부천대학 matlab project

8/8/2019 matlab project

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MATLAB ProjectMATLAB Project

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() .

, () , .

( ) , () .

(: ) ( , ) .

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(ordinarydifferentialequation:ODE) () , (partialdifferentialequation:PDE) () .

f (dependent variable), x t (independent

variable) . , .

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xtttxf !

xx ),(

txt

txf!

xx

x ),(2


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(order) ,

(degree) .

(2) (1) (4) (2)

1 1

(2 1 ODE) (4 1

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xfdxdf

dxfd sin

3

2

2

!

0

2

2

4

42 !

xx

xxx

y

u

x

u


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- f(f(x,y)) () 1 (lineardifferentialequation) .

(a) f(f(x,y)) () 1, f(f(x,y))

1.

(b) (x,t,) . sinf( sinf(x,t)),

( ) .

(nonlineardifferential

equation) .

g(x)=0 (homogeneous equation) , g(x)0 (nonhomogeneous equation) .

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dxdfe xfe xx


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I( (a,b)) u(x)=f(x)

,

f(x) I (solution).

. c .

.

n n

, (general solution) ,

(particular solution) .

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),,...,,,(

1' nnnuuuuxfu

!

!! cdxxgxuxgdtdu )()()(

? A !!! )()()( xgdxxgdxd

cdxxgdx

d

dx

du

)(xgdt

du! ! cdxxgxu )()(


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Symbolic Objects

Symbolic objects area special MATLAB datatypeintroducedbytheSymbolic Math Toolbox software.Theyallowyoutoperformmathematicaloperations inthe MATLABworkspaceanalytically,withoutcalculatingnumeric values. You canuse symbolic objects toperformawidevarietyofanalytical computations:

Differentiation, includingpartialdifferentiation Definiteandindefiniteintegration Takinglimits, includingone-sidedlimits Summation, including Taylor series

Matrix operations Solvingalgebraic anddifferentialequations Variable-precisionarithmetic Integraltransforms

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Symbolic Variables

Todeclare variables x andyas symbolic objects usethe syms command:

>>syms xy

You canmanipulatethe symbolic objects accordingtotheusualrules of

mathematics. Forexample:

>>x + x +y

ans =2*x +y

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Symbolic Numbers

Symbolic Math Toolbox softwarealsoenables youto convertnumbers to symbolic objects.

To createa symbolic number, usethe sym command:

>>a= sym('2')

Thefollowingexampleillustrates thedifferencebetween a standarddouble-precision

MATLAB dataandthe corresponding symbolic number. The MATLAB command

>>sqrt(2)

returns adouble-precisionfloating-pointnumber:

ans =1.4142

Ontheotherhand, ifyou calculatea squarerootofa symbolic number2:

>>a= sqrt(sym(2))

yougettheprecise symbolic result:

a=2^(1/2) 9

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Toevaluatea symbolic numbernumerically, usethedouble command:

>>double(a)

ans =1.4142

Youalso can createarationalfractioninvolving symbolic numbers:

>>sym(2)/sym(5)

ans =2/5

ormoreefficiently:

>>sym(2/5)

ans =2/5

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MATLAB performs arithmetic on symbolic fractions differently

thanitdoes on standardnumeric fractions.Bydefault, MATLAB

Stores allnumeric values as double-precisionfloating-point

data. Forexample:

>>2/5 + 1/3

ans =0.7333

Ifyouaddthe samefractions as symbolic objects, MATLAB finds their

commondenominatorand combines themintheusualprocedureforaddingrationalnumbers:

>>sym(2/5) + sym(1/3)

ans =11/15

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dsolve

Symbolic solutionofordinarydifferentialequations

ex)dsolve('eq1','eq2',...,'cond1','cond2',...,'v')

symbolicallysolves theordinarydifferentialequations eq1, eq2,...using v as theindependent variable

symbolic

xu+u=1 (u)

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dsolve help

ezplot help

subs help

double-precisionfloating-point

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dt

dvCi

c!


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dt

dvCi

c!


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부천대학 matlab project

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