20 4 20

i 1 1 1.1............................ 1 1.2............................ 4 2 11 2.1................... 11 2.2......................... 11 2.3....................... 19 3 25 3.1............................. 25 3.2............................. 27 3.3............................. 29 4 31 4.1.............................. 31 4.2.............................. 33 4.3.............................. 37 4.4........................ 40 5 41 5.1.................... 41 5.2....................... 41 5.3......................... 42 5.4........................ 43

1 1 1.1 x, y, z f f(x, y, z) ( ) f(x x, y, z) f(x, y, z) lim x 0 x (1.1) f x 1. y, z., () y, z., (x, y, z),, xf (1.2)., 2,. 1, f(x x, y y, z z) ( ) f(x, y, z) x ( ) y ( ) z (1.3), x, y, z x, y, z 1. (1.3) 2. x, y, z dx, dy, dz f ( ) ( ) ( ) df dx dy dz (1.4)

2 1 f., g, h f (df) gh (1.5)., g f h f (df) gh 0 (1.6). ( ) ( ) ( ) (df) (dx) (dy) (dz) ( ) (1.7) (dx), (dx) (df) (dx) ( ) (1.8)., x, y, z 1 u, v, w x x(u, v, w), y y(u, v, w), z z(u, v, w) (1.9), v, w ( ) ( ) (df) (dx), (du) ( ) ( ) (df) (dx) (du) (du) (dy) (dy) (du) ( ) (dz) (1.10) ( ) (dz), (du) (1.11), ( ) ( ) ( ) ( ) ( ) ( ) ( ) (1.12)

1.1. 3. v, w, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (1.13) ( ) ( ) (1.14). (1.12), (1.13), (1.14),. (1.12), (1.13), (1.14) [x, y, z]/ [u, v, w] ( ) ( ) ( ) [x, y, z] ( ) ( ) ( ) [u, v, w] ( ) ( ) ( ) (1.15) [( ) ( ) ( ) ] [ ( ) ( ) ( ) ] [x, y, z] [u, v, w] (1.16).,, (x, y, z)/ (u, v, w)., ( ) ( ) ( ) (x, y, z) ( ) ( ) ( ) (u, v, w) (1.17) ( ) ( ) ( )

4 1. (1.16) f r, s, t, [ r, s, t ] [x, y, z] [x, y, z] [u, v, w] [ r, s, t ] [u, v, w] (1.18)., ( r, s, t ) (x, y, z) (x, y, z) (u, v, w) ( r, s, t ) (u, v, w) (1.19). 1.2 a b a b a b cos θ (1.20)., a a,, θ a b. (1) a b b a (2) a a a 2 (3) a b 0 a b (4) (λa) b a (λb) λ (a b) (5) a (b c) a b a c (1.21)., a,, a a 1 e 1 a 2 e 2 a 3 e 3 (1.22) e i e j δ ij (1.23) e 1, e 2, e 3., (1.22) e i a i a i. a a 2 1 a 2 2 a 2 (1.24) 3

1.2. 5,,. a b a 1 b 1 a 2 b 2 a 3 b 3 (1.25) a b (a 0, b 0) c 3 (1) a c b c (2) c a b sin θ (3) det[ a b c ] 0 (1.26)., (2) θ a b., (3) det[ a b c ], e x, e y, e z e 1, e 2, e 3., a, b 0 c 0. (1.26) (1), (2), (3) c a b c a b. (2) a b a b,, (3) a b., a b a 2 a 3 b 2 b 3 e 1 a 3 a 1 b 3 b 1 e 2 a 1 a 2 b 1 b 2 e 3 (1.27). a b e 1 e 2 e 3 a 1 a 2 a 3 b 1 b 2 b 3 (1.28). (1) a b b a (2) a a 0 (3) a b 0 a b (4) (λa) b a (λb) λ (a b) (5) a (b c) a b a c (1.29)

6 1., (1.26) (1), (2), (3) (1.27)., (1) a 1 c 1 a 2 c 2 a 3 c 3 0 b 1 c 1 b 2 c 2 b 3 c 3 0 (1.30). 2 (a 1 b 2 a 2 b 1 ) c 1 (a 2 b 3 a 3 b 2 ) c 3 0 (a 1 b 2 a 2 b 1 ) c 2 (a 3 b 1 a 1 b 3 ) c 3 0 (1.31)., c 1 : c 2 : c 3 a 2 a 3 b 2 b 3 : a 3 a 1 b 3 b 1 : a 1 a 2 b 1 b 2 (1.32), t ( a 2 a 3 c t b 2 b 3 e a 3 a 1 1 b 3 b 1 e 2 a 1 a 2 b 1 b 2 ) e 3 (1.33)., (2) c 2 a 2 b 2 sin 2 θ a 2 b 2 a 2 b 2 cos 2 θ (a 2 1 a 2 2 a 2 3)(b 2 1 b 2 2 b 2 3) (a 1 b 1 a 2 b 2 a 3 b 3 ) 2 (a 2 b 3 a 3 b 2 ) 2 (a 3 b 1 a 1 b 3 ) 2 (a 1 b 2 a 2 b 1 ) 2 2 2 2 a 2 a 3 a 3 a 1 a 1 a 2 b 2 b 3 b 3 b 1 b 1 b 2 (1.34), (1.33) t 1 1., (3) a 1 a 2 a 3 a 2 a 3 det[ a b c ] b 1 b 2 b 3 b c 1 c 2 c 3 2 b 3 c a 3 a 1 1 b 3 b 1 c a 1 a 2 2 b 1 b 2 c 3 2 2 t a 2 a 3 a 3 a 1 a 1 a 2 2 0 b 2 b 3 b 3 b 1 b 1 b 2 (1.35)

1.2. 7, t 1., (1.26) (1), (2), (3) (1.27). 3 3 3 a, b, c a (b c) (1.36) 3. 3 a 1 a 2 a 3 a (b c) b 1 b 2 b 3 c 1 c 2 c 3. (1.37) a (b c) b (c a) c (a b) (1.38)., 3 a, b, c., 3. a (b c), a, b, c, a (b c), a, b, c., a (b c) (1.39) 3. 3, a (b c) (a c)b (a b)c (1.40).,,, a (b c) (a b) c. 2 e x, e y, e z e u, e v, e w, e u, e v, e w e x, e y, e z e u P 11 e x P 21 e y P 31 e z e v P 12 e x P 22 e y P 32 e z (1.41) e w P 13 e x P 23 e y P 33 e z

8 1., P ij P 11 P 12 P 13 P P 21 P 22 P 23 (1.42) P 31 P 32 P 33 e x, e y, e z e u, e v, e w. (1.41) [e u e v e w ] [e x e y e z ] P (1.43). e x, e y, e z, (1.41) e x, e y, e z P e x e u e x e v e x e w e y e u e y e v e y e w e z e u e z e v e z e w., e x, e y, e z e u, e v, e w (1.44) e x Q 11 e u Q 21 e v Q 31 e w e y Q 12 e u Q 22 e v Q 32 e w (1.45) e z Q 13 e u Q 23 e v Q 33 e w Q ij Q (1.44) e u e x e u e y e u e z Q e v e x e v e y e v e z (1.46) e w e x e w e y e w e z., a b b a, Q P t P., Q t P (1.47)., (1.45) [e x e y e z ] [e u e v e w ] Q (1.48)

1.2. 9, (1.43), Q P P 1.., (1.47) (1.49) Q P 1 (1.49) P 1 t P (1.50). (1.50),.,., t P P I det P 1 1. e x, e y, e z e u, e v, e w det P 1,, det P 1..,. a e x, e y, e z e u, e v, e w a [e x e y e z ] a x a y [e u e v e w ] a u a v (1.51) a z a w, a u a v P 1 a x a y (1.52) a w a z. (1.52).

11 2 2.1 r f(r), f., r A(r), A., r., r. 2.2 2 r r dr dr. dr (x, y, z) dr dx e x dy e y dz e z (2.1)., r (x, y, z) 1 (u, v, w) x x(u, v, w), y y(u, v, w), z z(u, v, w) (2.2). x, y, z ( ) ( ) ( ) dx du dv ( ) ( ) ( ) dy du dv ( ) ( ) ( ) dz du dv dw dw dw (2.3)

12 2, (2.1) dr dr du r u dv r v dw r w (2.4). ( ) ( ) r r u ( ) ( ) r r v ( ) ( ) r r w ( ) e x ( ) e x ( ) e x ( ) e y ( ) e y ( ) e y e z e z e z (2.5)., 3 r u, r v, r w,, r α r β 0 (α β) (2.6), (u, v, w). (u, v, w) r u, r v, r w e u r u /h u, e v r v /h v, e w r w /h w (2.7), e u, e v, e w., h u, h v, h w h u r u, h v r v, h w r w., ( ) 2 ( ) 2 ( ) 2 h u ( ) 2 ( ) 2 ( ) 2 h v (2.8) h w ( ) 2 ( ) 2. (2.7), dr ( ) 2 dr h u du e u h v dv e v h w dw e w (2.9)

2.2. 13., (x, y, z), u x, v y, w z, h x 1, h y 1, h z 1. (2.5) (2.7) e u, e v, e w e x, e y, e z e u 1 ( ) e x 1 ( ) e y 1 ( ) h u h u h u e v 1 ( ) e x 1 ( ) e y 1 ( ) h v h v h v e w 1 ( ) e x 1 ( ) e y 1 ( ) h w h w h w. h u e z e z e z (2.10) [e u e v e w ] [e x e y e z ] P (2.11), e x, e y, e z e u, e v, e w P ( ) ( ) ( ) 1 1 1 h u h v h w ( ) ( ) ( ) 1 1 1 P h u h v h w (2.12) ( ) ( ) ( ) 1 1 1 h v., e x, e y, e z e u, e v, e w, P., u, v, w x, y, z u u(x, y, z), v v(x, y, z), w w(x, y, z) (2.13), u, v, w ( ) ( ) ( ) du dx dy dz ( ) ( ) ( ) dv dx dy dz ( ) ( ) ( ) dw dx dy dz h w (2.14)

14 2. (2.9),, (2.1) ( ) ( ) ( ) e x h u e u h v e v h w e w ( ) ( ) ( ) e y h u e u h v e v h w e w (2.15) ( ) ( ) ( ) e z h u e u h v e v h w e w., (2.11) [e x e y e z ] [e u e v e w ] P 1 (2.16), ( ) h u ( ) P 1 h v ( ) h w ( ) h u ( ) h v ( ) h w ( ) h u ( ) h v ( ) h w (2.17)., P 1, (2.12) P, P P 1 t P P 1., P P 1. (1.15) P [x, y, z] [u, v, w] 1/h u 0 0 0 1/h v 0 0 0 1/h w (2.18) P 1 h u 0 0 0 h v 0 0 0 h w [u, v, w] [x, y, z] (2.19)

2.2. 15., (1.18) P P 1., (1.16) [ ( ) ( ) ( ) ] 1 1 1 h u h v h w [ ( ) ( ) ( ) ] (2.20) P [ ( ) ( ) ( ) ] [ 1 h u. ( ) h v ( ) 1 1 h w ( ) ] (2.21) P 1 (u, v, w) 1 (r, s, t) u u(r, s, t), v v(r, s, t), w w(r, s, t) (2.22)., [e u e v e w ] [e x e y e z ] [e r e s e t ] [e x e y e z ] [x, y, z] [u, v, w] [x, y, z] [ r, s, t ] 1/h u 0 0 0 1/h v 0 0 0 1/h w 1/h r 0 0 0 1/h s 0 0 0 1/h t (2.23) (2.24)

16 2, e u, e v, e w e r, e s, e t h u 0 0 1/h r 0 0 [u, v, w] P 0 h v 0 0 1/h s 0 [ r, s, t ] 0 0 h w 0 0 1/h t ( ) ( ) ( ) h u h u h u h r r st h s s tr h t t (2.25) rs ( ) ( ) ( ) h v h v h v h r h w h r r ) ( r st st h s h w h s s ) ( s tr tr h t h w h t t ) ( t [e r e s e t ] [e u e v e w ] P (2.26) rs rs., t P P I h r, h s, h t ( ) 2 ( ) 2 ( ) 2 h r h 2 u h r 2 v h st r 2 w st r st ( ) 2 ( ) 2 ( ) 2 h s h 2 u h s 2 v h tr s 2 w tr s tr ( ) 2 ( ) 2 ( ) 2 h t h 2 u h t 2 v h rs t 2 w rs t rs (2.27). (u, v, w) e u, e v, e w α( u, v, w) α [e u e v e w ] [e u e v e w ] Γ α (2.28)

2.2. 17., 0 Γ u 1 ( ) hu h v 1 ( ) hu h w Γ v Γ w 1 h u 1 h u ( hv 1 h v ( ) hu 0 1 ( ) hv h u ) 0 0 1 ( ) hv h w ( hw 1 h w 0 0 0 0 1 h w ( ) hu 0 ( hv 0 0 1 h u ( hw 0 0 1 ( ) hw h v ) ( ) 1 hw 0 h v 0 ) ) (2.29). (2.28), (2.29)., (2.5) r u, r v, r w r α r β h 2 αδ αβ (2.30) r α γ r β. (2.30) γ γ (r α r β ) r β γ r α r α γ r β 2h α γ h α δ αβ (2.31)., α β r α γ r α h α γ h α (2.32)., α β γ α γ β γ α γ β., γ α β. α r β β r α r α α r β r α β r α h α β h α (2.33)

18 2., (2.31) r β α r α r α α r β 0 (2.34) r β α r α r α α r β h α β h α (2.35)., α β γ α.,, α r β β r α,.,, r β γ r α r α γ r β 0 (2.36) r α γ r β r β γ r α r β α r γ r γ α r β (2.37) r α γ r β r α β r γ r γ β r α r γ α r β (2.38) r α γ r β 0 (2.39). (2.32), (2.33), (2.35), (2.39), (2.28), (2.29)., α [e x e y e z ] 0 α [e u e v e w ] [e x e y e z ] P (2.40) α [e u e v e w ] [e x e y e z ] α P [e u e v e w ] P 1 α P (2.41)., P 1 t P (2.28) Γ α Γ α t P α P (2.42)., t P P I α ( α t P ) P t P α P t Γ α Γ α 0 (2.43)

2.3. 19, t Γ α Γ α,, Γ α., [x, y, z]/ [u, v, w] [r u r v r w ], Γ α Γ α t P α P 1/h u 0 0 0 1/h v 0 0 0 1/h w α r u α r u h u h u r v α r u h v h u r w α r u h w h u 0 r u α r w h u h w t r u t r v t r w [ ] r u r v r w r u α r v h u h v r v α r v h v h v r w α r v h w h v r u α r v h u h v r u α r v h u h v 0 r u α r w h u h w r v α r w h v h w r w α r w h w h w 1/h u 0 0 0 1/h v 0 0 0 1/h w α h u 0 0 h u α h v 0 0 h v r u α r w h u h w r v α r w h v h w r v α r w h v h w 0 0 0 α h w h w (2.44). (2.44) (2.33), (2.35), (2.39) (2.29). 2.3 (r, θ, ϕ) x r sin θ cos ϕ, y r sin θ sin ϕ, z r cos θ (2.45)., r r, θ r z, ϕ r x. (2.5)

20 2 r r sin θ cos ϕ e x sin θ sin ϕ e y cos θ e z r θ r cos θ cos ϕ e x r cos θ sin ϕ e y r sin θ e z (2.46) r ϕ r sin θ sin ϕ e x r sin θ cos ϕ e y. 3 r r, r θ, r ϕ,., (2.8) h r r r, h θ r θ, h ϕ r ϕ h r 1, h θ r, h ϕ r sin θ (2.47), dr dr e r rdθ e θ r sin θdϕ e ϕ (2.48)., e r r r /h r, e θ r θ /h θ, e ϕ r ϕ /h ϕ, e r sin θ cos ϕ e x sin θ sin ϕ e y cos θ e z e θ cos θ cos ϕ e x cos θ sin ϕ e y sin θ e z (2.49) e ϕ sin ϕ e x cos ϕ e y., (2.11) [e r e θ e ϕ ] [e x e y e z ] P, P sin θ cos ϕ cos θ cos ϕ sin ϕ P sin θ sin ϕ cos θ sin ϕ cos ϕ (2.50) cos θ sin θ 0., (2.12)., P P 1 t P sin θ cos ϕ sin θ sin ϕ cos θ P 1 cos θ cos ϕ cos θ sin ϕ sin θ (2.51) sin ϕ cos ϕ 0., (2.16) [e x e y e z ] [e r e θ e ϕ ] P 1, e x sin θ cos ϕ e r cos θ cos ϕ e θ sin ϕ e ϕ e y sin θ sin ϕ e r cos θ sin ϕ e θ cos ϕ e ϕ (2.52) e z cos θ e r sin θ e θ

2.3. 21., (2.20) ( ) ( ) ( ) ( ) sin θ cos ϕ sin θ sin ϕ cos θ r θϕ ( ) ( ) ( ) ( r cos θ cos ϕ r cos θ sin ϕ r sin θ θ ϕr ( ) ( ) ( ) r sin θ sin ϕ r sin θ cos ϕ ϕ rθ,, (2.21) ( ) ( ) sin θ cos ϕ r ( ) ( ) sin θ sin ϕ r ( ) ( ) cos θ r θϕ θϕ θϕ sin θ r cos θ cos ϕ r cos θ sin ϕ r ( ) θ ϕr ( ) θ ( ) θ ϕr ϕr sin ϕ r sin θ cos ϕ r sin θ ) (2.53) ( ) ϕ ( ) ϕ rθ rθ (2.54).,. (2.44), α [e r e θ e ϕ ] [e x e y e z ] Γ α Γ α Γ r 0 0 0 0 0 0 0 0 0. (ρ, ϕ, z), Γ θ 0 1 0 1 0 0 0 0 0, Γ ϕ 0 0 sin θ 0 0 cos θ sin θ cos θ 0 (2.55) x ρ cos ϕ, y ρ sin ϕ, z z (2.56)., ρ r

22 2, ϕ x. (2.5) r ρ cos ϕ e x sin ϕ e y r ϕ ρ sin ϕ e x ρ cos ϕ e y (2.57) r z e z. 3 r ρ, r ϕ, r z,., (2.8) h ρ r ρ, h ϕ r ϕ, h z r z h ρ 1, h ϕ ρ, h z 1 (2.58), dr dρ e ρ ρdϕ e ϕ dz e z (2.59)., e ρ r ρ /h ρ, e ϕ r ϕ /h ϕ, e z r z /h z, e ρ cos ϕ e x sin ϕ e y e ϕ sin ϕ e x cos ϕ e y (2.60) e z e z., (2.11) [e ρ e ϕ e z ] [e x e y e z ] P, P cos ϕ sin ϕ 0 P sin ϕ cos ϕ 0 (2.61) 0 0 1., (2.12)., P P 1 t P cos ϕ sin ϕ 0 P 1 sin ϕ cos ϕ 0 (2.62) 0 0 1., (2.16) [e x e y e z ] [e ρ e ϕ e z ] P 1, e x cos ϕ e ρ sin ϕ e ϕ e y sin ϕ e ρ cos ϕ e ϕ (2.63) e z e z

2.3. 23., (2.20) ( ) ( ) ( ) cos ϕ sin ϕ ρ ϕz ( ) ( ) ( ) ρ sin ϕ ρ cos ϕ ϕ zρ ( ) ( ) ρϕ (2.64),, (2.21) ( ) ( ) cos ϕ ρ ( ) ( ) sin ϕ ρ ( ) ( ) ρϕ ϕz ϕz sin ϕ ρ cos ϕ ρ ( ) ϕ ( ) ϕ zρ zρ (2.65).,. (2.44), α [e ρ e ϕ e z ] [e x e y e z ] Γ α Γ α Γ ρ. 0 0 0 0 0 0 0 0 0, Γ ϕ 0 1 0 1 0 0 0 0 0, Γ z 0 0 0 0 0 0 0 0 0 (2.66)

25 3 3.1 Γ p u u(p), v v(p), w w(p) (3.1)., (u, v, w) Γ r., dr dp h du u dp e dv u h v dp e dw v h w dp e w (3.2) Γ r., dr dp, s., s ds. ds (h u du) 2 (h v dv) 2 (h w dw) 2 (3.3). s, (3.2) 1. t., t dr ds (3.4) Γ., Γ dr t ds dr t ds (3.5)

26 3. f Γ f ds (3.6) Γ. s 1, (u, v, w),, Γ r., s f, (3.6)., A Γ A dr (3.7) Γ. (3.5) A t ds (3.8) Γ., Γ, (3.7) (3.8) A Γ. s 1, (u, v, w),, Γ r., s A A u, A v, A w, (3.7). p Γ A dr Γ ( ) du A u h u dp A dv vh v dp A dw wh w dp (3.9) dp., Γ v, w,, u, p u., f ds fh u du (3.10) Γ Γ,, A dr A u h u du (3.11) Γ Γ.

3.2. 27 3.2 Σ p, q u u(p, q), v v(p, q), w w(p, q) (3.12)., (u, v, w) Σ r., q p,, p q. p, q,, (dr) q, (dr) p, (dr) q h u (du) q e u h v (dv) q e v h w (dw) q e w r p (dp) q (dr) p h u (du) p e u h v (dv) p e v h w (dw) p e w r q (dq) p (3.13)., ( ) r p h u p ( ) r q h u q q p ( ) e u h v p ( ) e u h v q q p ( ) e v h w p q ( ) e v h w q p e w e w (3.14)., p, q p q,, r p r q 0. (dr) q, (dr) p Σ ds ds (dr) q (dr) p r p r q (dp) q (dq) p (3.15)., r p r q. { } (v, w) ds h v h w (p, q) e (w, u) u h w h u (p, q) e (u, v) v h u h v (p, q) e w (dp) q (dq) p (3.16)., (α, β) (p, q) ( ) α p ( ) β p q q ( ) α q ( ) β q p p (3.17)

28 3., ds, ds r p r q (dp) q (dq) p { h v h w (v, w) (p, q) } 2 { h w h u (w, u) (p, q). ds } 2 { } 2 (u, v) h u h v (dp) q (dq) p (p, q) (3.18) n r p r q r p r q (3.19) ds n ds (3.20). Σ u,,., p v,, q w,,, ds h v h w (dv) w (dw) v e u (3.21) ds h v h w (dv) w (dw) v (3.22).,. Σ Σ, Σ Σ., Σ Σ. f Σ f ds (3.23) Σ., A Σ A ds (3.24) Σ

3.3. 29. p, q A ds Σ { } (v, w) A u h v h w Σ (p, q) A (w, v) vh w h v (p, q) A (u, v) wh u h v dp dq (p, q) (3.25)., (dp) q, (dq) p,, dp, dq. p, q 1, (u, v, w),, Σ r., p, q A A u, A v, A w, (3.25)., Σ, p v,, q w., f ds f h v h w dv dw (3.26),,. Σ Σ Σ A ds Σ A u h v h w dv dw (3.27) 3.3 (u, v, w) dv dv (dr) {(dr) (dr) } h u h v h w (du) (dv) (dw) (3.28)., α, β (dr) αβ. f Ω (3.28) f dv fh u h v h w du dv dw (3.29) Ω Ω., (du), (dv), (dw),, du, dv, dw.

31 4 4.1 f f f dr df (4.1)., dr. dr t ds f t df ds (4.2). (4.2) f t., f f,., f df/ds 0, f f., f. f r a r b f dr df f(r b ) f(r a ) (4.3) r a r b r a r b., f f,., f (4.3) 0., A f. (u, v, w) f f 1 ( ) e u 1 ( ) h u h v e v 1 h w ( ) e w (4.4)

32 4. (4.4). f u, v, w u e u h u, v e v h v, w e w h w (4.5)., ( ) ( ) ( ) f u v w (4.6).,,, f f f ( ) e x ( ) e r 1 r θϕ r f ( ) e y ( ) e z (4.7) ( ) e θ 1 ( ) e ϕ (4.8) θ ϕr r sin θ ϕ rθ ( ) e ρ 1 ( ) e ϕ ρ ϕz ρ ϕ zρ ( ) e z (4.9) ρϕ., f (4.4). (u, v, w) f dr h u du f e u h v dv f e v h w dw f e w (4.10). f ( ) ( ) df du dv,, u f e u 1 ( ) h u ( ) dw (4.11) (4.12)., v, w, f (4.4).

4.2. 33 4.2 A A ( A) S σ A dr (4.13)., σ, S. S n S ( A) n 1 A dr (4.14) S. (4.14) A n.,., A A,., A 0. (4.13), A f σ 0,, A 0.,,. σ ( f) 0 (4.15) (u, v, w) A A 1 {( ) ( ) Aw h w Av h v h v h w 1 {( ) ( ) Au h u Aw h w h w h u 1 {( ) ( ) Av h v Au h u h u h v } } e u e v } e w (4.16)

34 4. (4.16). e u e v e w h v h w h w h u h u h v A A u h u A v h v A w h w (4.17)., f (4.4) ( f) 0,,. A, f f(u, v, w) u u 0 A u h u (u, v 0, w 0 ) du v w A v h v (u, v, w 0 ) dv A w h w (u, v, w ) dw v 0 w 0 (4.18), A A f.,,, A { ( Az ) A { ( Ax ) { ( Ay ) ( ) Ay ( ) Az ( ) Ax } } } e x e y e z (4.19) { ( Aϕ ) ( ) } 1 r sin θ Aθ r A r 2 sin θ θ ϕr ϕ rθ { 1 ( Ar ) ( ) } Aϕ r sin θ e θ r sin θ ϕ rθ r θϕ { 1 ( Aθ ) ( ) } r Ar e ϕ r r θ θϕ ϕr e r (4.20)

4.2. 35 { A 1 ( Az ) ( ) Aϕ ρ ρ ϕ zρ { ( Aρ ) ( ) } Az ρϕ ρ ϕz { 1 ( Aϕ ) ( ) ρ Aρ ρ ρ ϕ ϕz ρϕ } e ϕ zρ } e ρ e z (4.21)., A (4.16)., (4.13) σ γ 1 : (u 0, v 0, w 0 ) (u 0, v 0 v, w 0 ) γ 2 : (u 0, v 0 v, w 0 ) (u 0, v 0 v, w 0 w) γ 3 : (u 0, v 0 v, w 0 w) (u 0, v 0, w 0 w) γ 4 : (u 0, v 0, w 0 w) (u 0, v 0, w 0 ) (4.22) 4., σ σ γ 1 γ 4., γ 1, γ 3., γ 1 t e v, γ 3 t e v A dr A dr γ 1 γ 3 v0 v v 0 {a v (u 0, v, w 0 ) a v (u 0, v, w 0 w)} dv (4.23)., a v A v h v., a v (u 0, v, w 0 w) w 2 ( ) av a v (u 0, v, w 0 w) a v (u 0, v, w 0 ) w (4.24) 0 v0 v ( ) av A dr A dr w dv γ 1 γ 3 v 0 0 u 0 v ( ) ( ) av Av h v v w v w 0 u 0 v 0 0 u 0 v 0 (4.25) u 0 v

36 4., 2 v v v 0., γ 2, γ 4., γ 2 t e w, γ 4 t e w A dr A dr γ 2 γ 4 w0 w w 0 {a w (u 0, v 0 v, w) a w (u 0, v 0, w)} dw (4.26)., a w A w h w., a w (u 0, v 0 v, w) v 2 ( ) aw a w (u 0, v 0 v, w) a w (u 0, v 0, w) v (4.27) 0 0 w0 w ( ) aw A dr A dr v dw γ 2 γ 4 w 0 0 ( ) 0 ( ) aw Aw h w v w v w 0 w 0 u 0 0 w 0 u 0 (4.28)., 2 w w w 0., σ σ { ( Aw ) ( ) } h w Av h v A dr v w (4.29) 0 0 σ w 0 u 0., σ n e u, S h v h w v w, (4.14), { ( A) e u 1 ( Aw ) ( ) } h w Av h v (4.30) h v h w 0 0 w 0 u 0., ( A) e v, ( A) e w, u 0, v 0, w 0 u, v, w, A (4.16). u 0 v 0 u 0 v 0

4.3. 37 4.3 A A A V ω A ds (4.31)., ω V, ω ω. A 1 A ds (4.32) V,.,., A 0. (u, v, w) A {( ) ( ) 1 Au h v h w Av h w h u A h u h v h w ω ( ) } Aw h u h v (4.33). (4.33). A (4.16) ( A) 0 (4.34).,.,,, A A 1 r 2 sin θ A ( ) Ax { ( Ar ) r 2 sin θ r θϕ ( ) Ay ( ) Az ( ) Aθ r sin θ θ ϕr ( ) Aϕ r ϕ (4.35) rθ } (4.36)

38 4 A 1 ρ { ( Aρ ) ρ ρ ϕz ( ) Aϕ ϕ zρ ( ) Az ρ ρϕ } (4.37)., A (4.33)., (4.31) ω σ 1 : (u 0 u, v, w ) σ 2 : (u 0, v, w ) σ 3 : ( u, v 0 v, w ) σ 4 : ( u, v 0, w ) σ 5 : ( u, v, w 0 w) σ 6 : ( u, v, w 0 ) u 0 u u 0 u, v 0 v v 0 v, w 0 w w 0 w (4.38) 6., ω ω σ 1 σ 6., σ 1 σ 2., σ 1 n e u, σ 2 n e u A ds A ds σ 1 σ 2 w0 w v0 v (4.39) {a u (u 0 u, v, w) a u (u 0, v, w)} dv dw w 0 v 0., a u A u h v h w., a u (u 0 u, v, w) u 2 ( ) au a u (u 0 u, v, w) a u (u 0, v, w) u (4.40) 0 w0 w v0 v ( ) au A ds A ds u dv dw σ 1 σ 2 w 0 v 0 0 ( ) au u v w 0 v 0 w ( 0 ) Au h v h w u v w 0 v 0 w 0 (4.41)

4.3. 39., 2 v, w v v 0, w w 0. σ 3 σ 4, σ 5 σ 6 A ds ω { ( Au ) ( ) ( ) } h v h w Av h w h u Aw h u h v u v w 0 0 0 v 0 w 0 w 0 u 0 u 0 v 0 (4.42)., V h u h v h w u v w, u 0, v 0, w 0 u, v, w, A (4.33). 2 f 2 f ( f) (4.43) 2. (u, v, w) 2 f (4.4), (4.33) {( ) 2 f 1 h u h v h w h v h w h u ( h w h u h v ) ( ) } (4.44) h u h v h w.,,, 2 f ( ) 2 2 f f 2 ( ) 2 f 2 ( ) 2 f 2 (4.45) 2 f 1 r 2 ( r ) r2 1 ( ) ( ) 1 2 f sin θ r θϕ r 2 sin θ θ θ ϕr r 2 sin 2 θ ϕ 2 rθ (4.46)

40 4 2 f 1 ρ ( ) ρ ρ 1 ( ) 2 f ρ ϕz ρ 2 ϕ 2 zρ ( ) 2 f 2 ρϕ (4.47)., A. ( A) ( A) 2 A (4.48) 4.4,,. (1) (fg) ( f)g f g (2) (fa) f A f A (3) (fa) f A f A (4) (A B) B ( A) A ( B) (5) (A B) (B )A (A )B B ( A) A ( B) (6) (A B) (B )A (A )B A( B) B( A) (4.49)

41 5 5.1 1 f(x) b a df dx f(b) f(a) (5.1) dx..,. f, (4.3) r a r b f dr f(r b ) f(r a ) (5.2). (5.1), (5.2). 2. 5.2 A A ( A) S σ A dr (5.3), 2 3 σ 1, σ 2., σ 1 σ 2 1 γ,, σ 1 σ 2., σ 1 σ 2 ( A) 1 S 1 ( A) 2 S 2 A dr A dr (5.4) σ 1 σ 2

42 5, γ., σ 1, σ 2 γ t 1, t 2., ( A) 1 S 1 ( A) 2 S 2 A dr (5.5) (σ 1 σ 2 )., σ 1 σ 2 σ 1 σ 2., Σ 3 Σ i σ i, ( A) i S i «P A dr (5.6) i σ i i. (5.6) ( A) ds A dr (5.7) Σ. (5.7)., A., f (5.2),. Σ 5.3 A A A V ω A ds (5.8), 2 4 ω 1, ω 2., ω 1 ω 2 1 σ., ω 1 ω 2 ( A) 1 V 1 ( A) 2 V 2 A ds A ds (5.9) ω 1 ω 1

5.4. 43, σ., ω 1, ω 2 σ n 1, n 2., ( A) 1 V 1 ( A) 2 V 2 A ds (5.10) (ω 1 ω 2 )., ω 1 ω 2 ω 1 ω 2., Ω 4 Ω i ω i, ( A) i V i «P A ds (5.11) i ω i i. (5.11) A dv A ds (5.12). (5.12). Ω Ω 5.4. (1) ( f)g dr [ fg ] rb r a f g dr r a r b r a r b (2) ( f A) ds fa dr (f A) ds Σ Σ Σ (3) f A dv fa ds f A dv (5.13) Ω Ω Ω (4) B ( A) dv (A B) ds Ω Ω A ( B) dv, (3) A g f g dv f g ds f 2 g dv (5.14) Ω Ω Ω Ω

44 5., f g ( (f g g f) ds f 2 g g 2 f ) dv (5.15) Ω Ω. (5.14), (5.15).

45 33 33 21 5 33 35 34 34 42 4 16 7, 13 15 7, 13, 14 22 20 19 28 44 31 32 32 32 25 26 3 7 11 12 22 20 41 4 40 41 25 25 26 25 11 1 29 29 9 11 11 1 31 4 37 38

46 37 37 25 27 37 37 7 41 43 3 7 4 9 4 11 1 31 27 28 31 7 28 28 27 3 3, 14 7 39 40 39 39 3