Tóm tắt kiến thức giải tích 2, Study notes of Calculus

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M (^) &

• I (^) CH PHAN DONG LOAI MOT 1 - (^) Dink (^) ngha New (^) floy) xicink tre (^) string long train (^) ( (^) = EB thi rich (^) phanting (^) laiI mode the C (^) , Jfxdlhim (l

2. Tink char

(^1) Godde = (^1 3) ([f(x, y) + g(x, (^) y)]de = Jf(xd + (^) lgl

2. (^) I afkyde = Jopf(x, (^) ) de^4 New C^ = (^02 1) ,^ Expe^ = ( + x d + (thd
3. AB (^) : Cho (^) f(x. ) lien (^) tu ii ABI (^) +(x, %. 2)

X = X(t) (^) , y =^ y(+), a+ =b^ It(x,de = (^) 1 f(x, (^) y() ,^ (x()+^ yc)d+^ HTE (^) Gric (^) Dude =I frecs (^) , rysing]/+^ r

y =^ y(x)^ ,^ axxb^ l^ flude^ =f,^ y]^. He (^) yiae Trangkhong (^) gian Last y.^ 2)de^ =^ 1x^ ,^ y^ ,^ 2).x^ +^ Ti^ +zied

X = X(y) , <yed

Stude

• ICh PHEN^ DUGNG^ LOAI HAI 1.^ Dinhnghia
• Cho F(x,y) = [P(X ,) (^) , G (^) (x (^) , i)a ham rector x tren (^) dig (^) my tron B (^). Khicto tich (^) phascry Loci #I wa (^) FdrTheEB : 1P(xidx + (^) Ody = (P(xdxQy
• MLH giva tich^ phan (^) driong loai I^ valua : (Plxdx^ +^ Qudy = (Fril.^ caM

• Khanhau^!^ -Tich^ phan strong loai IK^ phy thro was^ hing lis rich^ phan tren^ EB^.^ Tick^ phan (^) doing La #phythu (^) vaohung lyich (^) phan tren EB^ =^ 1 P(x,dx^ +^ Qxdy = -J P(xydx +^ Q

(^3). AB : Cho (^) P(X.Y) , Q(x.y) lien (^) tu trong minmi D chia EB (^). (^) (G, (^) R) y = y(H) 1 P(xQudy (^) x = x(t) , (^) y = (^) y(t) ; (^) ((x,dx + (^) Q(xydy = (^) /[P(X+, y)x +^ Q(x+ 1 y)y X (^) = X(t) (^) 1P(xidx + (^) Quiyldy = (^) (P(xy , y)x + (^) G(x+ , y)]dy (^) Trongkhang gran, (ap" (x, (^) y. 2)d + Q (x, (^) y, z)dy + (^) R(x. y, 2)dz = (^) (TP(x+, y+, 2 + )x! + (^) Q(x+ y+ , 2 +)y+ + (^) R(x+ y+ (^) , 2 +)zi]d (^4). (^) Cony this Green :

· Diem M(x, 4) ma curing any 2ctio x dink Kii X(t) , y(t) egLien bu hay atien tot waring cong Cresta de ca Mthia man it cuing any Litnhattai 2 gia tri teta, b]

~ A2 [Kicha (^) tiembrgL #C don (^) gran. Da EBstiem (^) stane wi (^) trung nhau (^) Agl DL (^) Khep Kin (^). Chin (^) () cus (^2) de (^) quy tinh la (^) ngvie chin Kin (^) sing ho

• (^) Min (^) phang D (^) tgt min (^) lien (^) Thing new nhif (^) A, BED (^). #C lin (^) tuc NAB ED (^). Mien (^) phong Datgl min don lien Khitha (^) : D lien (^) thing va nee detgian Khep kin 2 nam (^) true trang D thi D'crdiene < se (^) namtras (^) trang D (^). NeuDphas min don lien (^) thigl misa lien

· D22 too x clink bi x = X (H) , y = y()gL tron Fing thur new^ Cothe" Chia thank which oak who va xt , xi lies to

• Trung mp^ Oxy^ ,^ cho D^ la^ microtong^ bien^ li^ dong^ congon^ gian^ Khep kin^ ,^ tron^ Fing^ Khur^ C^ ,^ P(X^ ,^ y)^ ,^ P(,^ Y)^ ,^ Q(x.Y)^ ,^ GY]^ lituc^ Trang D^ : GP(dx +^ Q,^ y)dy^ = / · Ling (^) dung tinh^ dien Rich^ minphangD :^ Sp^ = //oxdy =^ & (^) Oxy-y*x

& O / ① AT (^) CONG KHONG^ GIAN

• Tink^ dien rich^ mat (^) zong Dien tich^ macang 2 = f(xy) chinhchien^ xuing mathing Oxy ( D^ do finh^ the^ Lingthic :^ S^ = (11 +^ (f)+^ (f)^ dxdy TCH PHAN (^) MIT LOAI MOT (^1) Binh Ughia
• Tick (^) phan during kaimas^ latich^ phan^ codang^ : 1)f(x,^ y^ ,2)dS^ =him

2. Tink^ char · 1/1ds =^ dien tich^ mar (^) cong · ([f(, y, 2) + (^) g(x, (^) y. 23]b =f(x,^ y,^ 2)ds + //g(x, (^) y , z)ds ↑ 2 = (^) 2(y) : I^ /zeds^ all] Ax · Daf(x , y, 2)d) = aff(x ,y, z)dS · New S (^) = S, @S2 thi

1. fixed^ =

+, y, 27d +

If (x,^ +,^ z)ds) (^) living (^) to va^ x = x (^) (y, z) va^ y =^ y(x, z) ICH (^) PHEN MIT (^) LOAI HAL

1. (^) Mat dink (^) bring B^ =^11 +^ z +^2

• Marlong S (^) tgl mai tron new (^) F(x,y , 2) cicas (^) tao ham (^) ring cap mat F (^) , F!F lien (^) tu (^) vathing (^) doing thi (^) bang Orin (n -) · MCS (^) &gL masich King (mi2^ phia)^ mis^ himsas^ tink^ in^ taims^ Mix,^ Y^ ,^ 2)^ Sarchonn^ : (.^ (,Y,2)^ ,^ nex,^ 2)^ ,^2 ,^ (X,^ Y,2)^ Lentur^ tes^.^ Kristic

2. (^) Dinh (^) nghia Cho P(x, (^) y, 2) (^) , Q(x,y, 2) , R(xy,2) xa (^) climb tren (^) mat from (^) , (^) fish hung S (^) , losa, crsB, war) : Tick (^) phanmatloit : I^ :

1. [P(xy,^ 2)vs^ +^ Q(x,y , 2) (^) crsB + (^) R(x,y,2) csg]dS (^) Eghsch phon (^) mai lat ma P, Q, R (^) tren (^) mar (^) tich huings. MH : I = (^) /Payd +^ Q6zdx +^ Roxdy S

3. Datich (^) phan luai hai (^) v tich (^) phan kep

1. M(x,^ y,^ 2)dxdy^ = 1)) Rixy.^ z(x,^ i) dya (^4). Carb (^) tink rich (^) phan mat kai^

hai

Cach (^1) : Dra (^) v tich (^) phan mat las mit I

• GS^ :^ z^ =^2 (x,^ y) ,^ in^ ↑^2 , F(x,^ y,^ z)^ =^2 -^ z^ (x,y) =^0 , i^ =

(t +^2 +^ 2)

(2x - 24) =^ Ca^ , cas, cosf) , &S = 11 +Z +^ &, dxd ↑ = /[Pusa

• (^) Quep-Rus]dS : /[P. +^
• R = [P(y2(2) +^ Q(x, (^) y , 2x)(-zi) +^ R(x, y , 2)]dxdy

Th, F(xy,2) = 2(y) - z = 0. i

=in (12-1^ =^ pos ,^ cep , 18)^ , d^ =^1 +^ 2x^ +^2 , dxdy F (^) : /Pasa

• Quss + (^) Rosj]dS = /[P +R [Dy2Qy2 - Rxy]dy Cach (^2) : Jack (^) thank 3 tich (^) phan I = Phydz^ +^ Adudx^ +^ Roxdy^ = 1 Pasad^ +upd^ + words^ =^ I^ +^ +^ I^ =PzdydzQ(xy2dxdRx^2 x

( :^0 (n,^ tris)^ =

() :^ <(n,^ wil^ ki (0) : z =^ (n^ , (^) tri

5. (^) Cong this (^) Ostrogratki Gauss Cho Sla (^) mo kin (^) - ~ la (^) va The^ do barquant b S.^ Nei^ P (^) , Q (^) , R va car (^) dao ham^ rieng cap (^) mos no no lien (^) the tren min (^) this Plyd +^ Qxdz + (^) Rody = 1))(dxdyd Dau"+^ "nei^ hig wirt hung rangoor e (^) , "-"neuing we (^) up hung vao (^) range
6. (^) Cing this Stokes Cho (^) Slama (^) cong , tron (^) , (^) coctinh hing v (^) bien (^) Listing ang Khep Kin C (^). P (^) , Q (^) , R va ca (^) dao ham (^) rieng cap mat (^) wachung lien (^) tuc tren S^. Khiato : I (^) = &P(ydx +^ Q(x,y,^ z)dy^ +^ M(x,^ yz)d^ = () dx dy · Hung can^ wasa^ hang auding (^) cong Khep Kin^2 tran^ theo^ quy Fai^ ban^ tay phai

• long their stokes^ indic vint^ drivday : & Plyvidx^ + (^) Glady - (^) Rhyzidn = /a co a

2 ~^ ~ So d (^) Khao Sat (^) Su Hi TU Cia (^) chul Bre1 : Khao sar (^) su his tu (^) try o via cruis ↓. Neal htt (^2). (^) New (a) (^) phan doth (^) dinken (^) Limphnn(Ghsdtchun D'Alambert, Cauchy (^) d xt h (^) u yetia (^3). (^) Nei (a) (^) phank (^) , this t can (la =^ 0)^ Thi (^) chuyin sang bon Bri (^2) : Khao sat^ su his Hu dis^ Kien (^). Neil ch^ dan^ dais (^) Th (^) dung tu chin^ Leibni j Bris :^ Khossu (^) ha m aa^ Churching am^ bang or tinchuan^ tich^ phan , so sand^ , D'Alambert^ , (^) Cauchy

Gu (^) LUY THA ↓.^ Min^ his tu (k) Churt (^) lig this la (^) chut anX" a R.Taphp t gitx the hu (^) thig min (^) ha (^) chilThia

2. Ban^ Kink^ he tu

(R= + a) (r=^0

↑

chur ho fu Fx ,^ (x-x)^ <^ R

Choa(x,^ ant^. Whi (^) : () (^) ChhouxER , (^) ChurchiuRgL bankinh - (^) phix(x-x

3. Das^ hi D'Alembert j Choa(x-ER.^ GS^ :n^ : Bankin^ hu R

.^ Dan^ hiem Cauchy Chon(X-X ,^ E^. GSmaT BankinhhuR 5 - . Car bioho (^) sa min^ he (^) tu co^ chu, (^) luy tha Bri 1 : (^) Tim bankinh^ hi, (^) fu R Bri 2 :^ X^ su hi (^) tu we chui s twinhing in bien (^) IX-X) = R (^). Chisd chiandas (^) , En, Ich (^) so sand (^) , Ksd (^) +ch D'Alambert va (^) Cauchy (^6). Tinh char -. Tang ca^ chu^ hiy this^ limes kam^ lien^ tus tren^ min^ his zu is^ no

2. (^) Trong (^) Khoong histy. (^) (ana-]^ =(x - x
3. (^) Trang (^) Khong hist : (^) ((an()dx(a(x)"d =(x - v

• C 7.^ Chuc^ Taylor-Maslaurin ·^ Cho^ f(x) x^ tink trang lancin Xo va^ to ham^ capty Y (^) taixo · Khi(x-X chu^ TaylorfKhach Macar^ :

• Cho f(x)ha vi (^) vohan (^) tring Ihoan^ (x-2, x +^ 3) (^) , 320 va IM30^ : (^) (f/XM (^) , Ext(X- (^3) , X +^ 2). Whi o f(x) co the bi dien^ thank^ chic^ Tayler (^) fai xo : f(x) (^) =x

· Phan^ tich^ mot so^ ham^ c^ ban^ thank^ chuc^ Manlaurin

(^1) S es IR^6. sin

IR

2. Inkt)^ = (1, 1] 7 ,^ Cog^ X^ IR (^3). ~x-a)--^ (d^ -n^ + 1)xv(-1, 1) 8. R (tx)" (^) al (- (^1) , 1) acta^ R : (= (^1) , 1) Ir (^). sinhx)!

R