工程硕士网络辅导第一讲

Transcription

1 < > < R R [ si t R si cos si cos si cos - sisi < si < si < < δ N δ { < δ δ > }

2 δ < < δ δ N δ { < < δ δ > b { < < b R} b] { b R} [ { > R} { R} } [ b { < b R} ] { b R} { R} X X Y : X Y X R : X R X R X X <

3 X < < X g g g g g g g g T T T X M X M X X Y U R

4 : U Y u g : X U u g g u g u u g u F N{ δ } F N{ δ } F X Y N δ N{ δ } { δ } { R < δ δ } > < < X Y Y g X g g g g g g g g g

5 t T t t t T t T t t t t t X t t α β T t t ρ ρ θ θ θ θ ρ θ ρ ρ cosθ ρ siθ θ θ θ c α α > e

6 log > l si cos t cot sec csc rcsi rccos rct { } A A ε > N > A > N A < ε { } A A lim A A } { A { } lim A A lim A } { A < ε A < ε lim A lim B A > B N > > N >

7 { } G > N > > N > G { } lim > N } N lim G > N > > N > G { > N N lim { } G > N > > N < G si { } L L k { } { k L} } { } k { } } } lim { } { { k k { k G > N > k N > G lim A c lim c ca lim A lim B lim ± lim ± A ± B lim A lim B lim AB

8 lim A lim B lim A B lim lim { } lim A > > N > > N > lim A < < N > > N < lim A > > ε > A ε < < A ε ε A > A A < < > A > N > N { } N > > N > lim A lim A < N > > N < lim A lim A lim B A > B N > > N > { } lim A lim B A B { } } lim A {

9 M > N > > N < M lim A > ε > A ε < < A ε ε > N > N A < < A M m { A A } > > N < M { } M R N > > N < M lim lim { } lim e lim A N > > N c b b c lim A c { } lim lim lim { N > > N } M < M lim ε > > N N < ε M { N m N N } > N lim < ε M M ε L

10 lim µ µ µ µ µ λ l λ > >! sisi < si I sisi d I cossi d I < < I I > > I I I I > I > si < si I sisi d < sid cos I cossi d > cos d > I I < < I [ ] [ ]

11 [ ] e e > < si φ si φ < φ < φ < < < φ si si si < lg lg > > < > < < X

12 > > ρ cosθ θ > ρ < ϕ < cosϕ φ φ l e e e e l l g g g

13 5 T T b < b b t t t b b t b t b t t t u u u b b b > T b [ ] [ ] [ ] [ ] [ ] D 4 4 rct t t t t

14 A t rct t > < > < > D u < u u u u > u u u si si k { } k k si k k lim } k k { k k L k si k k { } k k L { }

15 sg < > > [ ] < < [ ] [ [ ] < < b c b c b c b c t t t t t

16 lg lg > > < > < < b < b b t t t b b t b t b t t t u u u b b b > T b rct t t t t A rct t

17 t m{ m{ } d } m{ m{ } < > } d d d 97 d t [ t] dt lim [t] t : < < t [ t] dt t [ t] dt t [ t] dt L t [ t] dt t [ t] dt t [ t] dt k k k t [ t] dt udu < udu t [ t] dt u t k du dt k t [ t] dt k [ u k k ] du udu < t [ t] dt < t [ t] dt < < t [ t] dt lim.95-- e D A B C D

18 lim e lim e lim e lim e lim lim e e lim e e B A B C D lim e lim lim e e { 4 } D D b b dσ D b b b b si cos e e 5 si I d I

19 I D b dσ D b dσ b b I dσ dσ b dσ D 4 I b dσ b D D 6 L lim { } D 6 < 6 { } < lim 6 < 6 A A 6 A A A lim A > lim < < lim

20 > < < lim lim lim lim N > N < < lim lim lim lim lim lim lim lim lim k k k k L k k < < lim k k k λ > > lim λ λ λ λ lim < N > > N < N > { } < >

21 { } lim lim λ A λ λ A lim lim A A A > λ A lim > lim!! > > < { [] > } lim A A A A < < { }! lim! < L <! lim l lim lim l lim lim l l l > L

22 lim > L lim A A A A lim A A > L lim lim L lim lim lim lim lim lim { } lim lim lim { N > > N } M < M

23 lim ε > > N N < ε M { N m N N } > N lim < ε M M ε ' > δ > δ > δ < lim > δ > δ δ > δ > δ < ' > δ > δ δ δ > δ >

24 ε > A X > > X A < ε A A lim A A A G > A X > > X > G lim lim > G lim < G lim A lim lim lim A X > > X A < ε A A lim A A

25 A * N δ { < < δ δ } > ε > A δ > δ < δ < < δ A < ε A A lim A A A > δ δ ε > A δ > δ < δ < < δ A < ε A lim A δ > δ ε > A δ > δ < δ δ < < A < ε A lim A A ± lim lim ± lim ± lim A ± lim A ±

26 lim B ± A B ± lim A ± lim A lim B A B δ δ > lim A δ δ > lim A g φ δ δ δ > φ < < g lim g limφ A lim A M > M lim g lim g si lim lim e ± lim A C lim C CA lim lim A A lim g B lim g B lim ± g A ± B lim g AB lim A g lim g B lim g A B

27 lim lim lim A > > lim A > N δ { < < δ δ > } N δ > lim A < < lim A > > ε A δ > < δ A < ε A ε < < A ε < ε A > A A < < > A > lim A lim g B A > B N δ { < < δ δ } N δ > > g > lim lim A < lim A lim

28 lim u A u u u u lim u u u u lim u A lim A A α siα lim α lim α α e α α lim si lim si lim si si lim limsi lim lim limsi si α β α lim µ β µ α β µ α β α β µ α β µ α β

29 ~ si ~ t ~ l cos ~ ~ l > e ~ λ ~ λ λ R si ~ 6 lim α α α β N δ { < δ δ > } lim A A [ b] b [ b] b

30 N δ { < < δ δ > } α α N δ { < δ δ > } lim lim lim lim lim lim lim lim lim lim lim lim lim lim

31 α lim α > N δ { < δ δ } N δ > > M > N δ { < δ δ } N δ M > N δ g ± bg g g g u u u u u u u u [ b] [ b] [ α β ] [ b] [ b] M > [ b] M M > [ b] > L > k k L k k

32 b [ b] k lim > k k [ b] k k [ b] [ b] M [ b] m [ b] M m m m M [ b] k m [ b] [ b] [ b] [ b] b < b b b < b > b < b b b < b b LLL b [ b] {[ b ] LL} [ b] b < L b b b L b d b b b lim d lim lim b } { b } { lim lim b A A b

33 b > < lim lim lim b lim [ b] < < [ b] [ b] [ b] [ b] [ b] b b A b A F A F [ b] F b b > b > A > F A < F b b A > F b F < F b F A A lim lim lim

34 lim lim lim lim si lim e e 4 4 e e lim e e e e e lim lim e e 4 lim si lim si lim si lim si lim si lim e e 4 e e 4 lim si lim si lim e e 4 e e 4 lim si lim 4 si lim e e si lim si lim si lim

35 si lim si lim lim lim si si lim e lim lim lim lim e lim lim e e e e e e cos lim e e cos lim e e cos lim cos lim e e e lim lim lim lim

36 l lim e lim l l lim lim lim e l lim l lim l e l lim l lim l si cos lim si cos lim si si cos si lim si si lim e si lim lim cos 6 si cos lim e lim lim lim lim si l lim e cos

37 si l > cos < lim l lim si si lim lim _ lim si lim cos b 5 b e si lim cos b 5 lim si cos b e lim e si lim cos b lim e b 4 cos b b 5 b 4 lim. g A A A cos e cos u e u cos e

38 cos e e lim k t e k k k e k e e cos e lim t k e e lim cos e t k e lim k e lim k k e ϕ ϕ ϕ ϕ φ ϕ < ϕ si φ φ si φ e e lim e e lim e lim cot b lim cos si b

39 lim cos si b cot lim cos cot si b cos cot cos si b cos cos cot si b si b cos si cos lim cos lim b b e e e cos.5 [ [ ] si lim si si lim lim si si si cos lim lim lim F A F [ b] F b b > b > A > F A < F b b A > F b F < F b F A A [ lim A [ lim A M >

40 X > > X M [ X ] [ X ] M > [ X ] M M m{ M M } [ M [ [ b] < < b b b F F b F < F b b b > [ b] F b b F < b < c c b c b c b b c c < c b c > b c b b c lim lim b b b b b c b c

41 lim lim b c b c b c b c c b c lim > lim ε > X > > X < [ X X ] m [ X X ] [ X X ] [ X ] > X [ ] F [ ] F F m m F F F F F e e e > lim < e < 4e < e < < e

42 > > > L lim C lim

43 lim lim lim α A α A α β β α

44 lim α α lim lim lim lim b [ b ] b b lim [si l si l ] t si l t si l t lim t t [si l t si l t] t

45 lim h h k k h k lim h lim h h h lim t h h k. t t rct si e > lim rct

46 lim e si rct > cos si e < lim lim cosh lim e h h h h lim h lim [ h h h h h h ] lim h e e h h e h h h

47 lim lim lim h h e e lim lim h h e h h e h h h h h h e h α h e α h h e h h e lim h e h h lim h h h lim h h h lim h h h lim h h h h lim h h lim [ h h h h h ]

48 h h lim lim h h h h cos > g g lim lim cos lim lim lim lim lim g lim lim cos lim lim _ g g /

49 ' > δ > δ > δ < lim δ δ δ > > > δ > δ < < cos lim e si e

50 cos lim si cos si lim l cos lim si < lim lim cos si lim [ ] lim lim e lim si lim si si lim

51 lim lim si si lim si [lim ] [lim si 4 lim si e 4 α α β α β β ] A

52 A o o A d lim A d d d d lim P d Q P p E d P Q p E d Q P R PQ P P g ± [ g ] ± g

53 [ g ] g g g g [ ] g g ± g d ± dg g d g g d c cd c d g g d g d g [ g h ] g h [ g h ] g h g h g h o e 4 e d d l rct lc Ce rct

54 e C 4 rct e e 4 k [ [ ] k k < < k [ ] 4 k 4 k. ' ' ' lim lim 4 lim 4 4 k lim 8k ' k

55 [ ] [ ] d d d d lim d d d d λ e λ λ λ e λ e L λ λ e λ si cos si

56 cos si si g [ g ] C k g! k! k! k C k k g k L k k! g g si 99 si si si 99 si! 98 si

57 99si si cos 99si 98!! l!! 9!! 9!

58 du u ϕ ϕ ; u d d u u ϕ u du [ ϕ ] d d du d du d { [ ϕ ]} u ϕ rct l [l rct rct l rct l ] si >

59 l si l si cos l si si [cos l ] u v rcte d d l e e rcte e e e e e e l e si e si l

60 d d e e e e e e u u u d u du u u u ϕ [ ϕ ] d { [ ϕ ]} d u ϕ d u u F u du F

61 6 4 l l k ϕ

62 ϕ ϕ g g lim g g g g g g g [ ] g g g lim

63 t t t T ϕ t t t T t d t t d t d d d d dt d t t t t t t t t t t t [ t] t t t d d t [ t] t si t cost t si t cost t si t cost t k t

64 d d t si t cost t cos t bsi t t bcost b cot si t t t t t b si t si t b cott cost b si t t

65 4 9! 4 9! 5 δ > [ δ δ ] l si lim e si si lim e 9! 9 si si lim lim e l si lim e l si lim l si lim lim lim si lim lim si

66 si lim lim si lim lim lim si si lim lim 6 lim lim lim lim lim si l lim e lim

67 lim si si lim e l si lim e o lim si lim lim lim p q e l

68 l lim lim lim lim

69 N δ N δ N δ > lim

70 < lim N δ N δ [ b] < b b

71 b < b > b b b < b > lim < ε > δ > < < δ ε < < ε ε > < < < [ b]

72 b > ε > δ > < b < δ b < < b b ε ε b ε b > b < b b < < b b [ b] [ b] [ b b b ] [ b ] b b ξ ξ ξ b

73 [ b] b C [ b] [ b] [ b] m ξ [ b] ξ b ξ [ b] b ξ b b b A B b b b AB K AB b b b ξ AB

74 F b b F [ b] F F b ξ b F ξ b b ξ b ξ b θ b b < θ < ξ h h ξ

75 c b c b g b g c g g b [ b] [ b] L > L L < L < b > < b [ b]

76 g [ b] b g b g g b ξ b g b g ξ g ξ ξ ξ ξ m m

77 ξ ξ m m m m m m m m m ξ [] ξ M m [] ξ M ξ ξ M [ ] [] M

78 M M m [] ± ξ M M M M M ξ M M ξ M ξ ± M ξ M ξ M ξ m ξ ξ { } ξ M ξ ξ ξ M ξ [] F F F F

79 F F F ξ F ξ F [ ξ] ξ ξ F F F > F [] F F > F F F ξ F ξ F F g g F g g g g g

80 4 g ξ ξ ξ g g > < rct < 4 > rct < 4 < rct 4 rct

81 4 rct ] [ 4 rct ξ ξ 4 rct < < 4 rct ] 4 [rct 4 rct >

82 > > 4 ϕ < ϕ < ϕ rct ϕ C[] ξ ξ ξ ' ξ F F C[] F F F ξ F' ξ ξ ξ ξ ' ξ ξ

83

84 ] < < < > < [ δ δ U δ > δ < < > δ δ

85 A A A > < > A A lim A A >

86 A 4 > A A > A 4 A lim A < < > < >

87 9 [ b] [ b] [ b ] [ b] [] [] < 7 []

88 e l l l l l [ e ] e [ e] e l e le le l e l l m mi l [ e] [ e] b b

89 b b b b b b lim A lim B b 4 l 4l 4 4l lim >

90 lim 8l 5 > 4 > mi l l l e e < e > e lim l lim l

91 e e I > <

92 L k k > k < k k L e e cos

93 e e si e e cos e e si 4 e e cos 4 4 >

94 lim cos lim cos > λ λ λ > >. λ λ

95 . λ λ λ λ λ[ ] < < > > λ λ [ b] b ξ b ξ ξ b ξ b ξ ξ b ξ F b F b F ξ b F ξ

96 F b ξ b ξ ξ b b ξ ξ ξ b ξ b ξ b ξ ξ ξ ξ ξ b b ξ [ b] b b b b ξ ξ ξ ξ b b b b b b

97 b k > l k e e e e k > e > e e < e lim lim c c c lim [ ]

98 lim c c c c c c c c lim c [ ] lim ξ lim ξ e l c < < b b b l > b b b l > b b b b l > e c

99 b > t t tlt t t t t lt t t t > t t t > t > C lim lim C C lim lim C si

100 si lim si lim lim b ± ± b b lim ± lim b lim ± si lim lim si lim ± b e

101 e lim lim e lim lim e lim lim e lim lim lim lim e lim lim e

102 b lim [ lim [ lim k] e e ] e lim e e l e 4e <

103 l lim e l l < l l > > l > l < l [

104 F F F F F F F > F > F < < F < F F > > F > F F > F F F > F > ] [

105 ξ ξ ξ k ξ ξ ξ lim lim lim lim

106 " l 4 " l 4 [ ] si [ ] si

107 [ ] cos >

108 p α α

109 α ξ ξ b! L R! R ξ! ξ R

110 ! L ξ!! b! L o!

111 o si si si o o! 6 t t t sec

112 t sec sec t 4 t 4sec t sec t! o e e X e e e e e e X e L L e!! L e e! e! e e ξ L! e ξ si 6 lim

113 6 lim 6! 6 si 6 o si 6 lim 6 6 lim o 6 6 lim 6 6 lim si 6 lim 6 6 si 6 lim 6 si 6 lim 6 lim

114 6 6 lim lim 6 6 lim 6 si 6 lim 6 lim 6 lim lim lim g g g

115 lim g lim g lim g cos lim. cos l l e lim lim lim l cos l cos

116 cos si lim si lim cos cos cos l l e lim lim cos l cos lim lim. 6 lim cos e si 6. cos

117 cos lim e si cos lim e si si si cos lim 4 si cos si lim lim lim cos l l e e cos l lim l e e lim cos l lim l e e

118 cos lim cos lim e e e e e lim e e cos e cos lim l l lim lim l l l lim l lim

119 l lim lim l l l lim l lim lim lim e 4 lim lim e l e

120 l lim lim l lim l lim lim lim lim lim lim lim ' '' 4 o ' ''

121 lim si lim si si lim si si lim lim 6 6 lim 6 si lim si e

122 lim si e lim lim [ F

123 F ξ ξ F b b > > e > b l l l l > e l ' ' < b > > e l b l b < < b l b < bl l b < l b > b [] b

124 m { [] [] } ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ

125 ξ m ξ ξ ξ ξ { } ξ m { } [] [] ξ ξ δ > δ δ m { } [] δ δ δ δ

126 lim lim lim. lim I R F F I F I I F I F C I C

127 { F C} d F C F I C t dt d d C si cos F si

128 b b cos e / R <. e lim lim lim lim e lim e lim e ; <

129 < ; e F < ; e F < ; e F < ; e F >

130 F rct F 4 4 < t > 4 d C ϕ ϕ d ϕ C d si b cos

131 d d rct d si b cos d t rct t C t b b b C t d cos dcos cos cos d l d l cos C d d d C l

132 d rcsi C d d rcsi d d rcsi C d l l dl l l d l l rcsi l C rcsi d rcsi drcsi rcsi C d cos si dcos cos si C

133 dcos cos cos dcos cos l cos l cos l cos C 6 d d cos si d l si C C ϕ t ϕ t dt F t C ϕt t ϕ d F ϕ C d si t t > d costdt

134 d cost cosdt cos tdt cost si t dt t C rcsi d d > sect d C t t si t d costdt d cost dt sit cost cost si t cost si t dt dt si t cost si t cost l rcsi C I cost dt si t cost

135 cost si t si t cost cost dt si t cost l I rcsi C I d 4 4 t d 4dt 4 t 4 t t rct C t rct C u dv u v v du si d dcos

136 cos cos d cos cos d cos si cos C l d l d l C m l d rcsi d d l l t m rct e si bd l d t t l e e t t d l e de e e l e e l e l e C d e

137 e l e e e e l e C d si d si cos si I d 4 d si 4 4 d

138 e e d e t t l t d dt t e d l t dt e t t l t dt t t l t dt t t l t 4t dt t t t t l t 4t l C t e 4 e l e e C

139 e d P R P Q Q P R P Q P P Q P Q Q A Q k k P Q P Q

140 A A A k L k Q p p 4q < M N p q P p q Q Q k k 4q < p q M N M N L p q P Q M p q p q k k N k b p d

141 b p A A A B B b p A d B b p A A A A A A b A A A b p d p A B C D E A C B D E B

142 d d d d d l 4 C si cos si t t R R u v t t cos t t dt dt t t R si cos d

143 si d cos t t si t t d dt cos t t l cos C si cos t cos R Rsi cos dt d si cos si si cos si R si cos R Rsi cos t si R si cos Rsi cos

144 t t Rsi cos [ Rsi cos R si cos R si cos R si cos R si cos Rsi cos ] d cos si t cos d dt cos si tsi dt t t rcsi d rcsi d rcsi d

145 rcsi l si C d si si d si si cos t d d cos dt t t si d cos dt si dt t t l t l t C 8 4 t 8 dt 4 t t 4 t cos l C 4 cos 8 cos

146 d d si si si cos d t d 4 4 si cos cos t cos t d t 4 t l t t C

147 [ b] [ b] L i i i λ m ξ ] S i i [ i i ξ i i i i lim S lim ξi i λ λ i ] ξ i [ i i ] [ b] [ b s

148 lim S lim ξi i λ λ i [ b] b I b d lim S λ b s s d t dt b b [ b] [ b] [ b] [ b] [ b] [ b]

149 b d d b c R b c b d d d b [ A Bg ] d A d B b b c b g d [ b] b d g d g d b g d > b [ b] [ b] [ b] b d b d [ b ] m M b m b d M b g [ b]

150 b b b m g d g d M g d [ b] g [ b] ξ b b b g d ξ g d b g [ b] d b ξ b d b ξ [ b] ξ ξ d b [ ] [ ] d d T T d T d b d b

151 [ b] b d I sisi d I cossi d I < < I I > > I I I I > I > < sisi < si I sisi d < sid cos cossi > si I cossi d > cos d > I e d si si m e mi [ ] [ ] e d e d e d

152 M l d N d P d P < M < N M N < P M < P < N N P < M < < M d N P d < P < M < N > [ b] F b [ b] F C ] d t dt C F b C [ b F b F F b

153 d b b d d d d si d. si d. si cos d cos si 4 4. d si cos d

154 > ] d [] [ d d d [][] d d d [] d cos d cos cos cos d cos cos d

155 dsi d si l b b d b ϕ ϕ d ϕ ϕ F ϕ t b β d α t ϕ t dt ϕ t ϕt t ϕ ϕ α b ϕ β d F C b β α

156 I b b d b d t t dt t b d d t t b c t d c c b t dt t u 4 u d 4 4 d 4 4 u du u sect du t sectdt 4 t rccos u 4t

157 4 rccos d 4 4 cost dt cos t du t t sec rccos u 4 t t d si t rccos si t si t si t d si t rccos si t si t t dt 5 d u l u l l 5 l cos 4 d d I d u du I 4 5 d u d du

158 cos 4 d I I cos ] d d I [ cos d I 4 I I cos d 4 4 I d 4 4 [ ] si d si d si d si d si d si si d si d d t d dt si d t si t dt t si t dt si t dt

159 g ] [ b F [ b] b b b g d F g F g d d e l e e e e l l d d l e e e e e d e e J si d t si e d cos d J I cos tdt cos d si d si d cos

160 si I cos I I I L J J si cos d I!!!! L!!!! I I si cos e e 5 si d

161 4 5 8 I t e t dt e t t dt A t e t A e A t e dt t t e dt t t e dt t e A d d d

162 t d dt d t t dt [ b] [ b] t dt t dt d F [ b] F t dt [ b] t dt F [ b] [ b] F t dt [ b]

163 d d [ b t dt ] F [ b] F t dt F t dt [ b] [ b] [ b] M > M F t dt M lim F F t dt [ b] d d t dt lim [ t dt t dt] [ t dt] lim lim lim ξ dt ξ

164 ξ F e F [] t dt <. [] b t dt [ b] F t b t dt b t dt [ b] d d [ b b t dt β α t dt [ b] ] α β β t dt α

165 [ b [ b] ] d d α β β t dt α β t dt β β α α α C

166 d T > T F t dt G F G C C F G t dt G G G F G C G t dt u t G u d u u d u G T

167 T T d d d d T d T T d T T d d C T T d d C T T d d T d d d T d d T d T T T b d T > T T

168 F t dt C b R T g F g b F t dt C t dt C b C g t dt F g b g T g R T g T t dt T t dt t dt T g t dt T T t dt T T t dt R T cos si t dt 5 6 g 5 6 g

169 g C[ > g t g t dt ϕ t dt [ [ [ ϕ [ [ [ g t[ g [ t dt] t dt [ t dt] g t] dt ϕ [ > F > [ b] dt [ t ] dt t [ b] b t g t dt

170 [ b] > F [ b] F > F [ b] b F b dt < F b t dt > t b b c F [ ] si lim c l t b dt t lim b l t t dt b si lim l t b dt t cos cos lim lim l l

171 cos lim c c [ g g t dt e g u du e g lim e e e e e C C C e - b b b d b t dt

172 F si t t t dt F d d t u dt du cosu du cosu du cos cos cos t dt I I t t dt rct t dt u t dt du

173 t t dt u u du u du u rct u du 4 4 u du 4 4 u du t dt 4 F t t dt F F F t t dt t u dt du F u u du F F [ ] t dt t t dt F

174 t dt t dt [ ξ ] ξ > ξ F < ξ F F F F lim A F t dt F F du u t dt u du F F u du

175 u du A F lim lim u du F A lim F lim lim u du A A A F F g d d g t dt g t dt g t dt g t dt g t dt I g t dt g t dt

176 I I t u dt du g u du g u du g g u du g g u du lt lim t e X > > X > dt lt e t l dt e lt e lim dt c c R d c d c d c d t c

177 b b d [ b] b d b b b d d d b b t b d b d b b b d dt b d b t dt b t dt b b b b d b d t e [ e < < > > < t dt e t t e dt

178 lim t t e dt t t e e t [ b] b d [ b] b [ b] F F [ ] t dt F F F F [ ] [ ] ξ

179 [ ξ ] ξ F F F I si d cos si cos 4 d I si t cos d 4 d si cos d si cos cost si t 4 d 4 dt t si cost[ t t 4 t ] dt

180 4 si t cost t 4 dt t t I I si cos d si cos 4 d 4 < si cos d 4 ξ si cos d ξ 4 4 si cos d 4 ξ ξ t I ξ ξ 4 si cos d

181 ξ ξ < t t dt e dt cos t t dt e dt cos e t dt < t dt > ξ ξ cos si e > > k ] k k e d [ ξ ξ ξ ξ ξe ξ ξ

182 ξ ξ ϕ e ϕ [ ξ ] ξ ϕ ξ ϕ ξ ξ ξ ξ ξ ϕ ξ e ξ ξe ξ ξe ξ ξ e ξ ξ ξ ξ ξ ξ ξ ξ [ ] cos d ξ ξ ξ tξ ξ η

183 ξ ξ tξ η η tη cos d cos cos ϕ cos ϕ [ ] ϕ ϕ ξ ϕ ξ siξ cosξ ξ cos ξ ξ ξ ξ tξ cos d cos si cos d

184 ξ cosξ siξ ξ cos ξ ξ ξ cosξ siξ ξ cosξ ξ ξ ξ ξ tξ cos d cos d si si cos si d cosη η siη η si d η si d cos η η siη η η η tη si t dt

185 si t dt t u si u du siu du si [ ] si si cos si si tdt si t dt si tdt 4 si tdt sitdt sit dt [ ]

186 I ξ i i I lim ξ d λ i i i I di b d I b d F b F g [ b] D { b g } A b [ g ] d [ b] A b d

187 A d b < < < L t t d 9 4 d 9 4 : α t β t t t A β α t t dt

188 9 4 9 A 4 9 d 4 cos tdt cost si t t 4 A 4 d 4 t d t si t si t dt D D 4 6 ρ cos ϕ ρ siϕ { α ϕ β ρ ρ ϕ } β α dϕ A ρ ϕ cos > A r dϕ r ϕ r ϕ ϕ ϕ dϕ cos dϕ 8 cos tdt

189 > l l e e A e e d l d e e e 6 D { b } V d b D { b } V d b

190 7 6 [ ] d V V d 5 < S S S S A d A d 6 6 A A A

191 [ ] d [ ] d l 6 l l d 4l 4 l 4 4 A A A

192 A [ ] d V [ ] d 6 d

193 l [ ] b d b t t α t β l [ t ] [ t ] β α dt ϕ α ϕ β ρ ρ l ϕ [ ρ ϕ ] ρ d β α ϕ r cosϕ > l cosϕ siϕ cosϕdϕ ϕ dϕ cos dϕ 8 costdt 8 b A b [ ] d

194 t t α t β A [ t ] [ t ] β t dt α A d A 5 d

195 5 5 4 d 6 A A 6 5 A t si t cost t > 5 cost cost dt cost cost cos t dt ' ' dt ' ' dt t 8 si dt 6 cos t 64 dcos t

196 t si t si tdt ' ' dt t si t costdt D 6 6 g [ b] { b g } b b b [ ] d g d b d [ g ] d [ g ] [ g ] R R R R d 4 R R D p > P > p X Y X p D

197 V 7 5 p p p p A p d p p 6 M p d [ p p ] d 5 p p p d p p p X V [ p p] p p p] p [ p d [ p 4 p] p p 5 5 p d

198 4 5 7 p p 5 V 84 XA 5 p 4 7 p p 5 5 dp gh da h g da

199 dp R dr R p R d R L M O P m P L d P df O m g l F [ ] M L d L m M gmm g d l L l R R R

200 R df O d R dw W R d 4 4 [ R R ] R d R R m

201 dv d dm 48 d dw 48 d 4 w 8 48 d 4 8 d 89 kgm

202 V [ ] d V dv dv [ ] d [ ] d d dv d V dv d [ b] X Y D { R b X d b d b b b }

203 I b b d d b b F F b F t t dt t dt F F ξ ξ t dt

204 ξ F > b I b b d b b d b b b d I b b < I b b b d I I b b > b b b d

205 I b b b I I d I I b I I b b ξ d b 8 ξ b b ξ b d b 8 ξ b b ξ ξ b ξ > ξ ξ I ξ I I b ξ ξ 8 k > k si

206 < < t t k si S si si t S t S S S si k si t t kt k si t si t t S si t si t d cost t t si t S t si sit d cost t sit

207 S t t si t S S > 6 S t si t cost t cost S < S > S t 4 cost t si t t S t > t t S S cost dt S S lim cos S t S cost dt S < cost dt cos cost dt cost dt

208 cos S t dt cost dt S S lim [ b] b > b ξ S S b ξ t t S S t t d b S S t t d ξ b t F t S t S t t t d t F ξ > b t t d F b ξ b t b

209 F < F b b b d > Ft b t > F t t t t t b t b t t t t b t t F b [ ] t t b t ξ > ξ t t t F ξ F b ξ b F b l 6 6 l l l l l 6 6 S [l l ] d

210 6 4l 6l 6 l S 4 S 4l 8 6l 6 l S6 4l 6 S4 8l 4 6l 6 l 8 6l 6 l S4 l l

211 k k l k Pk d k dp k k d k d P k k d k 6 k 6 k l

212 P k k k 6 k l 4 k P k l P

213 [ lim A [ A d A d lim d A [ b lim B b B d [ b b B d lim d B b b d lim d A b d lim d A A A

214 d d d d d g [ d g d g d d g [ g lim λ g λ λ d λ g d d p g d g d d d > p > p lim p λ p >

215 d 5 l lim l < l < 5 5 l d p > 7 6 X > X > > rct d d e p d l p p > p l l e p p d l d e B l lim l B e p < e d

216 lim p p p < b d b b d b d d b d g [ b b g d b g d b d b d g [ b g lim λ b g λ d b g d λ b b g d b d λ b p b d b d b g d p < p

217 p lim b λ b b d si d d si si si d d p < t d dt d dt si si t si rct d p d rct d p rct rct d d p p rct p p p < p <

218 rct p q p > q rct lim p q p q p q > < p < I sect 5t 5 d dt t t d t t dt d si t rctsi t 4si t > d d rct rct rct

219 rct 4 rct d rct d rct d rct d lim 4 b 4 4 b lim [l b b l d l b d l ] d sect sect t t dt sect t t dt t

220 d t dt t t dt rcsit t d e rccose e sect lsec t e d sect t tdt I t t t t rccos dt e rcsi e rccos e l d I! l l d I I L I I I

221 b lim b k k b b k ξ k lim! l l k! b d! l l k l k l k lim l l k k k e l l k k l k lim l l d k

222 k k [ ] [ ] k L ξ k l k l d lim l lim l k k l d l! lim lim e lim k k si k k sid k si ξ k si k liml L

223 Α l d. Β l d. C l d D l liml. L lim l L k lim l k l d l tdt l tdt 4l 8l 4 d. d lim [ B ] A / e B / e / C / D e e : / d / / [ ]

224 lim lim[ l ] / e e. e t e / lt lt l t. t l d l C. C l. e d. t <

225 t d t dt dt e d d. e F S e > F t > S t t t Ft. St S S t St. F F S. I S e d e t t FtS t te t S t te t. t II S t t e t

226 Stt t 4 S t 8 t e S > e S. e cost si t dt cost dt si t si t d si t si t < <

227 V d d d > t t F t t dt [ ] F F F [ ] F t t dt t t dt F t dt t dt t dt t dt t t dt t t dt F > [ ] F u d u t dt t F t dt t dt t dt dt t dt t dt t dt

228 > F F > F F t t dt e e d C Ce C e b < lim { }{ } < b < < b lim lim lim lim lim o o o o lim

229 < < < b o o < o o lim t [ t] dt lim [t] t : < < t [ t] dt t [ t] dt t [ t] dt L t [ t] dt t [ t] dt t k k t [ t] dt t [ t] dt u du dt k [ u k k ] du k k k udu t [ t] dt t [ t] dt udu < udu < t [ t] dt <

230 t [ t] dt < < t [ t] dt lim cosucosudu d t > [ dt] C d A B cos cos C D - : t siu t dt cosu cosudu C > [ ] [ ] η d η

231 ' " d " [ ] ξ ξ!! ξ ξ d d d ξ d [ ] [ ] m M m M m d d ξ d M d

232 lim d si d si d cos d si si si I cos d si < I d lim d lim I si si si > α lim α[ t α t α] dt α 4α α α lim 4α α α α [ t α t α] dt

233 d lim dα α [ d d] α 8 α lim α 8α α α α α cost dt β t tdt γ si t dt A C α β γ. B α γ β. β α γ. D β γ α. [ B ] lim β t tdt t lim lim α cost dt cos CD lim 4 γ β lim B. si t dt lim lim t tdt si t γ β

234 > < F t dt A F. B F. C F F. D F F. [ B ] F t dt F F FB. < F > dt F dt F. F F. B. [ β ]

235 < α < β β α d < β d α β α d β d α α β α α d α α d β α α β ξ α α β ξ α α β [ ξ ξ ] < d [ α β ] α F α t dt t dt F α α F α t dt α α ξ < ξ o α β α d t β α β dt d > β α β α α d β d α β t α β dt β d α α βt α β dt β d α α βt β t dt < α > [ ]

236 [ ] η d [ ] η ξ ξ!! ξ d d ξ d ξ d [ ] [ ] m M m M m d d ξ d M m d M [ ] [ ] η η d d

237 ' " [ ] d "

238 9 9. d d... d d d d

239 d d d d d... d d d d d... d d i... i I I c... c c c c... c

240 d d d... d L p p C A B C C D 5 p p

241 A B D i i i < i mi R < R < 4 9. d d d g d g

242 u d v d d g d C d d g d d g d d g d d d d d d d d C C

243 d d i i > < d d g d d d d u u u g u u g u u g u u du d g u u l l u l u u u lu

244 du ulu d l lu lc e C d d p q d d p q d d p d d p d lc p d p d Ce

245 q p d d q d p C l l d q d p e e C d p d q e e C d q e C C d p e C C d p d p e p C e C d p d p e p C e C Q e p C d p Q e C d p C d e Q C d p C d e Q e d p d p

246 d p p q e p e d p d p e q e e p d d p d p d e C q e d d p p e q e d C d d d si d si d e C e d C si d C cos e p d d si si d si d C cos C

247 si d d e C si e d C si d C cos C C cos d d p q u

248 u u u u u d C C 7 d d p q or d d p q 7 u u p u p u u q q

249 u p u q u u u u C d u C C udv vdu v udv vdu d uv d u u d d d d d d d

250 d d d l l l c udv vdu u udv vdu v d u u udv vdu v d l uv uv u u v v udv vdu u u v udv vdu u v u v d u v u v d rct u

251 udv vdu u v udv vdu u v u d v u v u u u u d d d d d d d d d d d d d d d rct d l rct C e d l u u u u v v

252 p F k L k < k p k p p k F p L p k p p dp d l p p l p

253 c e p c pd e c c u u u u C u u l C C C k F L d d p p d d dp d d d p dp d d p p pp d pp

254 dp p d p p d d p p d d pdp p d l p l l c dp d d c d d d ± c c c c 4 c c c d d p dp d ±

255 d p p pp d pp p p C p p p C C Ce p M α ϕ tα tα t ϕ ϕ t cosϕ siϕ α θ φ θ θ

256 tα d d tϕ d d d d d d d d d c c c m k > t

257 t d dt k t d d m mg k dt dt m k mg k t t e m C ge m dt e k t m k mg t t mg C e m C e m k k C mg k mg t d t e m k dt mg m t t t e m C k k k C k m g C k k m k g

258 t mg k m k t g k m m k e t e k m t k m m k t mg m g t ~ t t k k lim t b t t t m lim [ k lim t X t g m k k m g t k m t e t e k t m k m t mg m g t k k g mg k mg k t] m k Q P Asiω t k > g Aω d dt k d dt Asi t ω

259 p t t p k p Asiω t p k dt e e kt kt p e Ae siω t kt t p e t kt Ae siω t dt t t k t kt k t u t e Ae siω tdt Ae k tu t t t Ae t τ dτ Ae k τ u siω udu dt siω udu k t siω udu P S S h S S h S

260 ρs d pds S ρs d ps d S p p P ρ S S h h P ρ S d ρ S ps S S S S p d ps p S S S h ρ ρ p S h p e p p P S ρ ρ S S

261 S e ρ p h h p l ρ H S h s S hv µ gh v t t dt d dt S d h µ h S g dt t S S d h S d µ t g dt µ g dt

262 t µ g h S d d p lim d p [ lim p p d p D d d p q lim p d p c c c c[ ] c[ ] c[ ] α

263 α. A. B. C 6 d d l lc d e. D e 6. d rcsi C e rcsi rcsi 6 e C C e d d : D C u u u

264 C C :. d d d d d d d d d d p cos D cos cos cos cos cos p D p

265 A B C d d d d C e d d d d d d d d d 4 d 4 d

266 Y X Y X : : : pdp d p l p lc p

267 d c ± d l l c c c c ± c c c m c ± c c e m c c e c c : c e e c c u u u C u

268 u C l C C l d lim e lim d t u d du e e t dt ; lim

269 lim u d t e e lim d e lim d d cos si d d 6 d d u uu d d u cos u u si u t du dt d d u u t cos u cos C t u u C 6 d d si C

270 C l csc cot C 6 l t cos cos si cos L A B e P L AL AB AB P L P AP AB t dt 6 C 6 t dt

271 C 6 C

272 d d t d d t t... t t d d d d t k t t d d t t... t d d k D t L D D t D L D D t α β R t k d k d t D... t L

273 D α β L D βl D L α D t t L t i... I t I.. ξ ξ ξ I i... t si si b ξ t ξ t ξ i t i L c i i L b c t i t i L i λ λ... λ m R i i λ... e e e t t t λ λ m I si cos si cos

274 t t cos cos si D t t c c L D i t i L L D t D t L D D t t t X t t L D c c L L L X t ω ω ω siω t cos ωt t c si ω t c cosω t ω t c t c ω t siω cos t ω ω t

275 t c c t t t c c t L D p q L D c L D Y c c D t L c c c c c c e 4

276 Y C C Y l l d d t d d... d t d t... L D L D L D λ λ λ L... L D L D b L λ λ λ b λ L λ λ 5

277 t t e λ λ L D e λ λ L λ λ t t te λ λ L D e e α ± iβ L λ Cost e Sit L D α t α t z t u t iv t dz dt du dv i dt dt z t u t iv t D D L ut vt L λ t αt cos βt si βt e L D L D λ λ D L e L e λ t α ± iβ e αt αt cos βt e si βt L D λ < k k 6

278 e e α t λt k λt... D k te t λt e L α ± iβ k k cos β t e α t si β t L t L D λ D L e < cos β t t k α t k k L µ λ µ µ > c µ cos µ t csi µ t c c µ t t R < c c c e c e µ t µ t µ 4 t t t t cost 4 c e c e c c si t t t t t t c e c t e c t e c c t c t e 4 e α t si β t 7

279 t c c tcost c c t si t 4 d d t d d... t d d... t t t t Y t c t Y t L t i α t D i i P t e d d L D b t d t dt α t t P t e Pt t t α t Q t e t Qt Qt α t t Q t e L D P t α t e t Q α Q t α α b Q t P t 8

280 α t Q Pt α Q t tr t Rt Pt α t t R t t Q t t t bt c e t t bt b 6 t c b t t b 6 c b t t t t ct t t t c c e 4te t t t t c c t e t t t e 4cost t t c e c e cos t 9

281 H ω β ω H si β t c cosω t c siω t β ω ω H t ccosωt csiωt β β ω ω si βt iβ H t c tcosωt c ω t t te 4 9 t t t e siωt t d d t d d t... t d d t t... t > t <

282 s l t s d t d t s l t d dt t d d d ds s 7 7 t t ccos l t c si l t 4 6 d dt d 5 6 dt > e t t l t e t t t C e C e t t e C C l l.l b

283 b b b c b b c b b c c α b.l b α β c p p p

284 q p k k λ q pλ λ λ λ c c λ λ λ λ λ λ c c 5 4 q p B. A. B. C. D

285 b 4 C C [ ] C [ ] e e e e e e e e 4 4 cos Y Y 8 C C e si e 4 si 8 m k > µ t 4

286 m c k c m k m F m t t λ v m v t c m µ t ω µ ω v F k m t µ λ ω λ µ ± µ ω µ ω q µ ω λ µ q λ µ q < µ < ω λ µ ± q i e 5

287 C C e e e e A. B. C. 6 6 D. e C C e > < e e si 6

288 * A b C D e e E si F cos e b c b c B A. b c B. b c C. b c D. b c δ R P m t m t t d dt d δt P t e si t m dt d dt t δ t lim t t δ t lim t t si t t dt 7

289 cos si 4 4 e l lim d d si d d e e si 8

290 r r r r c b r λ r θ r r r r r r r b r α α r b r r b r r r r r b b cos α r r r r b b r b r r r b cosα r r b r r r r r r r b b r b r r r r r b v r b b r b r b r r r r r b b si α r r r r b b

291 r r r r r r r λ µ b c λ c µ b c r r r r b θ // b r r r b c b c r r r r r r b c r r r r r r b c b c r r r b c r r r r r r r r r r r r r r r r r b c b c c b b c c b c b r r r r r r b c b c r r r r b b r r r r r r b θ // b λ λ b r r r r r r b c b c O P b c OP OP i r b r j c k r OP b c b c OP z r b r b b r r ± b b ± b i r b ± r j ± k r b λ r λ i r λ r j λ k r λ r λ λ λ

292 r b r b b b r r r r r r r r r r r r r r r i r j r k cosα i r r r cos β j cosγ k r α β γ O O Oz cosα cos β cosγ r cos α cos β cos γ r r v i j k r r r r r r r r r i j k j k i k i j r r r r r r r r r j i k k j i i k j r r r r r r i i θ j j θ k k θ r b r i r r j k r b i r b r j b k r r b b i b b r j b b k r r r r i r r j k r i j k b b b b b b b b b r b r b b c r c c r r r r r r b c b c b b c c b b c c r r r r r r r i j b i k b r. r 4 b r b

293 5 A B C ABC S.. A B C D r r r M M r r z z r r r r Ai B j C k M z A B C z z A B Cz D r r r r Ai B j C k M z M z M z z z z z z z r r r r M M i j k 5 z 5 z 4 P : A B Cz CD P z P P A B Cz D A B C 4

294 M z v l m l t m t z z t r < t < t z z l m M M z z t t z z z z t < t < l : 4z : z t l 7t < t < z t L L r r v v α r r α α L β L v r r α α L v r r F z L L Oz S Y z F z F S 5

295 z L : Oz S z L M L M L M L M L Oz z k k > Oz S : z k L : z k k L l l L L L S L : Oz z S Oz L L Oz z Oz z S S L : Oz S z P R> z 6

296 R z z z b c b c z z b b > z b b.. Ω R r Ω u Ω : Ω R T r... Ω Ω u r r r u... z ; w z F z z z Ω u v u v z z z z z { } D w D 4 D D D 7

297 D D D D D -- D R R d : r R D r r r r R r rlimr ε > δ > r D r r r < d < δ < ε lim r lim r r r r o r r r r r r o g g r r r r rlimr o lim lim lim lim lim lim lim t t t t t t t t lim lim 8

298 lim i lim lim ϕ lim lim lim ϕ Si Si... r : D R R D r r r r limr ε > δ > r D d < δ r < ε r r r r r k D k lim k r k U ε R U δ R U r < ε o r r r r r r U ε R U δ R U D r r δ r r < ε δ 9

299 u v Ω u v Ω Ω u v Ω u v Ω Ω R CΩ Ω P ΩP Ω P mi P P m P P Ω P Ω Ω R CΩ m mi P M m P µ P Ω P µ P Ω P Ω Ω R CΩ PQ Ω P Q P Ω ξ P ξ Ω P Q Ω PQ Ω P ξ PQ Ω P ξ z R lim R

300 : D R R z lim D z z z z z z z z z : :

301 P U P P D B A A B o ρ δ P A B P d A B ρ d P P P d P P P P P P P P P P lim P P P A

302 d si si C A. B. C. D. A. B. C. D. d d A. B. C. D. D z P A P B z z

303 z z C P dz d d P P D P grd z z P P v ϕ ϕ d lim v r { v v } grd v r z z z si cos z 4

304 v u z v v u u v v v u u u v u z v v v u u u v u z d d. l z z z v u u v v v u u v u z z z C z B z A v u β α β α v u z uv v z v u z u z v z u z z v z v u z u z v z u z z β αβ α β α v z v u z u z v z u z z β β α α β α z C z B z A 5

305 v u z C B A u z C B A αβ β α α α v z C B A β β β α β β α α C B A C B A v u z v v u u v u d ± dv du v v u u ± ± u v d ± v v u v u u udv vdu v u d v u v u v vdu udv v u z v v u u z z dz v v v u u u dv v du u v v z u u z z z dz v v z u u z dv v z du u z dz F F F d d F F 6

306 b b z z z z d d z z dz dz u cosv z z u si v z z z uv z u v z v u v cos v si v F d dz d dz u v v u v si v cos v d d d cosθ l r siθ l cosθ siθ z v v i k lim z z z z dz ' ' ' z ' ' ' z z z u v u v z u u u z v v v 7

307 v u v u w ψ ϕ w u w v ϕ ψ ψ ϕ ψ ϕ v w u u u u w ' ' ' ' ' ψ ϕ ψ ϕ ψ v v v v w ' ' ' ' ' ϕ ψ ϕ ψ ϕ z b ϕ ϕ d dϕ b b b u u t z h t z g t z z u u u t t z z u g u g u u z ϕ ϕ z ϕ ϕ ϕ ϕ 4 4 z F c zc bz z F bf F c z ' ' ' bf F F ' ' ' ' ' ' ' ' c c bf F bf F F bf F F '' '' '' ' ' ' ' ' '' ' '' F b bf F F bf F F c F F F F c 8

308 u u u u u u α β e v u α β β α β α 9

309 r l r l r r grd r l grd r l r l t C r l lim t D r r r t r T grd l r D l r R r r r M r r T r r l r r r l grd r M M A. i B. j C. i j D. i j

310 M v r i r r j u r i r r j v r u M d 5 4 d 5 d t C R t α t β z z t r v t r t t t z t C P T t t t C P t t t z z z t t t C t t z t z z cost c si t > c > M 4 z ct t t z 4 c ct c z 4 c z F z S z P z z

311 z z S z p S p z S S z F z z F z F z F r S z z F z F z z z z F z z F z z z F z F S z 5 : z z L 5 8 z R z S : z S : L z G z F M M grdg grdf v v L z M 6 z z M z t t

312 z M M M M M } t t t M M : Φ t t t t Φ Φ!! Φ Φ Φ k k k ξ M U M U k k k! θ θ!. < <θ M θ θ M H θ M θ θ θ θ θ M M H 4

313 ρ o Lgrge Tlor ] 4 [6! ξ η ξ Ω t s Mi r r.. i i i i c b P m i L z P m i i i i z z Mi r z F z P z P P.. z F t s z z Mi r z G z F z P z P P.. z G z F t s z z Mi r 5

314 r r grd L R : R M R U M grd M r M M H r M M H r M M H AC r H M M r T M B M M A B C i i Ai Bi Ci AC i ibi

315 b b... b i i i i i i i i i i i i i i i i i i i i i i i b i.. F t s Mi F L λ λ ;.. z G z F t s z Mi z G z F z z L µ λ µ λ m i i i i c b P m i L z P m i i i i z z Mi r m i i m i i m i i z z z z i i i i i i i i i i z z P z F z P z P P.. z F t s z z Mi r z F z z z L λ λ z F r λ 7

316 r r λ grd F r F z F G z z z z z P z P r Mi s. t. F z r F P P P λ grd F z P z z z G z zλ r λ F z µ G z L r r r z z λ grd F z µ grd G z S : e z z A B C D A B C b z c z c z z 4 z 4 5 z 4 5z z 5 L : z 6 / / 4 z 5 / 8 5 z 8 z c 8

317 b c b c z g z M z mim z g z z S z S : g z M : z A. B. C. D. F F F > F < F A. B. C D. z z z M M z M M C A. B. C. 44 D p p / p / 4 9

318 zu l l l z z 6r bc b c b c 8 6 z D z D 6 z z D z z D

319 lim S lim D R i ξi η i σ i D lim S lim ξ η σ D i D i i i dσ lim ξ η σ D i dσ dd i dσ i i σ dσ b b > b ; b D 6 dd u v dudv D D R D R

320 g D D dd g dd D D D D dd dd D D m M ms dd D MS D D g D ξ η D g dd ξ η g dd D D D cos si dd 4 D D cos si dd D D D dd cos si dd D dd D : r si dd r t D D dd D D D : r dd D lim r r

321 ] b b [ b d b d D { b } dd D b d d D { c d } ξ ξ ζ ξ dd D c d d d dd D : > D I d si d d e d e d D e d e dd D I [ ] D dd D : [ ]

322 4 z z d d d > D D ρϕ D { ρ ϕ ρ ϕ ρ ρ ϕ α ϕ β} dd dϕ ρ cosϕ ρ siϕ ρdρ β α ρ ϕ ρ ϕ ρρ θ ρ ρ θ θ θβρρ θ θ α lim ε l ε < dd z z D dd D > 6 z D S D z z dd z z F z S F F D D F z dd F z 4

323 Ω h > z h 8 Ω Ω h 9 A A A h h 4 A A M D M M M Ω { z z R z } z z R 8 Ω ρ z z Ω Ω Ω J z ρ z dddz J z ρ z dddz J z ρ z dddz g F g F C C D I F b F F u u g t R I g dσ D b dt F C g C 5

324 b D R I g I F b F I D D dσ { } D { } D D I D I D dσ D dσ D dσ D D dσ dσ dσ dσ I D { } D : M dσ 6 6 I dσ D 4 D { R } dd rcsi dd [ b] b b d d b 6

325 z Ω R Ω z dv lim ξ η ς V i i i i i Ω z z dv dddz Ω z dddz u v w dudvdw Ω Ω { z z z z } { b} D D Ω z dddz dd D z z z dz b d d z z z dz Ω Ω dddz { z z z }

326 Ω z dddz Ω z c b z c c > D z b c 6 Ω Ω ρ ϕ z : Ω α ϕ β ρ z z dddz ρ ϕ dϕ dρ α α ρ ϕ Ω z z Ω z ϕ ρ ρ ϕ ρ ϕ z z ρ ϕ ρ ϕ ρ ϕ ρ cosϕ ρ siϕ z ρdz zdddz { z H} H H [ [ ] t F t z dddz z h Ω z : > t lim t t F t t h h r siθ cos r siθ si z r cosθ r ϕ θ ϕ ϕ Ω Ω *

327 Ω z dddz Ω * r siθ cosϕ r siθ siϕ r cosθ r r cosθ θ siθ drdϕ dθ 8 I z dv Ω Ω z z z z 8 F t z dddz u F t t z t Ft 4 ρ ρ dρ F t 4 t t AB L λ i L dl dl lim ξ i ηi li AB L dl dl > L d l L L L

328 L L L dl dl dl L [ ] λ µ g dl λ dl µ g dl L m L dl M L L L L ξ η L dl ξ η L t L t α t [ β L L L L ] dl [ t ] [ t ] dt L [ α β ] dl [ ] d L ρ ρ ϕ ϕ [ α β ] dl [ ρ ϕ ] [ ρ ϕ ] dϕ L t L t z z t t [ α β ] dl [ t ] [ t ] [ z t ] dt β dl t t [ t ] [ t ] L L dt α β [ ] [ ] [ ] z dl t t z t t t z t dt α L dl L > L 4 4 dl L 5 5 dl L OABO L 4 z R L z L dl R dl L L 4

329 r θ cosθ r θ siθ r θ cos θ θ 4 4 dl L 4 L 4 4 R z c z Rc R cost si t t z t z 7 8 ρ z dl si t kt dt m m L z zρ z dl t kt m m L dt r F X Y L R AB L r F d l X d L AB r L AB Y d lim λ i F r L r d l d d L r r t t t L [ X ξ i ηi i Y ξi ηi i ] F z X z Y z Z z AB L r r F z d l X z d Y z d Z z dz L AB L AB L r r r t t t z t d l d d dz 5

330 r r F d l L AB L AB r r F d l A B C L L L L L AC r F d l L AB r F d l L BC r F d l r r L F d l L r r r r F d l F dl L L L r r F dl t L t [ α β t ] A B t α t β F r Ω L Ω F d l X d L AB r r L AB Y d [ X t t t Y t t t ]dt β α r r F d l X d Y d L AB L AB B r r F l dl L AB r X cosα Y cos β dl F cosθ dl L AB dl [ t ] [ t ] dt [ ] d r l cosα cos β L AB L L r r t t t z t B t α t β L AB r r F z d l X z d Y z d Z z dz β L AB X t t z t t Y t t z t t α Z t t z t z t dt T A 6

331 d L L B I d d z dz L A 57 B4 L L A 9 I d 4 L d 8 I z d z d dz L L z t α < α < cosα siα I z d z d dz L z L A B C A A B C r V L : L T L : L : B A V cost P F r bsi t P P A B b F r b P F r F X Y D D D X Y D r 7

332 D r F r d l Xd Yd D D Y X dd L 9 I d 4 d 8 L e d e d L A B L b b F X i Y j L r F r r r D r dl L r r F dl L F r dl r C D C Φ d Φ X d Y d r g rd Φ F X i Y j r r Φ Φ X Y r r D F dl L Y X r r r F X i Y j M M Xd Yd Xd Yd L M d X d Y d 8

333 X X d C X d C Y C d d c Q d Q d t t t d Q d d Q d Q Q si d d L L si cos u u du si d d u cos si C A B cos d si cos d d bd C C 4 b 8 b 4 b 8 b d d C? C b 9

334 S R z S S z ds lim ξ η ς S λ i z S ds ds > z ds S S S S S S z ds z ds z ds S [ λ ] S i S i z µ g z ds λ z ds µ g z ds m S z ds M S S S S ξ η ζ S z S i S i S S S ds ξ η ζ S z z S z z D ds dd S z z ds D z z dd

335 F F Fz S F z D ds dd F S z ds D F F Fz z dd F z z ds I S z S I z ds S I 4 l S S 5 5 z ds S : z z 4 S S 4 S S z J ρ z R z R ρ 4 4 J z ds R dϕ d R ρ S R ρ S z z S z ds ds S r F z X z Y z Z z Ω R S Ω S F r z S S r r r r F z ds lim F ξ η ς S λ i F r z S d r S d S ds ds cosα ds cos β ds cosγ S r r F z ds S r r r r F z ds [ X zcosα Y zcos β Z z cosγ ] S i r i i i z ds ds

336 d dz cos α ds dz d cos β ds d d cosγ ds ds z z cosαcos β cosγ d dz dz d d d d d cosγ ds d dz cosα ds dz d cos β ds dσ dσ dσ z dσ z dσ z dσ z γ < γ α < α β < β dσ ds r r F z ds X z d dz Y z dz d Z z d d S S S S S S S S r r r r F z ds F z ds z S S r r F z S r r r r F z ds F z ds S ± ± S S r r F z ds r r r i j k r r r F i F j F k F F F zd d S z z / z z

337 d dz S S z z S d dz S I z ds J z d d I S S 4 r S S : z d dz dz d zd d S z R z d dz dz d zd d S z r r > z D z z I S d dz dz d z d d S z z I S d dz dz d z d d z grd z z z z z z z z 4

338 z Z z Y z X z F r z P z z Z Y X z div F z Z z Y z X z F r z z z Z Y X z k j i z F rot r r r r k X Y j Z z X i z Y Z r r r R Ω Ω Ω C z Z z Y z X z F r Ω Ω dv z Z Y X Zdd Ydzd Xddz Ω Ω dv divf ds F r r r S S S S z Z z Y z X z F r S S C ds rotf ds Z Y X z k j i d l F S S S r r r r r r r r C dz zd d C : z z C 5

339 d zd dz C d dz dz d zd d S z 4 S z v i j zk z z h h I z d dz dz d z z S 9 u d d S S d dz dz d z z z d d z S > z z z z z z S S : b cz d Ω Ω I d dz dz d zd d H S Ω I z d z d dz L L z tα < α < tα z > S S ddz dzd e zdd [ lim e e 6

340 Ω S u u z v v z Ω Ω u vdddz S v u ds v v v u v z u u z Ω u u u u u z Ω u v u v u v dddz z z r r cos u Ω : z R I u ds r r r v v r r r r r i j zk r r ds Ω r r cos u Ω I u ds r r r r cos u Ω I u ds r r Ω P b c Ω r r cos u I u ds r r Ω r v v r r r r P r i b j z ck r r ds r r cos u I u ds u P b c r r Ω r r r r r r Ω Ω r r r r r r r r r r cos ds ds ds ds ds r u r r r ds grd u ds u ds u d S 7

341 { u } u u u u LL u S u k k S u k k u S S S u u S 8. u { S } u lim S S lim S u

342 u lim uk lims k S L L R S L < lim S lim lim S S lim S lim 8. 4 S m m m m m lim S m m rct

343 S m m rct m rct m [rct rct ] rctm rct rctm 4 lim S m m u lim u u S S limu lim S S S S u lim u u lim u u : u lim S lim S lim u. u lim S lim S : S. u α αu u α u u v u ± v u ± v ± α u v

344 [ ] : N 5 L L

345 lim * S k k k S k k lim S lim k k k S k k S L L * S * lim S * lim S lim S S 8 8. u > u 8.. u { S } 8. u { S } 8.8 p p p d p p d p m m m m d d d p p p p m p d

346 p > p q k q q k q q < q q p p > p p k k 8.. p 8. N > > N u v v u u v v S v k N > N M > > N k * { * } S < M u v S uk S < M S u k 8.4 b lim b A A b A b A b

347 lim A. b A > b ε > N > > N A ε < < A ε ε b A > A A < < b A b < b p u lim u ρ u ρ < p > u < ρ p u p p > u p u p u p u u u u p 8.7 > p > lim e p p p lim[ e ] lim[ ] lim p p p >

348 8.8 [ d] [ [ d d d [ d] S [ k k k ] [ lim lim S lim[ ] [ ] [ d] u 8.4 u > lim u ρ < u ρ > ρ u limu u ρ u lim ρ < ε > N > > N u u ρ ε < ρ u ρ < ρ ε ε > < < u u ρ p q < u N < qu N u N < q u N L u N p < q u N u N p q p u N p

349 u u > lim u ρ < u ρ > ρ u limu u ρ N N d l l d ll 8.9 lim < lim k k

350 8 u!! u! lim lim u! 8 u > v > lim < e u v v u u v u v > > u v u v u v u v u v u v u v u L v u < u v v u v u > u 8.7 > L u { u } u u L lim u u u k R u k u uk u 8.7 } 8 {

351 { lim lim A } A A A > N > N > A > N < < A A 8 8.5: u u u u u 8.8 u u u u u u u u u u u u u

352 lim lim ξ ξ M > M M ξ M lim lim 8 lim si C si 84 l l l > lim l p l < l < < l < p l

353 84 85 u u u u u u u S u u u u u u u L u u u u L u u u u u S u u l 86! u! u > lim u u! lim! lim e < e > e lim u e u e e > u u > u limu e 87 [D ] u

354 u A lim u u B lim u u C lim u u D lim u u u lim u u u lim u u u u lim u AB u C u lim u u D 89 lim b b lim b { b } N > M > > N b M b M b b 8 4 t d α > α t t 4 t t d t dt t < dt < t t dt < < < α α α α > p α α

355 u v 8 [C ] A u v B u v C ABu u v D u v v A BDC u v u v u v C 8 u l [ ] A u u B u u C u u D u u u C 8 cos b b [ ] B A B C b D lim cos b lim [si b ] b 4 84 b l b > [ ] D A B

356 C b D b b b lim l lim b l b l 85 u u [ ] A B C b D A u u A

357 u L D u u u u L D u S uk k u D D u u u I I S S u I

358 S u si D ± L R k 6 k si D cos D R k k ± L { } si { R k k ± L} D! D { } e D φ!

359 u { } L < < lim N M > > N M <

360 < M < M < > R > < R > R R < R > R R R R 4

361 r r r 5

362 lim ρ R ρ lim ρ R ρ lim lim R lim R ρ R lim R lim ρ lim ρ 6

363 < ρ lim lim R > ρ R ρ R lim lim ρ lim < ρ lim R R ρ ρ > ρ R lim 7

364 lim R 6 lim R 8

365 9 lim k k < > k k 9 k lim k 9 9 < 9 > lim 9 9 R

366 u u lim u 4 lim 4 < < > limu u u L

367 L d d L d lim lim d R ± ± lim ± lim < >

368 lim ± R b R b R mi{ R R} b b R R S I lim I lim

369 lim S S S I I S t dt dt t dt t R R R R R R S R R S R R R

370 R R R D D D D D D D! L L 4

371 ! L! lim k k k! k! R D R D L M > D M L D D D 5

372 e cos si l α e! cos! si! l ] α α α L α! α < α < ]α > [ ] α 6

373 e e! e 7

374 !!!! ] [ e e e e e e rct rct rct < dt t dt t 8

375 { Cos t Si t L} [ ] cos cos md cos si md si si md ; m L L m m m m m m [ ] b cosd si d L L cos b si ~ cos b si 9

376 L b si d L ~ b si ~ cos cosd L b α α α α cosd si d [ ] [ ]

377 S cos b si S S [ l l] l l l cos d l l l L l b si d l l l L l l cos b l si l ~ cos b si l l l [ l]