, = = i, j= ij i j = λ λ A = ( ) λ = 0, ( =,, ) ij i= i i A λi = 0 λ A = ( ) A = ( ) ij ij λ λ λ f = λ = λ m mi f 5 Q α β Q = α, β 74
α + β = p p α f (, ) = p + p α 6 = L (,, λ ) = p+ p λ( ) α α α α L = p αλ = 0, α α L = p ( αλ ) = 0, β p α λ = α p α 6 = α β α β 6 p p 6 p p = α β α = α β β α β lim f(, ) =+ (, ) α β α β 6 p p 6 p p = α β α = α β β α β 75