PHN I: CC LNH THNG DNG TRONG GII TCH

CU LNH M T LOI HM

GII HN-O HM-TCH PHN

limit( )f 0

lim ( )x

f x

symbolic

lim( , )f a hoc lim( , , )f x a lim ( )x a

f x

symbolic

lim( , , , ' ')f x a left

lim ( )x a

f x

symbolic

lim( , , , ' ')f x a right

lim ( )x a

f x+

symbolic

diff ( ),diff ( , )f f x

( )df f xdx

= (bin mc nh l x)

symbolic , f= f(x) (srting)

diff ( , , )f x n , diff ( , )f n ( ) ( )n

n

n

d f f xdx

= symbolic ,string

( )int f ( )int ,f x ( )f x dx symbolic, string ( )int , ,f a b , ( )int , , ,f x a b ( )b

af x dx symbolic, string

quad(f,a,b) ( )ba

f x dx

inline, handle

rsums(f,a,b), rsums(f,[a,b]) Tng Riemman ca f trn [a, b], xut dng bar( th)

inline, handle,(2010 c thm symbolic)

taylor(f,n) ( ) ( )1

0

0!

knk

k

fx

k

=

symbolic

taylor(f,n,x0) ( ) ( ) ( )1 0 0

0 !

knk

k

f xx x

k

=

Symbolic

factorial(N) Tnh giai tha: N!

compose(f,g) f(g(x)) f=sym(f(x)),g=sym(g(x))

compose(f,g,u,v) f(g(v) f=sym(f(u)),g=sym(g(v))

finverse(f) Tm hm ngc ca f Symbolic

TNH TON TRN BIU THC

subs(f,x,a), subs(f,x,a) ( ) ( )f x f a Dng 1: symbolic, string Dng 2: mi hm

feval(f,a), feval(f,[a,b]) ( ) ( )f x f a inline, handle (1) polyval(p,a) Tnh gi tr ca a thc p ti a

eval(biu thc s) Tr v gi tr ca biu thc dng thp phn.

simplify Rt gn biu thc

simple Vit biu thc dng ngn nht.

pretty(f) Biu din f theo dng vit tay Symbolic

solve(f(x)) Gii pt f(x) = 0 C th thay: F=f(x)

solve(F,G) Gii h pt f(x,y)=0,g(x,y)=0 F=f(x,y),G=g(x,y)

fsolve(f,x0) Gii pt f(x) = 0 trong khu vc gn x0 handle

fzero(

sym2poly(f) Tr v vector h s ca a thc theo th t bc cao n thp

a thc

poly2sym(a) Tr v a thc c cc h s tng ng vi cc phn t ca vector a

Vector hng

[x,m]=fminbnd(f,a,b), Tm gi tr nh nht trn [a,b] handle

dsolve(pt1,pt2,k1,k2,bin) Gii phng trnh vi phn , h pt vi phn vi bin c ch ra.

C th thay : F=pt1,G=pt2

input(Thng bo) Nhp d liu s t bn phm vi thng bo nm trong .

input(Thng bo,s) Nhp chui t bn phm.

disp(string),disp(x) Xut chui hoc gi tr ra mn hnh.

fprinf Ghi d liu vo file text hoc xut d liu ra mn hnh

Xem Help

strfind(S,s) Tm chui con s trong chui ln S, kt qu l th t ca phn t u tin trong chui con.

S,s l cc chui k t.

strcmp(S1,S2) So snh hai chui (ging hay khc nhau)

char(x) Chuyn bin x sang dng chui (string) x l mt symbolic (!)

num2str(a) Chuyn s a sang dng chui(string) a l mt gi tr bng s

V TH

ezplot(x(t),y(t),[t1,t2]) V ng cong tham s vi t chy trn [t1,t2] Symbolic,string,inline,handle

ezplot(f,[a,b]) V th hm f vi bin chy trn [a, b]. Symbolic,string,inline,handle

ezplot3(x(t),y(t),z(t),[t1,t2]) V c tham s 3D

fplot(f,[a,b] V th hm f vi bin chy trn [a, b]. m-file, handle, inline, string

plot(x,f,tnh cht) V th ca f theo x, x l min c ch ra theo(2) Tnh cht (3)

V im, tp hp im

plot3(x(t),y(y),z(t),tnh cht) V c 3D dng im

polar(phi,r) V ng cong trong ta cc R l hm theo phi, phi l min c ch ra trong(2)

fill(X, Y, C) T mu min ng kn vi honh , tung bin nm trong X, Y bangwg mu C

surf(x,y,z) V mt cong

surfc(x,y,z) V mt cong vi ng mc

mesh(x,y,z) V mt li

meshgrid(x,y) To ma trn li t cc vector x,y

set(gca,xtick,[x1,x2]) nh cc gi tr t trn Ox

set(gca,ytick,[y1,y2]) nh cc gi tr t trn Oy xlabe(str), ylabel(str), zlabel(str)

Gn tn cho cc trc Ox, Oy,Oz Str l chui k t

title(string) Gn tn cho hnh

legend Gn tn cho tng th trn hnh.

(1) Khai bo cho hm inline: inline(f(x),x), v d: f = inline(sin(x),x); Khai bao cho hm handle: handle = @(danh sch i s, bin) biu thc nh ngha. V d : f = @ (x) sin(x)+x*cos(x) g=@ (x,y) sin(x+y)-x*y

(2) Khai bo min chy ca x trong trng hp ny c 2 cch

a. x = linspace(a,b) hay x=linspace(a,b,n) (n im chia trn [a, b]). V d: x=linspace(-2,3) (trn [-2,3] c 100 im chia). x= linspace(-2,3,70)( trn [-2,3] c 70 im chia)

b. x= a:d/n:b : trn don [a, b], s im chia c tnh t quy c : on c di d c chia thnh n dim V d: x = 0: 20/100:1 c ngha x thuc [0,1], on c di 20 c chia thnh 100 im. Vy mi on con di 1/5 v [0,1] c 5 on chia tng ng vi cc im: 0, 1/5, 2/5, 3/5, 4/5, 1.

(3) Tnh cht bao gm (tra cu bng LineSpec) a. Line Style b. LineWidth c. Color d. Marker (Marker s th hin cc im chia)

i. MarkerType ii. MarkerSize

iii. MarkerFaceColor & MarkerEdgeColor

C php:

1. plot(x,y, kiu ng v, LineWidth, gi tr, MarkerFaceColor, gi tr , MarkerEdgeColor, gi tr , MarkerSize, gi tr )

2. Kiu ng v th hin theo th t LineStyleColorMarkerType. v d: - -mo; :rx; -bs. Nu ch chn Marker v khng chn Line Style th ch c marker xut hin trn th.

Line Style Specifiers

Specifier Line Style

- Solid line (default)

- - Dashed line

: Dotted line

-. Dash-dot line

Marker Specifiers

Specifier Marker Type + Plus sign

o Circle

* Asterisk

. Point (see note below)

x Cross

'square' or s Square

'diamond' or d Diamond

^ Upward-pointing triangle

v Downward-pointing triangle

> Right-pointing triangle

< Left-pointing triangle

'pentagram' or p Five-pointed star (pentagram)

'hexagram' or h Six-pointed star (hexagram)

Note The point (.) marker type does not change size when the specified value is less than 5.

Color Specifiers

Specifier Color r Red

g Green

b Blue

Specifier Color c Cyan

m Magenta

y Yellow

Specifier Color k Black

w White

PHN 2: LP TRNH TRONG MATLAB (tm tt nhng vn cn thit nht) A. CC HM TON HC

sin(x), cos(x), tan(x), asin(x), acos(x), atan(x), sinh(x), cosh(x) abs(x): tr tuyt i hoc modun ca x. sqrt(x): cn bc 2 ca x. exp(x): ex log(x): ln(x) log10(x): log10 (x) a^x: ax

B. CU TRC IU KIN 1. Cu trc if

a. if iu kin Nhm lnh end

b. if iu kin Nhm lnh 1 else Nhm lnh 2 end

c. if iu kin 1 Nhm lnh 1 elseif iu kin 2 Nhm lnh 2 else Nhm lnh 3 end

2. Cu trc switch case (p dng khi c nhiu iu kin tng ng vi nhiu nhm ln khc nhau) TRNG HP = dy k t hoc dy s (TRNG HP=[TH1 TH2 TH3]) switch TRNG HP case TH1 nhm lnh 1 case TH2 nhm lnh 2 case TH3

nhm lnh 3 .

otherwise nhm lnh n end

V D

Gii phng trnh bc 2: 2 0ax bx c+ + = dng cu trc if

a=input(nhap a:);

b=input(nhap b:);

c=input(nhap c:);

delta =b^2-4*a*c;

if delta >0

disp(Phuong trinh co 2 nghiem thuc phan biet:);

x1=(-b+sqrt(delta))/(2*a) x2=(-b-sqrt(delta))/(2*a)

elseif delta==0

disp(Phuong trinh co nghiem kep:);

x= -b/(2*a)

else % truong hop nay la delta < 0

disp(Phuong trinh co nghiem phuc:);

x1=(-b+i*sqrt(-delta))/(2*a)

x2=(-b-i*sqrt(-delta))/(2*a)

end

Gii phng trnh bc 2: 2 0ax bx c+ + = dng cu trc switch case

a=input(nhap a:);

b=input(nhap b:);

c=input(nhap c:);

delta =b^2-4*a*c;

if delta >0 choice =1

elseif delta==0 choice=2

else choice=3

end

switch choice

case 1

disp(Phuong trinh co 2 nghiem thuc phan biet:);

x1=(-b+sqrt(delta))/(2*a) x2=(-b-sqrt(delta))/(2*a)

case 2

disp(Phuong trinh co nghiem kep:);

x= -b/(2*a)

case 3

disp(Phuong trinh co nghiem phuc:);

x1=(-b+i*sqrt(-delta))/(2*a) x2=(-b-i*sqrt(-delta))/(2*a)

end

C. CU TRC VNG LP (s dung khi nhm lnh c lp li nhiu ln) 1. Vng lp for (s dng khi bit s ln lp ti a)

for i=m:k:n Nhm lnh end i l bin m, bt u i t m n n, k l bc nhy ca i. Nu khng c k, bc nhy mc nh l 1.

Nu k < 0, i li t m v n (trng hp ny m

Script M-file Function M-file

Khng s dng tham s u vo hoc u ra

C th chp nhn tham s u vo v tr tham s u ra.

Hot ng trn d liu ca workspace

Cc bin trong thn hm mc nh l cc b.

Thng dng t ng thc hin mt chui thao tc cn thit thc thi nhiu ln.

c tc dng m rng ngn ng MATLAB cho ng dng ca bn.

VD: gii pt bc 2 dng Funtion

function X=ptbac2(a,b,c) %ptbac2(a,b,c) giai phuong trinh bac hai ax^2+bx+c=0. if nargin0 X(1)=(-b+sym(sqrt(delta)))/(2*a); X(2)=(-b-sym(sqrt(delta)))/(2*a); elseif delta==0 X=-b/(2*a); else X(1)=(-b+i*sym(sqrt(-delta)))/(2*a); X(2)=(-b-i*sym(sqrt(-delta)))/(2*a); end end end