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1 " ( K p( pasals! ( kg / m 3 " ( K! v M V! M / V v V / M! 3 ( kg / m v ( v "! v p v # v v pd v ( J / kg p ( $ 3!

2 % S $ ( pv" 3 ( ( 5 pv" pv R" p R!" R " ( K ( 6 ( 7 " pv pv % p % w ' p% S & $ p% v ( J / kg ' s s % S& $ % v P% p (J P ( 8 C v % p P% p %" 3 C v C p

3 P% p v %" p% v + v% p R%" % v v% p R%" P v ". p % v Q% v p Q% v %" p p% v R%" Q p". v p / v ln p + / ln v pv / ( % p % v + P% p + Q% v " * v + p - p v % p p % v + p v / p v. 3 3 p v ( v ( p + % p v + % v 9 ( p

4 % v v ( ( ( p v P P PU PU 3 v NP Ov % p tan / NPU / NPU 3 % v % p % p v % v ( N / m % p v NU NU 3 % v % v v U U 3 ( p v ( p v w ( p + p ( v v p ( v v + ( p p ( v v ( p + p ( v v pv p v 3 v # v w pd v p v v ln ( J / kg. v # v w pd v v pv p v / ( J / kg

5 ( x x ( 3 x x p! t x p! v v v v ( + v (!! s!! ( + s! ( + ( + s + s + s s ( 5 s x x + % x t ( x + ( x+ + % x+ % % x % x + % % 6 % % x 6 x ( 5 ( * - % x 6 x 6 x 6 x

6 6 6 x 6 s 6 x s % % v p s ( Pa v p p + % p p + s ( Pa x x+ % x 6! % x % p ( Pa 6 3t % p 6 6 6t 6 x /! ( m / s f ( t x + F ( t + x ( m.! ( p p! + s! p p!

7 o C p ( N / m 3! 9. ( kg / m 8 ( m / s ( NEWTON ( p ( *! + - p! / p / / p ( m / s ( LAPLACE! /. o C 33 ( m / s p! R" / R" ( m / s ( 3 5 o C ! ( SI

8 9 ( m / s 35 ( m / s at 8 o C x x x x S x x x x ( ( x w p v v + ( ( p p ( v v ( J / kg w x T! # & d x ( J / m x x T! S # & d x ( J x 3! ( J / m ' p ( v v p p s ( Pa 3 v v vs ( m

9 w v s ( J / kg x w3 # v s! d x x w s d x! # # (% p d x ( J / m / p V p w x x f ( t x ( m s ( x a 8 /9 6 f 6 6 f ( t t x 6 x + s ( m / s E T + V T V ( x + aos 8 * t - ( m 9 : ( m 8 ( J / m x ( T! a 8 # sin 8 * t x + - dx x ; ( x + > 3! 8 a # < os 8 * t - dx? ( J /

10 T 3! 8 a ( J / m E 3! 8 a ( J / m a 8 a s 8 s m ( x + 8 a os 8 * t - s ( s sm os 8 * t 8 a s m x s m s 6 6 x S E 3! s m ( J / m 9 a sm << : a << : 9 a os8 t ( m x ( aos8 * t x + -

11 W ps & ( p + s S & 8 a p 8 S a sin8t + Ssin 8t ( J / s ( W S S W 8 a S! S8 a ( W ( 3 3 w! 8 a! s m (% p! ( W / m + x x ( 5 W ( W 3! s 9 9! s 9 m m 3 (% p! ( W

12 W ( 6 8 / 9 M M ( && + 8 ( p p S W sm % p 3 9! a s m W 9! 8 ( m! W 9 8 sm < 7 a < 87 ( m 8 s m ( 7 & p p s! & p &&! S + & + 8 M k t Ce os( 8 t A ( m! S k k 83 8 M p p / p s. 7 5 s ( N / m. 7 s ( µ ba 5

13 e t B 83 8 M S >>! : 9 ( 8 : ( x x x x < x & s f 3( u f u & s % p f ( t x f ( t + x & 6 f 3 ( t x f 3 ( t + x 6 t 6 s + f 3( t x + f 3 ( t + x 6 x M

14 6 x s 6 x x F F 3 ( t f 3( t F ( t f ( t + C F f C f ( t x + f ( t + x & f 3( t x + f 3 ( t + x s f 3( t x f ( t + x & s s x + x x & i % p i x x & % p x & t % p t p & & & i + t ( x % pi + % p % pt ( x

15 % pi! & % p! & % pt! & t & % p ;! (% pi % p! % pt ; & & & C i + t < < % pi + % p % pt! ( & & i! & C t % p % p!!!! % p & &! +!! +! i i % p!! R % p! +! R ( ( % p t! T % p! +!!! % p & &! +!! +! t i t i i & 3 & R i i 3! T.! +! R!! R! +! T!! +!!! T. w w w i t w % p & w % p & w % p & i i i t t t

16 ! R! T 3! >>! R T T! <<! wi w + wi R R!!! T +! T ( * ( R R!! R ! T.! T. T T ( z " " i "

17 ( 5 " t " " i k sin" t sin" i k z & os " + & os " + & os " ( m / s i i t t z % p + % p % p ( Pa i t p p + % p p + s ( Pa % p Z! & & ( Pa s/ m ( 6 Z % p Z & % p Z & % p Z & i i t t ; & os & os & C i " i + " i t os " t ; Z os " i (% pi % p Z os " t % pt < & & & < Z. % % %. i Z Z t pi + p pt C ; 3 & Z Z os" t os" i ; C R & R Z Z i t + C os" os" i C < C 3 & < Z t i T T C i3 os" C. Z os" t + Z os" i C Z R Z T Z Z T 3 i % p 3 R % p % p Z i % p Z w! & Z & w Z & w Z & i i t t i T 3. k sin" k sin" k sin " k k i t 9 9 v 9 v : 9 9 v :!! " i

18 k > k k k ( k + sin " i > " i > sin * - sin k " i " ( : + * : - 8 ( " sin ( k + * - sin k ( : + * : - ( ( s 3 ( s

19 & s & & l l l s & l s & s & ( s & l ( 6 6t! 6 6 x os ( 8t A ( * A os A x B sin x os ( t

20 9 : ( m 8 : x x l n A l sin 8 x x l n9 x ( n9 t + C sin & os * A - ( n 3 L l l n n n 6 s 6 x B l sin n x ( n t + n Cn os & os * A n - l l ( n 3 L x x l 6 x 6 A l os 8 3 7

21 m9 x ( m9t + C os & os* A - l l ( m 3 5 L m m m x A os ( pt A A p ( l x & sin & os ( pt A pl sin 3 8 pl m9 m: sin l p x l A p ( l x & os & os( pt A pl sin pl ( m+ 9 ( m + : os l l 6 6 x

22 h a E E ( N / m. 7 9 ( h/ a a + he µ + µ µ µ ( x y z V x y z t V u v w t t P x u t P u t P P3 P3 t u 3 t u 3 P

23 ( t t u u 3 x ( t t D P 6 u 6 t u 3 u t P P3 y z u 3 u s l m n t t u 3 u t t u t u t u 3 u + t t s u 3 6 u u s PP 6 u 3 s V ( t t 6 6 V V x E E x y 6 u 6 + V u 6 t 6 s 6 v V v w + E z + V w. 6 t 6 s 6 t 6 s 6 u 6 s 6 u 6 x 6 u 6 y 6 u 6 z & + & + & 6 x 6 s 6 y 6 s 6 z 6 s 6 u 6 6 l m u u + + n 6 x 6 y 6 z u l V v mv v n V E E E x y z u + u u + u v + w u 6 t 6 x 6 y 6 z 6 v u v v + + v + w v 6 t 6 x 6 y 6 z 6 w u w w + + v + w w 6 t 6 x 6 y 6 z

24 d D dt Dt 6 E V V 6 + V 6 + V 6 d V D u v w V t x y z dt Dt d dt D u Dt 6 v w t x y V 6 6 & F z 6 t i x i y i x y z z F i x + i y + i z 6 x 6 y 6 z V u i + v i + w i x y z 6 V 6 t 6 u 6 v 6 w 6 t 6t 6t i & i i & i i & i x x y y z z i & i i & i i & i x y y z z x ( 6 + E * + V & F - V 6 t A os k ( t x 6& 6 & & 6 t 6 x 6& 6 & : & : ka 6t 6 x 6& ka << A 6t 9 : k A << : 9 S S P % a n(l m n V ( u v w 3 V & n % a &% t ( lu + mv + nw % a & % t ( m % t % a % t V & n% a % a 3

25 I # ( lu + mv + nw da da s # V & n ( m 3 / s s S P % x % y % z P ( u v w yz u u ± x % 6 6 x P ( + P * x + x- % + x ( + P * x x- % + x 6 u 6 % x & % y & % z x v w ( 6u 6 v 6 w + * % x% y% z 6 x 6 y 6 z % x & % y & % z P 6 u 6 v 6 w + + F & V div V 6 x 6 y 6 z V ( 6u 6v 6 w + * d x d y d z lu + mv + nw da 6 x 6 y 6 z ### ## ( # F & V dv da V # V & n S

26 V V S % x% y% z!% x% y% z! % % % 6 u x y z 6 t ( x y z p x (% y % z x + % x x % x ( 6 p * p ± & 6 x + % x - (% y & % z % y % z ( * 6 p p ± & 6 x + % x - % y % z x + x % x % x! % x% y% z x 6 p & 6 x % x% y% z ( 6! + 6V! * F!- 6t 6t! p s! 6 u 6 p! 6 v 6 p! 6 w 6 p 6 t 6 x 6 t 6 y 6t 6 z! 6 V 6 t F p 6 u 6 s 6 v 6 s 6 w 6 s 6 t 6 x 6 t 6 y 6 t 6 z 6 V 6t F s

27 ! p u v w t % x% y% z % t % x% y% z V ( u v w V 6 6 t s ( + % x% y% z 6 F & V 6 t 6 s 6t F & V G V s t ( t t t u sdt + u v sd t + v w sdt + w x # y # z # # t V F sd t + V ( m / s

28 t F # dt V t V V ( x y z u 6G 6G 6G v w 6 x 6 y 6 z V F G t G sdt G G # V F G V G G s G V l G # sdt ( m / s! V! F G G ( 3 C C dp p F p mv m dv F dt dt 6! F G 6 t! V [ ]

29 C ds V ds V & ds C ( V C 3 V V V C C S n n ds C n V F 7 V ot V V V S C C C ( # V & d s lu mv nw d s u dx v d y C # ( + + C # * + + C ds ds # ( ud x + vd y + wd z C ( 6G V ds C C C x dx 6G y d y 6G # & # * + + z d z # d G # C # S G ( a + G ( a V & d s ( F 7 V & nd a w dz ds + - ds ( 6 w 6u+ F 7 * - + ( 6 u * 6 w ( 6 v * 6 u + V i i - i 6 y 6 z 6 z 6 x 6 x 6 y x y z G (

30 F 7 V V S F & V F & FG F G F x 6 y 6 z ( Laplaean t s G G s V DH sd s p p lim s sd DH! 6 s 6t F G s 6G 6 t 6 G F G 6 t 6 s F & V 6 t F G

31 ! T ### ( u + v + w d x d y d z! ; C ( 6G + * - + ( x * 6G ( y * 6G + # < z C V ### s d x d y d z! ( 6G + dv J V # * - ( 6t > C? ( J d v d x d y d z G x t y z 6 G 6 G 6 y 6 z x & f F 6 G 6t 6 G 6 x G f ( t x + F ( t + x ( m / s & 6G f 3( t x + F 3 ( t + x ( J 6 x O O t O ( " A

32 ( x y z x sin " os A y sin " sin A z os" ds ds dx + dy + dz d + d" + sin " & da 3 G t G t 6G 6 % 6 I 6G L 9 % 9 6 ( 6 K & J 6 N * M 6 6 ( 6 F G * - + * sin G 6t 6G & 6 9 % v 9 % 6 ( * 6 6G + 6 ( " 6G + 6 sin" 6" 6" sin " 6G ( m / s 6A + - % 6 6 G 6A 6 6 t & 9 % 6 s & 6t 9 %

33 6 s 6 ( 6 t 6 6G + * G 6t 6 ( * 6 6G ( G 6 ( G 6t 6 G G f ( t + F ( t + G G f ( t s f 3 ( t f & 6G 3( + ( 6 f t f t & & G + F ( t +

34 ( a G t F( F( G x F( F( G x x ( ( 6G lim a * & D a - f ( t + F ( t G F ( t + F ( t 6G G G ( s x ( 6 t F ( F ( ( G F 3( F 3( x ( G ( ( t 6 s ( G D H 6 s &. 6 s + ( G DH 6 s &.

35 F 3 ( F 3 ( x ( t 6G F 3 ( t + F 3( t s 6t t > t < t < ( t + > + F 3 ( t + t + x ( t ( t < ( t F 3( t F 3( { t } x ( t s ( + t x ( + t + ( t x ( t t > { } F 3 ( t + ( t + x ( t + ( t + > F 3( t ( t x ( t ( t > s + + {( t x ( t ( t x ( t } t s x ( a s s s a s a s s t << a : x ( s >> a : x ( t

36 t > t + t > a t < t + a x ( + t a x t s ( s s s ( t ( t < < t + a s ( > t + a < t t O a O t a x( t ; s ( t a < < t < ( < t a s s ( t s ( t ( t a < < t s ( < t a < t ( t + t a + t < a t < a t + > a t s t s a s + s s G & 6G 6 # t sdt 6 6 # t sd t

37 a + a < t < + t s s G # t dt + ( a + ( * - # ( t dt t s { a ( t } a & s ( a + t >> a & t t ± a s t < & ± as t > t ; + > G < ( + t G ( + t + ( t G ( t + zx z d z? t # t ; + > G < ( t + G ( t + ( t G ( t + z x z d z? t # G F G ( lim ( t + F ( t F 3( t D G ( tx ( t + G ( t + tg 3 ( t d t x ( t + ( dt [ tg t ] ( F 3( t F ( t ± D

38 P t 6G G G ( x y z x ( x y z 6t P G G 9 # G d P S d P P S da s da dp s #S 9 sdp G s t % P /9 G s 3 3 s 6G 6t & 6G 6 G s % s 6 s 6 6 t 6 6 G 6 t ( * 6 ( * 6 6G G s G P 6G G P 6 t [ tg t ] d G ( P tx ( t + ( dt

39 x ( t G ( t G x P P t G ( x ( G ( t x ( t t tg ( t t x ( t d tg ( t dt t P G a s s t < a : x s G P t t t t < a P O P x a < t < + a t t P O P O 9 ( t ( os " P s [ ] > a : x G. P a t < G ( P s & 9 ( t ( os " x x ( t s & 9 ( t ( os " ( t a ( t t s ( os " OP s G ( p ( { a t } t a t > + G ( P

40 a 9 a ( f ( t G 9 G ( f * t a D + - ( m 3 / s ( 6G + 3 lim * & 9 - f ( t ( m / s D 6 f ( t ( G 6G 6G 6G G 6 x 6 y 6 z 9G ; 6 C < 6 x C C ( + > f * t - C? C G G x ( m / s ( + f * t - f ( f ( t f f ( t os t sin ( 8 A f ( t

41 f ( t t H f ( t ( a os 8 t + b sin 8 t ' n n n n n f ( t os 8t f ( t C os ( 8 t A C os ( 9 vt A ( ± i8 t e os8t ± i sin 8t f ( t A Ce ia ( i8 t + 8 t + j i e i8t Ae i8 t ic sin ( 8t A d x + 8 x dt ( f ( t Ce Ae x Ae + Be i 8 t A i 8 t i 8t i 8t e j C A

42 AB x a os 8 t + b sin8 t C os ( 8t A ia A ( a ib Ce ia B ( a + ib Ce a A + B C os A b i ( A B C sina AB A A A e B B e i A ia B x A os ( 8t A + B os ( 8t A { A B } { B A } A osa + B osa os8t + B sina A sina sin8t a A osa + B os A b B sin A B sin A A i8t i8t A A e + i e + i t i t ( E Q ( E Q ( os 8 sin 8 ~ A A A i +i ~ + A ( i e i 8 E Q t A Re( A Sm( A A A A B A C a + b A + B + A & B os ( A A + A B b tan A a B A sina B osa A + A B sina A sina B B ( R e( A E os 8t + Q sin 8t E + Q sin ( 8t + G S m( A Q os8t E sin8 t E + Q os( 8t + G G tan E Q b C a + b A tan a C os A b C sina a A A

43 ~ A A E + Q R e( A A A A ~ A+ A ~ ~ R e( A & R e( A ( A + A ( A + A ~ ~ ~ ~ ( A A + A A + A A + A A A & A A t B A # Ad t B B A A sin8t & os8t ~ ~ R e( A & R e( A ( A A + A A ( + EE Q Q ~ R e( A & R e( A Re( A A G e i8 t 9 8 k 8 k : ( F G+ k G x

44 6 G + k G 6 x 8 t i k x G Ae + Be + ik x. e i G ( Ae + Be e i k x i k x i8 t G Ae G Ae i( k x 8t i ( 8t k x G A os ( k x 8 t + A A x i( k x 8 t G Be G B os( k x + 8t A B x ik x i k x Ae x Be x E! k A ( J / m w! k A! 8 A ( W / m 6 ( G + k G ( 6 ik G Ae + Be ik. Ae i k t G A 9 e i k t ( A ( m 3 / s

45 ( A A 9 9 6G ( + W ( p + s 9 * p +! 6G 6G - 9 ( W 6 6t 6 W 8! A! k A ( W s P s P. 3 3 G + B 9 e i k t ( 8! B 89 ( W G 8 A 9 e i k t ( ( m / s. e i k t ( 8

46 6G i8 s t A e i ( k 8 t i8 G 6 9 ( k >> & 6G ( A ( + i k 8 t * i k e ik G ( ( * + - m/s & G (. ik m / s i A p p + s p +! 6G 8! p e 6t 9 p i8! G ( N / m. i( k 8 t ( k >> & A ( # dt * i8 9 A ( i + i ( k 8t * k + - e 8 9 ( i + * k + - G ( m 8 + ik - e i ( k 8t k 8 G G A 9 e ( k >> i ( k 8t ( m. W! 8 k i k Ae 9 t 9 ( 8 ( W.! 8k! k A! 8 A W A W! 8 A! k ( A + w 9 39 * 9 - ( W. W ( W ( m ( W / m. & i8 t a e ka << A 9a & i k a e ika ( m / s. A 5 9 a & S & 3 ( m / s.

47 ( 3 k >>. A W 9 8! 3 ( m / s. G W 9 9 8! ( m / s. % p W! 9 ( Pa. & W ( m / s. 9! W 8 9! ( m. W s 9! ( ( O m R +m R O R z ( " A ( µ ba ( W / m

48 m + m R m R m lim mr mr R z P( " A z A " P +m + m m P R D P z z R P3 OP3 PP3 z R % P3 m i k m e 9 P P3 % z R R D ik m ( e G ( P 9 * me 9 ik m% z e i k + - ik m% z 6 e G ( P ( 9 6 z * + - m% z B B ik B 6 e G ( P ( 9 6 z * + - z " 6 6 % os " & % z os" & 6 z 6 ik B 6 ( e + G ( P * - os " 9 6 B ( + * ik - os" & e 9 i k

49 k << << : 9 G k >> >> : 9 B os " 9 " G ik B os 9 6G 6 6G 6" " k B Be i 8 t e i k k B w! " os 39 G + kb os " sin ( k 9 8 t " k B os " A ( W / m %" 9 sin " & %" " W 9! k B os " # 9 & " & d" sin 39! k B ( W 9 B os 8t w 3 os " W 9 ( W / m. k

50 F G G A 9 " G B os 9 % p & p p p + s p + p s p + % p ( Pa p p % p Z & & R i X ( Pa & s / m ( Z exp ( i8 t % p ( R i X & & & i8 t e ( os 8t i sin 8t ( m / s % p ( R os 8t X sin 8t i ( X os 8t + R sin 8t os 8 t ( % p ( R os 8t X sin 8t R + X os * 8t + tan ; ( 9 + > < R os 8t + X os * 8t + -? ( X + - R Z!!

51 % p % p os ( 8t + A % p & R + X & Z X % p & A A tan X R % p % p + % p R X 3 36 % p & % p R R os 8 t ( 9 + % p X X os * 8t + - X sin 8 t % p R % p & & 9 % p X R X Z A ia Z Z e R i X R Z os A X Z sin A % p & & sin 8t 3 37 % p % p R 9 % p X % p % p os 8 t & % p os ( 8t A Z % p ( X + os * 8 t tan - R + X R A & % p % p ; ( 9 + > ( R os8t + X sin 8t < R os 8t + X os * 8t -? R + X R + & + & R X

52 & % p R os 8 R + X R t & % p % 9 X sin8 os 8 R X X t p R X X ( t + * & X % p 9 w ( W / m w % p & & % p & os A R & ( W/ m w R e( % p & R e( R e( % p & & R e( Z & & ( W / m w p & ~ & % ( R i X ( W / m ( x i ( k x 8 t Ae % p 6 ik 6 x & i8 ( Z k & 8! ( Pa s / m Z i8!!! k i8! Z e i A & ( i + i k k ik * ( Pa s / m + k k A tan tan k ( : + * - 9 A <

53 % p 6G B os" % p i8! G G k Z i8! i! ( Pa & s / m ( ( Hz ( V 6 6t! ( kg /m 3 dv T! dv T p ( N / m f T T! V d v ( N [ ] s.! 6 V F p T! V 6 t ( N / m p

54 p s p s F &. ( 6 F ( s! T * + - 6t 6 t 8 t e i F s + k3 s 8 T k 3 + i E + iq 8 x s s e Q x + ie x i8t x & is # s d x e E + i Q Q x + ie x i8t ( m & 8 s Q x + ie x i8t e ( m / s. E + iq s s e Q + ie i8t ( m / s s Q + E 8 G i s i8 8 e i i t & & 6G i s Q ie i8t Q E ( 6 ( * 8 + i + - e + m / s s dt & ( + # * + Q ie - e 8 W s + ( ; C e * + > 3 T C 9! < -? C Q + ie i8 t Q ( W ( m.

55 Q W s 3 e w + ( ; C * + >! T C < -? 9 C ( W / m. 8 ; C T > C E < + +? C 8 ; C T > C Q < +? C ( ad / m ( / m ( T / 8 8 E 5 T Q 5 T ( 3

56 ( x y z t F G 6 G 6 g ( x y z t t g ( x y z t G ( x y z ( x3 y3 z3 ( x3 x + ( y3 y + ( z3z ( + G ( x3 y3 z3 t3 9 # * - g x y z t dv V ( ( t ( + * t - ( 3 g g G x y z e i 8 ( t ( + 8 * - G ( x3 y3 z3 t3 ( 9 # G x y z e i t d v V k 8 8 e 9 8 G A ( x3 y3 z3 e i t # e i t i k V G ( x y z d v F A + k A G ( x y z

57 i k e A ( x3 y3 z3 ( 9 # G x y z d v V g G ( ( 5

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq 49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r

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.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =, [ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b

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