New Advanced Higher Mathematics: Formulae

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1 Advcd High Mthmtics Nw Advcd High Mthmtics: Fomul G (G): Fomul you must mmois i od to pss Advcd High mths s thy ot o th fomul sht. Am (A): Ths fomul giv o th fomul sht. ut it will still usful fo you to mmois thm. Rd (R): Do t woy out mmoisig ths, ut thy might usful to sv tim i clsswok d homwok. Tigoomtic Idtitis: (fom Ntiol 5 d High) Liks tw tios Esstil Fomul to kow off y ht fo th m (G) cos Asi A si A t A cos A Squd cos ( cos ) si ( cos ) Compoud si( A ) si Acos cos Asi Agl cos( A ) cos Acos si Asi Doul si( A) si Acos A Agl cos( A) cos Asi A Oth usful os tht my usful fo homwok/clsswok tc. t A sc A cot A cosc A t A t t( A ) t A t ta t( A) t A Ect Vlus(you should kow ll ths, though th is o o-clculto pp, ulik High) si cos t udf. 0 udf. 0 Compl Nums Fo th compl um, z i, th modulus is giv y z d th gumt is giv y t Th cojugt is z i Ngtiv fcts: si( ) si( ) cos( ) cos( ) t( ) t( ) D Moiv s Thom sys tht fo y z (cos isi ), th z (cos isi ) ( ) Nwttl Commuity High School D Wtkis 05

2 Advcd High Mthmtics Difftitio Poduct Rul: du dv v u dv du u v Quotit Rul: d d d d v f ( ) f '( ) si cos t t l 0 sc f( ) f '( ) sc sc t cosc cosc cot cot cosc l f( ) f '( ) f( ) To difftit ivs d fuctio: d Itgtio Pmtic Equtios (wh f(), t y g() t ): Gdit (dictio of movmt) = d Spd = dt dt d y y y 3 d d dt d dt O Fomul Sht f ( ) f ( ) d sc t C si C t C C To sv you tim i hd qustios fo homwok/clsswok, o d to mmois: f ( ) f ( ) d t l sc C cosc l cosc cot C cot l si C sc l sc t C Itgtio y Pts dv du u d uv v d d d Volum of solid of volutio f() tw d : Aout is: V f( ) d Aout y is: V f( y) Nwttl Commuity High School D Wtkis 05

3 Advcd High Mthmtics Squcs d Sis Aithmtic Sis Gomtic Sis th tm u ( ) d u Sum of ( ) S ( ) d S tms Sum to S ifiity Impott Idtitis ( ) 3 k ( ) 4 ( )() 6 Mclui Sis ( ) f (0) f (0) 3 f (0) f( ) f(0) f (0)......! 3!! d i pticul: Vy usful to mmois: ! 3!! si... 3! 5! 7! 4 6 cos...! 4! 6! Lss sstil to mmois: t l( ) Fuctios Odd fuctio: f ( ) f( ) Ev fuctio: f ( ) f( ) (80 ottiol symmty) (li symmty out th y-is) Nwttl Commuity High School D Wtkis 05

4 Advcd High Mthmtics iomil Thom Th cofficit of th th tm i th iomil psio ( y) is C!!( )! y Vctos, Lis d Pls Agl tw two vctos: (High) cos Equtios of 3d li: though (, y, z ) d with dictio vcto d ij ck Pmtic fom Symmtic fom t y y z z y y t ( td ) ( t) c z z ct Equtios of pl: l Noml is m Poit o li = P (with positio vcto ) Vcto qutio Symmtic/Ctsi Pmtic (A) l my z k stc wh k ( d c y two oplll vctos i pl) Agl tw two lis = Acut gl tw thi dictio vctos Agl tw two pls = Acut gl tw thi omls Agl tw li d pl = 90 (Acut gl tw d d) Coss (vcto) poduct: i j k si 3 i j k Scl tipl poduct: ( c) 3 3 c c c 3 Nwttl Commuity High School D Wtkis 05

5 Advcd High Mthmtics Mtics mtics 3 3 mtics A c d c A d f g h i Dtmit d Ivs d dt A d c d A d c c f d f d dt A c h i g i g h ( A) A ( A) T T A T dt A dt Adt (A) Tsfomtio Mtics cos si Ati-CW Rottio y θ dgs si cos, Rflctio i y-is Dilttio y scl fcto 0, Rflctio i -is 0 0 Difftil Equtios ( ) Fo Py ( ) Q ( ) d, th Itgtig Fcto I() is d th solutio is giv y I( y ) IQd ( ) ( ) P d Scod Od Difftil Equtios COMPLEMENTARY FUNCTION (Homogous Equtios) Ntu of oots Fom of gl solutio Two distict l m d m y A Rl d qul m y ( A ) m Compl cojugt m p iq y p ( Acosq si q) PARTICULAR INTEGRAL (Ihomogous Equtios) Right-hd sid cotis Fo Pticul Itgl, ty si o cos y Pcos Qsi y P Li pssio y y P Q Qudtic pssio y c y P Q R Nwttl Commuity High School D Wtkis 05

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