m j NGHIEN CIIU -
HOAT DONG KHAM PHA TRONG DAY HOC NGUYEN HAM VA TiCH PHAN VUl S U H O T R O CUA PHAN MEM MAPLE
TS. PHAN ANH TAI - TnfAng Bai hpc SII GOn ThS. N G U Y I N NGOC GIANG - TP. Hd Chf Minh I . D a t v l n d e
Day hpe l i hoat dpng gilo vien (GV) td ehUe, d i l u khiln hoat ddng hpc t i p ciia hpe sinh (HS), qua dd hinh thinh d ngudi hpc nhung tri thde, kT ning mdi. Mdt trong d e phUong phip day hpc t o i n tieh cue l i day hpc khim pha. GV tao ra nhCfng tinh hudng de HS ty khim phi ra tri thCfe, ki nang mdi eho bin than. Day hpc khim phi d mpt sd ndi dung se phit huy dupe tinh tich eye khi cd sy trp giiip eiia cdng nghe thdng tin ndi chung v l phln m l m Maple ndi rilng.Trong bli vilt niy, chung tdi dUa ra mdt sd hoat ddng HS ty khim p h i tri thUc, ki ning trong day hpc nguyen him v i tfch phin vdi sy ho trp cua phan m l m Maple.
2. Khai niem day hoc k h i m pha
Theo Bruner, vile hpe t i p khim phi xly ra khi cic c i nhin phii sU dyng q u i trinh t u duy d l phat hiln ra y nghTa eua dilu gi dd cho bin t h i n hp. De ed dUde dilu nay, ngUdi hoc phii ket hpp quan sit v i nit ra k i t luin, thyc hien so sinh, lim rd y nghTa sd lieu de tao ra mpt sy hieu biet mdi m i hp chua ti/ng biet trudc dd. GV can cd ging v i khuyin khich HS tU khim p h i ra cic nguyin li, c i GV v i HS phli hoi nhip trong q u i trinh day hpc.
Trong day hpc khim phi, nhiim vu cua ngUdi day l i chuyen t i i cic thdng tin d n hoc theo mdt phUPng phip phil hpp vdi k h i ning hilu biet hiln tai cua HS. Giio trinh Cling c i n dUOC xly dyng theo hinh xoiy dc de HS xiy dung kiln thUe mdi t r l n eo sd nhCfng ndi dung d i hpe. Tuy nhien, dng cung khIng djnh ring: Viee day hoc ktiim phi khdng phli II HS t y khim phi tat c i cic dU lieu thdng tin, m i hp khim p h i ra sy lien quan gida d e y tudng v i cic khii nilm blng cich sCf dung nhdng d i d i hpe. J. Bruner da ehi ra bdn li do eho vile sU dyng phueffig phip niy, bao gdm: Thue day tu duy; phat trien dpng lue ben trong hon l i t i e ddng ben ngoii; hpe eieh khim phi; phit triln tri nhd [1 ].
3. Gidi t h i l u so lucre ve Maple 3.7. Dgicuang viMaple
Maple duoc Trudng Dai hpc Tdng hpp W/aterloo eua Canada xiy dUng va dUa ra tin dlu tien vao nam 1980.
Sau nhilu lln cii tien eho d i n nay. Maple da ed phien bin Maple 18.
Maple du d i p Ung cho moi tinh t o l n sd v i die bilt tinh todn tren ede ki hiiu todn hgc. Vile sd dung Maple tUdng ddi ddn giln, tUcmg t i c gida ngudi v i miy khi thuin tien. Cau hinh miy khdng d n \dn. Ngoai cic tinh nlng nay. Maple cung cd the sd dyng nhu mdt ngdn ngd l i p trinh. Uu dilm eua Maple l i ed r i t nhieu him khic nhau d mpi linh vyc (tren 2500 him) nln viec l i p trinh tren Maple dpn giln hdn rit nhilu so vdi cic ngdn ngd l i p trinh khic nhu Pascal, C, Visual Basic,...
3.2. Cdc cdu linh vi Maple stf dung trong bdi viit Cu phip tim nguyin h i m ciia him sd f(x):
>lnt(f(x),x);int(f(x),x);
Cu phip tinh tich phln cua him sd f(x)
> lnt(f(x),x=a..b);tnt(f(x},x=a„b);
Lenh niy dimg de tfnh tfeh phin cd dang: f/(x).
4. Hoat Adng kham pha trong day hoc nguyin h i m v l tfch phan vdi sU ho tixr cOa p h l n m l m Maple 4,1. Phdt hien nhtfng thudc tinh ddc trung cda Hi tuang
SUdyng phan mem Maple phit hiln nhdng thudc tinh die trUng qua d c bai t o l n cy t h i , tir dd d l xuat d e tinh c h i t cac bai t o i n , eic khii niem tdng quit trln CO sd nhung die trUng rieng biet d i khim phi. Trong day hpc eie djnh li, eic tinh chat v l nguyin him v i tieh phin, GV dua ra cle kiln thdc v l phUong phip tinh.
Thdng qua mdt sd vf dy cy the, GV eho HS tu khim phi cac die trUng khic nhau eOa ddi tupng minh mudn t l chUc day hpe. HS dupe khuyin khieh khii quit tif vidy ey t h i de dtf dodn mdt sd dmh ti, tfnh chit (vile chdng minh cac dinh li, tfnh chat da du doin ehung tdl khdng trinh biy trong b i i viet niy).
Vfdu:Tim
TrUdc h i t sU dung Maple d l tinh nguyen him:
> f:=sqrt(x)/2+2/sqrt(x);
> int(f,x):
Vay|f:^ + - ^ | f c - i , , C + WJ + C(l) Tiip tue stf dung Maple de tinh nguyin hdm:
> int(sqrt(x)/2^);
1 >..
-~x ' 3
V S y j : ^ & = i , " + C, (2) Sit dung Maple de tlnh nguyen hdm:
SZ.niMHtciiUoiivt
. NGHieNcmiC]
> int(2/sqrt(x),x);
4V^
Viy [-^dx = Ayf^ + C, (3)
niy, HS hinh thinh dU doan cdng thde tlnh dien tfch hinh trdn l i S = KR^.
Bai t o l n 2: Tinh dien tfch ciia hinh phing gidi han bdi elip: /
^ + ^ = Ha>b>0).
a 0 HS so sinh k i t q u i (1), (2) v i (3), nhln thay, d c him
•Jx 2
sd fix) = — v i gix)=—i= lifin tue tren c i c miln xic 2 \lx dinh ciia ehung thi:
v i f : ^ = i f V I ^ ; [ 2 ^ = 2 [ ^ .
J 2 2J 'JV^ '4^Khi dd, HS t y khim p h i duoc: "Nguyin hdm cua ting bdng tdng cdc nguyin hdm, nguyen hdm cua tfch mot so vdi hdm so bdng tfeh eda so vdi nguyen hdm cda hdmsodd".
Ttf dd, hinh thinh du d o l n v l tlnh chit co b i n cua nguyin him: Neu / , g l i hai him sd lien tyc tren X thi:
a) | [ f (x) -H g(x)]dx = | f (x)dx + |g(x)dx ; b)Vdi mpi sdthuc it * 0 tacd \}tf(x)dx = k\f{x)dx.
4,2, Hinh thdnh cdng thtfc todn
Phat hien, de xuat nhUng gil t h u y l t dU doln cic tinh chat die ^ e m cda eie ddi tUpng qua mdi quan he giii^ eic yiu td, HS bilt cich sing tao nhCfng kit q u i mdi tU cac k i t q u i d l ed. SCf dung phln mem Maple tinh tieh phln d l giii bii toln, tif kit q u i cCia mdt sd bii toan HS khim p h i hinh thinh edng thUetoln. Qua quan s i t diing mdt sd thao t i e tuduy nhutuong t y hda, khai quit hda,...
vdi sy trp giup eCia phln m l m l^aple, HSkhim pha hinh thanh dtf dodn mdt sd cdng thUe t o i n tif ehudi d e bai toan cd cOng deh gili (d dly chdng tdi ciing khdng trinh biy vile ehUng minh d c cdng thUc d l dU doan).
Vl du 1: Xlt chudi elc bii t o i n sau:
Biitoinl:Tinhdilnt[eheuahinhtr6n x^ + y^ =R^.
Tuang t u cich giii t r l n : Bien doi
b-= 103; = x" ia>b>0) b} I Do dd, diin tfch hinh elip j =4—\\Ja^ -x^dx
ai
Tinh dien tfch cda hinh phang trln phln m l m Maple:
> f:=(b/a)*sqrt(a/^2-x'\2);
. _b\la^-x'
> 4»abs(int(f,x=0..a));
n\ba\
Tif ket q u i eiia bii toin niy, HS hinh thlnh dUdoln edng thUc tinh diln tich hinh elip la 5 = luib.
Tuang ty, eic bii t o l n phang trln dly, ta cd mot sd bai t o i n trong khdng gian:
Bii t o i n 3: Tfnh the tich h i n h d u b i n kinh R.
Trong mat phIng Oxy.
x l t hinh phIng (H) gidi han bdi nOfa dudng trdn t l m O b i n kinh R cd phuong trinh y = ^JR^ -x^, true hoinh Ox. Quay hinh phang (H) quanh trye hoinh ta thu dupc hinh d u bin kfnh R.
Tfnh t h i tfeh hinh d u tren phan m l m Maple:
>V:=Pi*lnt(R'^2-xA2,x=-f^..R);V:=value(V);
V:=JA{R'
•x^)dx Bien doi x^ • = ± v « •Do dd, diin tleh hinh trdn S = 4J ^R^-x'dx Tfnh tieh phln t r l n phln
m l m Maple:
>f:=sqrt(RA2-x^2);
/•^A^R^-x"
>4"abs(int(f,x=0..R));
Ttf k i t q u i cCia bii t o i n
^
Khi do, cdng thdc tinh t h i tich hinh d u duac dy doln I I :
4 ,
Bli t o l n 4: Tinh t h i tfch hinh ehdm d u b i n kfnh R v i chilu cao A.
Trong mat phing Oxy, xet hinh phIng (H) gidi (Xem tiip trang 57) Slflig-THilNe8/2015*23
