Appunti Matematica II

Appunti matematica II

Indice

• Matrici ...................................................................................................................................................2-10
• Vettori nel piano e nello spazio ....................................................................................................... 11-14
• Spazi vettoriali .................................................................................................................................... 15-18
• Diagonalizzazione ............................................................................................................................... 19-21
• Geometria analitica del piano ........................................................................................................... 21-23
• Geometria dello spazio ..................................................................................................................... 24-28
• Equazioni differenziali ........................................................................................................................ 28-35
• Funzioni a più variabili ...................................................................................................................... 36-46
• Curve ed integrali curvilinei ............................................................................................................... 46-50
• Forme differenziali lineari ................................................................................................................ 51-54
• Integrali doppi ................................................................................................................................. 54-58
• Integrali tripli ..................................................................................................................................... 58-59
• Integrali superficiali .......................................................................................................................... 60-64
• Successioni di funzioni ....................................................................................................................... 64-67

--a=3=e=3 *r'*'v1 ffil) x7i,sAe*n x *-,.g,{ 1 =J=É !:;tn,Lt7snbz-"r;ij3 A=6.r)= jJe '&#. **oJrJhul**,t*L J;o,,^nni..t':^^>i ryl"**h ru;r,u Jr/l^nut,,,u.t,,,,313 §k'rl'?7 l,') ir rtl r t4ala il* ,ffi,. .l*trnit#,Wffufu,,*olrrh7'rfrrWffi Mì,ily,*W"*#Phni"Wffi Àl-'*ffi -;rnl,ì sllsqf"brL 1''"-,'.:#^r'tu,n' u[o *,il*W*A;m^ zp*e ,,,t*; t#:ff"f ha,tu Ju*t.,s*,y, :IIII Ji Lr P1ffi, ci:t'l'JA€ir,ry0Fr6 Slixfor:iJ ,l^'ltBffi"q: *ùYnftn,[n+rrrv'o àkY')* u;'l,to'Li-J-,rr-l- C, t_--'*-. --rla--,,-l:t---'È--I_l-tJ*L,4*a--;;l]-"]'h\tt)'r;ti'[::J'"W&rh:Ml r.t.bffiil"der;:;m *t^, o*l,n, A'$;ffi=à/ii$n'h'*"'4^"*T-t'fY*i,H; I:rfi =4'\r\ i[,A'-".n''I s,t#,,"lrJ t<t\LI #th}inàf"n1 4it-,1 -Jxl,4* Ii .i i ! ÉÀ t tt I t , u L fl t-!*-^ *,'*t*x *"kqqwh,u rnu*r* Ptft*br* V*-"i"À-h ='>l"r*J.#. "l; f,t';^^fuìirr* ,i,* ilUqùfrb$t\Atw.fr^:ue.r, L rhF^z,Ji:rnodi t1,4.'1xlx"lcyt"r.+T-t-,b;,.t,*,l" c^/vrr{o^"dt,1h!dt- ;,f,a W :Itn"tl*h 1':X:7./r], -,ui7ì ,([,[, o.(uil'1=**,.,&J+t Rt" i/+ .i+l -furr,,.*ldL9^; rra.rtgl*-"n.'["eJ,{'B iÈrl,=bt,t yi*!t f.r i,tg*ur*/,t, \{l"t* JrfpcJ ,,n* A, gr1 mrP,,tÀryw,^fnùf,; Bnrrr,r"m #É;[-m,'n^aiÌi"lniri*=V J4;X)3tz _l=lA(srÒ=bilr=Àr c,,ì'J), (eÒ41) +BÀ"lryt, rynlt^. =.46B) s-IAo'o fe)M=a .Bc 5) 6oJ"Y)=[c+4(Anr)c _t;J,A+JB0a(A*B) d..€'NìL r" =^a,t -a=Frc r'aiÉtHD Jrid11 ietqil l;,*ku ,ti:r***r*h,kmw,,;aT,O Y.# ^».t\?$Wr''r! lrl*;-.rt,o,&u^l,* ,l l J',t - I)y'lvt)Àtn:{r):,tf"'W7oU,ll'fuur*#J"lltl^;;rffi,i"rro4il$ L--EI4=b/o3'b/o,g',,''ì+:yh';eÉriili,lai-i >-'i ,i,-l -lLJ-I--l-LJo"ilrù**'na'ruicz i,i ,a.,-i ltl,,:l',i ill ._-L-Jnta-fbv --4{:ati =3- ':I"E{4D IJL-_-f+1r=(zir,l).c1-tt! _I:IL--=rÈ#.-= :tr L-.-l, 4=J:r{4-lLLtt-+"À,1olt lL-f1-zil l-r-Lr-.11.1" .Il+7 li rLll .LiÀ,; ot+ll UiIlr!.t. ryalt{NLrd%.k If ùut - rI-zIttx1.')r4 l'*^*( ln, l",>nilo,,tI .r) l**.a'a,^nMffi*,,t*/Jrfid"*l'( J"U.d* Xtfrc, M7'l:it l='l'r?l'o 'l?Yrlh*^")=ft,cr#ìr, :"r'-1"-: lIn'oqlE"ru--: ì;1),,(t Dl;$-ffi^=-!t- *#:,r,"YmY;fr*$wg1;fu§ll urkif@ftùi,1,*W aV o,lo,qtù,'ru:r'- -ll, -f=Attvvl)lt.! ltth, ,tt,V+,V..lt +w)2) l,tsw E=lll§blL <?7A fi?roOA xÉ;;i' , , ,,,tute'Y+&,,,, LY"#ffi%,W,#i-Tfu*:::y, **/**^*4'fWL fu&tL "@J*,t *h,fLlà &, ,"A,'y-- y.Lti)lzj4b+Lt.y+ rvtra -!,,o";riltl& I4rcÌ,vsoilWdfrl.y'1.t1 r,tt L'€tvv{a,uii:i:,^N*,*,i;irffiY':;#3:x:ily*i,1iu'il,i\';r':;,;h;fr;ù);i,*;,W;";';' il i^i|;^rfr*{r*;i,,*;.,"L, ;t*,.;'t^1,A. i"=uffi^r,*1" ^,*'v'y' ì;vti! thv'ltzfl ' tui;#,,',# 1T;:"i l,:," !--p?.'nl,');i r ili) iuu.: AUgw.141t \.,,.l--L-r !, trl -IJ{4, =" llt,.ilti +tnr1i.-tr,'(r r,zln',-.,,t1,, lr*r,Ì,ry,rN*l*,r-.f* v=»rr$r-,n 4 *!yr.q:1ìW',^*o;'oi,l',':,rr:f:l'fftil#:-|ft.#,'r/ì =wW; *-**1hW ffi;:*IY-h*;a* h^"* =!*,ft*(,o, iaWwld*Yi _=oy,wmw t- It rtsh/- o;l;-;;:#4, +|\) *Le H'ifTrpr,unt, n&,^,t*/.,"fffi;.W;W; fil,', ^T;;r'i,*rrr,,rt;*ro tti.t t!*.t,'Ì"5' ^^li?iff. q"\r^ih"utih-(u*) iix'I'[au")iWf -'.#Y'd r"r-''')ài1L'#:l;|'ì,',(Xt ^w el: r*&* b*l******; w:tLffir,*tr* fr.ff''*,vi, !,,!: --a-,.hff| +lu,v,-ut)<-ri., -{v,hy,$r,{fd (u.rs-u,q) il3ur},:=^r:hilfl _Jil*lr*-?.R§,* +ti 5t -l&*r*, +RÀt v.- ,nfuoil,.V"l,*,=+' ìir;<\ r . l / \ . r .^ t*"i,4l-f*L.t"i "h.4,r,w*7R,1-tfsoR;HA) p§$4\fi/.r!9*i,tV: +V+trsl+ V\,"-iur,V-tf,1a,v;w;ì --"- lwrwiwJil-i Jbkt thi WiIdo",. VlVt! wz|+Vckz!ffAr,u;n,*x,t: AiJ-+t), +VuR, Wt +rl.z$+ dax.4!,'u A=(ùU;:lMm* W.fTryLaj,t*+A+oiWra#Nffi*,ffi}t--tr..,Yl.\..-...1,,t...n..W*,*J tJ^.'n,: *.,ry**.-t?r-:tt*n {0,;,hanL__I--t-_-L--L- 4-IIh..--:IEAaL.-Iiy*iqi*H-xM*w*MtIIi ffiilE!_iJr H-, ;11\*ii ---.*['ArlLi,,,*-tsi; ùr.M. -jij b Él-Entìt-*wr--w.) t""bb4"*,1.3 -''-*d 4'? (W#, nT,X;il',ffS)il ,ffi- ffi nn"ft W3 ;lfi#1 h-zoo :y!:!!,ff1iìW*#,,..,\r#:ff: ,=jH:tiÀ.,,flffiiztr;b;&iffin*#rffi?#t*,e /\rr,,tt,,u :,t;p!. Jril*-1,,n4*;l t t *1hrt^ r*r,;n btlr;A"{lo"l*t* bl*Àr; ,karhawra=itrrsffiHfi "II*':É*hl'*iiirthpf ; ;Jt**a;fun&i -FÉi.-. &",*n.A; I yt",rrhbd,h'f,,r,,,*-:,{ffiry*,*'ffiffiij:t$ ;r{t-''n=o (*'}116( *&.t=o-:\ -l I.1,_OL xzll II -2r, Io'2-l ['lluxt't^.'"g+ky,oÉ J-?*t -t xt'srl(I *-, 'tu+4n-Q s7o.r:(-z Ytt*f:wY,{nrWi )'ffiw!ffi-f n-'il* f"" *ìx,lt *t I'x..-, S,ì,.1i1';ft)'^1. v'rj;r) el\n,16.';r: ilil'6;tlU.!qrr,,trl ,(til tt/) 0'i k,a1rt^II /f1I iill; t; k iI rynlrc" ù\rN.oM\;D: [i^-,1,J = -JL--:Ij"^#i+ _lfuffi-Fvilv,* t*;kt!!ÌM -i*,*:,#ruW{mW;;'d" tl rI *TT*\,"L r* r,*n ltvrrl;kt * AB,i.rb"Le.'r,,,gg@+e dt',ot ry.u»t rln1"e,n"y "^T';;.* .I ,h-=f *di (-t, l),rL^z u**,^^ Jrlt- otur,rn*,/'-o',1arw,*,,t-,lt ^tJ* cWo*,-J;r4lté»a.?rl ;;=^,ApU,z)J,t"z'*-7r!,-L-\-zt.Y,r,-J,?(1,3).ÉJn)";,45$r =j.{-!-:Ì:et:*M l,ffiilw H,^o1;,*u&';,,i::(;'y( *'(-\U. it(;t,21'r,ry\" fuvrz.,{l".é-qn'd,bt+,tScX|trt'dituth;cr,ell-ùl;Ant<Ilda A^^*d,llym ffihi.E-'r-41'i,rhJo\*.Lr,*w*.h*n z !_.x*tfr =*fuM"t##rWt*:t;'#M=Wffi:ffi*nilz:#tr!JL*,È.-.'tiLr#.'Iffr.il ^X:)(el b',Ib/r c'.)rco- = *r",4;& r*r"Ji^e Il[dlt*>d.-L u:=Àt:-lE-r- "* t"r,Bl.#h[(*1»rr;'-l!-r-:tie>*.rC-i lla&télz\'-tzltfrvwao lhtV$rk'i, I[r,*rxt rtsJ"*fr'4t;l\.'A='t-.fTeutt -:.J.-: , {_I/dà È-l;|Adrn .{1,f q.+ 4, ,I-IÈ-Is-E-rIL-r I-J>--Ndt;6tL',/i cùh,Llhtiqln,t" =zj.4*da,,.,I t"Y-.'t)àL Y,T, =o,APL,\oà*.. toL'?nr' ,n&zedth,;*ll à-ut L'?im ,!.dl,t^b*_ùf"W {lh&f*r};-S,É "imffiiffiw, =1 -itiY't,* '*:aI l,"iPit'i t "$lB."nlizc ffi,:*;w.,-v!&'-': -I txll{d.ir,--lF: *r'if'.b.J.''; itrax+by +Q +dio .t*-,E r -tJ'=o.ield i:eVrlfI lbIb<.+ Ii ot lo<É> i1 Àbu. c,l lgc/"t"ht"u sc7 t&- dl,r b,:b!.À ct=e,l='ln b''lb='f nIJLL* <',,[< J'r,À4,|U71l5 O,?to ,t'5,oÈohi %'o LeùtttiohrLe>7bìtot;oWI ,lo'(rc'^i AQ,^ = ii,l xt'-rcxWEffi*#aWrm'#*'ffi frvv"-Y-wWiffitrXfii;e; fl:::%, ==J/;'pq;+,::;'l-*;";;;,ffi,i p*'z;;,ri;' rnrt- p"4'v*'*#N' €,;'h*ht"'lnfro -$ uil .ft*arg\r,t t ^{i:;;{W Wr #d ''l'at"?: -I,1tl,rtl lYtl| I 1"" v=ffio-6I -I[-{t fr t<ry =&i'fr*"9'[*11,ùd, :f;.rtl^p,ryf gaJ* o?n;(*r,yn,t) 'l'?",(*",yo,,ra -"'ffi.' ti;\!;:)ll'f ,r,-L!,'*';.":*. ,)^ \Ì,*).t.e u,i)i,-^,,r*u,'r,-l- gl'f^*(X:iJlr*.lrt Pz.(,tgl'(*,,.1.,dr)1 X^,1 tyntÉA,?t*(xtyt,7r)0^r yz-t.i"lyr-y. ?1-2rl at-z*l>Qlr.-r, lrZ-x,q-zl,l'-lx5-rv -yr-v.,| lyr-v,lxt.u z5-2,ù ,*l^*'i,j:';*lxfu* ,r**JrO&<*byt.:.. ,,,, l.bty& a" . .-r.rur,.* 6fr-&* *nilt-- \''-- ,*lnrrtibu']-*-" o'\&:l 'ii:--- ;"e-A =c.e&^nolrfr,.-nàrh,in,Xd,,";\ 'lnJot Y*d"'**""h" I,'5) ,{ '''i'] JJ,;,rrrr*k,l,'l ,#r;(t, ,.:;?=,=,hS:..^ir* Iilf onr<;,Ala 1,!*^-Tl.;a,rr.t'r**'^i"-&"tr" "Jl^*;''*';J* },-?"'n*r1,1f.L'o *J J"ij^'.rtr-',.'r l* t-.la(xrl-* [tro/'4*l",'* (*b+,)-r;J- l"- \ t rqr,ì-";l ,,0) oilr.r,,-q\.l-'r',Wtu:*Aun*h' a*ux,"A-"&igra