D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j

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6 6.. [, b] [, d] ij P ij ξ ij, η ij f Sf,, {P ij } Sf,, {P ij } k m i j m fξ ij, η ij i i j j i j i m i j k i i j j m i i j j k i i j j kb d {P ij } lim Sf,, {P ij} kb d f, k [, b] [, d] f, d kb d 6.. 6..5 λ, µ f,, g, [, b] [, d] λf, + µg, 6.. f, + bg, d b λf, + µg, d λf, + µg, d d b λf, + µg, d d d λ b λf, + µg, d f, + µ b j g, d b d b λ f, d + µ λ f, d + µ g, d g, d f, g, d

b f, f, d b d d g, b b f, d g, d g, d 3 f, f, 6.. f, d b b f, f, d b f, d f, d d b f, d d b f, d f, d 6..3 6..3 6..3 R R f, g f,, g,, f,, g,, /, / R ij P ij ξ ij, η ij {P ij } f, + b g, S f + b g,, {P ij } m i j m fξ ij, η ij + b gξ ij, η ij i i j j i j fξ ij, η ij i i j j + b m i j S f,, {P ij } + bs g,, {P ij } gξ ij, η ij i i j j f, g lim S f,, {P ij }, lim S g,, {P ij} {P ij } lim S f+b g,, {P ij } {P ij } lim S f + b g,, {P ij } lim S f,, {P ij } + b lim S f,, {P ij }

3 f + b g R f, + b g, d f, d + b g, d R f, + bg, f, + bg, d f, d + b R R g, d f, g, R f, g, S f,, {P ij } m fξ ij, η ij i i j j i j m i j gξ ij, η ij i i j j S g,, {P ij } f, d f, d lim S f,, {P ij } R lim S g,, {P ij} g, d R g, d 3 S f, m, {P ij } fξ ij, η ij i i j j i j m fξ ij, η ij i i j j S f,, {P ij } i j f, d f, d lim S f,, {P ij } 4 R A, A χ A,, / A R lim S f,, {P ij } f, d R lim S f,, {P ij } f, d

4 f χ f f χ f χ f + χ f χ f f, d f, d f, d χ f, d R R χ f, + χ f, χ f, d R χ f, d + χ f, d χ f, d R R R f, d + f, d f, d f, d + f, d 6..3 b b d gh d g b d f, d f, d d d g h d h d d f, d b d d h d gh d b b d h d g g d h d 6..4 {, R, }, {, R, } {, R, }

5 f, d f, d + f, d f, d + f, d f, d f, d {, R, + } {, R, }, {, R, + } + + f, d f, d f, d f, d + f, d f, d + 6..5 e d + si d e d e e π π e + si d + [e ] π os + si 3 π + π 8 f, d [ + os + si ]

6 3 4 5 d e os os 3 d + d d 3 π os os 3 si os 3 d [ log ] e d [ si os 3 ] d t os dt si d 3 t 3 dt 4 + d + [ + ] 3 + 4 + 3 3 + 7 9 6 + 39 6 6 5 + + 6 3 + + d + [ + ] 6 3 + 4 + 3 3 5 6..6 {, R π π, } π {, R, } π π si d π π d si si d π [ os ] π π [ si ] d π

{, R, } 7 {, R, } d e e d e d e [ ] e d 6..7 6..6 {, b, } {, b b, b} f d d f f d t f ft dt f d ft dt d ft dt d t ft t ft d d ft [] t dt f dt dt t ft t dt t 6.. u + v 3 + u, v 3

8 uv E {u, v R u, v } u u 3 v 3 v J J det 3, u, v d J dudv dudv 3 + + + d E log v + u du dudv v + dv u u du v + dv os θ, si θ θ E {, θ R π, θ π} si + d E π π si ddθ π π dθ si d [ os ] π π π dθ 3 os θ, si θ θ si d os π 4 E {, θ R, π θ π } θ

9 + + d E π π π + ddθ π dθ dθ + d + d [ ] π + π 4 os θ, 3 si θ θ 3 E {, θ R, θ π } J, os θ si θ J, θ det 6 3 si θ 3 os θ d J ddθ 6ddθ e 3 d E π e 6 6 ddθ dθ 6e 6 π 6 dθ d e 6 6π [ ] e 6 d 6 4 π e 6 3 3 + b >, b > os θ, b si θ +, θ π b, J, θ det os θ si θ b b si θ b os θ

6.. u u, u, v u, v, det u v det v v u v u u det u v v v u v u u + v u v u + v v det u u + v u v u + v v 5.5.4 5, u, v u, v, det u v + det 4 3 uv E {u, v R u, 3 v 4} u u, v, det v u v det, u, v + 4 v 4u 3 4

+ + d 3 3 E vv u du 4 3 v 4u dudv vv u v 4u dv [ v4 v 3 4uv + u] du v3 6 + u 6 4u 9 + u 9 4u du [ 8 5 4 u 3 6 + u 5 9 4u 3 9 + u 5 78 48 3 + 5 5 ] u i φu, v, ψu, v, u, v ii iii u, 3 v 4 v 4u u, v u 6.3. z C {,, z R 3, z } + + z + ddz A d + + z + d [ ] z d + + z + z + d + + [ ] + log + + + log + log + [ log + log + + ] log + 3 8 log B

u + v 3 z w + z uvw E {u, v, w R 3 5 u 6, v, w } 3 6..,, z u, v, w u, v, w,, z J u, v, w J,, z det 3,, z u, v, w u, v, w,, z ddz J dudvdw 6u v w dudvdw 6u v w ddz dudvdw E 6 5 6 5 du du dv 6u v w dw u 4v dv 3 si θ os φ, si θ si φ, z os θ θφ 6 5 48u du 4 z E {, θ, φ R 3, θ π, π φ π } J si θ + + z ddz d π π d dθ π π J ddθdφ E π si θ dφ d π si θ dθ dφ 3π π π dθ si θ dφ π

3 6.4. {, R +,, } { } N os θ, si θ θ E {, θ R, θ π } I + + d E + ddθ π + d dθ π + d π [ ] + π 4 + lim I π 4 6.4. + + d lim I π 4 {, R + } { } N os θ, si θ θ E {, θ R, θ π} I d ddθ π d π [ ] E dθ π π d

4 lim I π 6.4. d lim I π 3 {, R, } { } N I 3 d 3 3 3 { [ 3 5 3 d 3 5 } 3 3 ] [ 3 ] 3 lim I 9 6.4. 3 d lim I 9 4 {, R, } { } N

5 I e d e d [ e ] lim I [ ] e e 6.4. e d lim I d 6.4. {, R, } { } N I I + + α d Cse α I α + + α d + + α+ + α+ [ ] + + α+ α Subse α, I [ α α + + α + α α { + α + α + } α α α < lim I lim + α + α lim α α ] + α α > α + α + ±

6 α > α lim I Subse α I { + + + } log+ log+ log + + + lim I + Cse α I + + d log + + log + [log + + ] [ + + log + + + log + ] + log + + log + lim I lim log + + + + + α > α α {, R + } { } N I I + α d + + α d os θ, si θ θ E {, θ R, θ π} I ddθ E α π dθ α d π Cse α α I π α α α d

α < lim I Cse α I π log π α 7 α > lim I + lim I + < α < π α 6.4.3 [, ] [, ] [, [, {, R, } {, R, } + α d + 3 d [ + 3 d + E + 3 d + [ ] [ + + + + + + + + ] E E + 3 d + + [ + + + 3 d ] + ]

8 lim + 3 d E E [, ] [, ] [, [, E E E {, R, } E {, R + 3 d E lim E [, } + 3 d + E + 3 d + [ ] + + + + + + + + 3 d + ] + 3 d [ + + [ + + + 3 d ] + ] 3 f, f,, + 3 lim d lim d + 3 E + 3 f, 6.4. 6.4.4 {, R, }

9 { } N I I e + p q d I e + p q d e p e q d 4.5.3 e p e q d lim e p Γp, lim e p d Γq I lim I ΓpΓq uv, u v J, J u, v det v u u v u I e + p q d E {u, v R u, v } E e u uv p u v q ududv {E } N E E IE IE e u uv p u v q ududv E IE e u u p+q v p v q dudv E du e u u p+q du e u u p+q v p v q dv v p v q dv E

4.5.3 4.5.4 lim e u u p+q du Γp + q, lim v p v q dv Bp, q I lim IE Γp + qbp, q Bp, qγp + q 6.5. m A ka ka A A + u JΦ v u v z u z v kjφ JΦ z z u u u u u u,, z z v v v v v v z z u v u v u v,, z z u v u v u v, u, v,, z u, v, z, u, v,, z z, + + u, v u, v u, v 6.5. z f, Φ,,, f,

,,,, z, z,, f f, + u, v f f f, z + u, v f, z, + u, v f + 6.5. 6.5. f 6.5.3 Φ, θ, f os θ, f si θ [, b] [, π],, z z, + +, θ, θ, θ f os θ + f os θ f si θ f si θ f + f θ f f si θ f os θ f si θ f os θ + 6.5. S f + f d π b b dθ f + f π 6.5.4 z z + z z z S + z + z d f + f dθ b π f + f

{, R + } + z + zz z z z S 4 8 + z + z + z d z d d z d d 4 [] 4 z z S + z + z d {, R + } z + + z 4 + zz d z z z z S 4 + z + z d d 4 z + + z 4 d z d os θ, si θ θ E {, θ R os θ, π θ π }

3 S 4 4 E π π 8 π os θ 4 ddθ 4 π 6 π 8 π [ 4 ] os θ os θ dθ 4 π d π π dθ 6 π si θ dθ 6 [θ + os θ] θ π θ π 4 dθ 4 os θ os θ dθ dθ 3 C : t, t Φt, z t, t, z Φθ, z + os θ os θ, + os θ si θ, z [, π] [, ], θ, z si θ os θ + os θ si θ si θ + + os θ os θ,, z θ, z si θ + + os θ os θ si θ + os θ + os θ os θ + os θ os 3θ os θ z, θ, z si θ os θ + si θ si θ os θ + os θ si θ si θ + si θ si 3θ os θ, + θ, z, z + θ, z z, 4 os θ, z θ

4 S S 4 os θ π dθdz dθ 4 os θ dz π os θ π dθ dz 4 os θ dθ π 4 os θ π os dθ + θ dθ 6 π π 4 os θ π dθ os θ π dθ i z, + θ, z, z + θ, z z, θ, z kjφ z ii C : t, t t b z d C d 6.5.5 6.5. + + z z z + {, R + 9} z + + z + + + zz z z + + z z + + + z + z z + + z z

5 S + z + z d d + z d os θ, si θ θ E {, θ R 3, θ π} S d + 3 π π d dθ 3 74 []b d 3 d E ddθ 3 dθ d 3 3 d t 3 4t t dt + d 3 t + 3 t dt + t + + t + 4.. 67 3 d 3 3 dt t + dt t t + + t t t t + 4 t t 3 3 4 t 3 d 3 ε d lim d π 3 ε, ε + +ε 3 3 S π d 4π 3

6 z + z z fz gz z gz fz θ fz + z, gz z z fz z S gz z S S π π ππ + fz + f z dz π + z + z dz π [ si z + z ] z z + z z dz S π π ππ gz + g z dz π z S S + S 4π z dz π [ si z z ] z z + z z dz 6.5.6 {, R, } M M ρ, d + d + d [ + ] 3,

7 M 3 8 3 M ρ, d 3 [ + ] 3 + d 3 ρ, d 8 3 3 8, 3 8 os θ, si θ θ E {, θ R, θ π } ρ, M M ρ, d π 4, d d M 4 π 4 3π M ρ, d 4 π π d os θ dθ 4 π d π d os θ dθ ρ, d 4 3π 4 3π, 4 3π 6.5.7 ρ, M ρ, d d d

8 M ρ, d d 3 3 3, 3 3 V V π 3 π 3 µ d b os θ, b si θ os θ + b b si θ + J J,, θ b θ E {, θ R, θ π} µ d E π b ddθ b dθ d πb ρ, k M M ρ, d k d d k πbk, M πb π π ρ, d πbk π d 3 os θ + k d b os θ + dθ π dθ π [ 3 3 os θ + ] dθ

9 M πb ρ, d πbk π d b si θ dθ b π k d π si θ dθ d, V V πb π π b