[:Matlab] Chap 1.

[:Matlab]

Chap 11: Symbolic Mathematics 1

Symbolic variable Factor() and simplify mathematical expressionSolve symbolic expression / System.Determine the symbolic derivative of an expressionIntegrate an expression symbolically

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2Matlab Maple 8 . Maple 8Matlab 7 Maple 5 .

Symbolic Manipulation . .MATLAB for Engineers3Manipulate symbolic expressions to SimplifySolve symbolicallyEvaluate numerically( )Take derivativesIntegrate Perform linear algebraic manipulations More advanced features include LaPlace transformsFourier transformsVariable precision arithmetic

11.1 , , , .MATLAB for Engineers4

,! .!MATLAB for Engineers5

Matlab .MATLAB for Engineers6

Matlab Symbolic Variables Two approachesUse the sym command to create Single variable( )Expression()Equation( )Use the syms command to create Single variables( ) .

MATLAB for Engineers7 Define x as a symbolic variablex=sym('x') orsyms x Use x to create a more complicated expressiony = 2*(x+3)^2/(x^2+6*x+9)

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Syms : syms Q R T D0

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D=D0*exp(-Q/(R*T))

MATLAB for Engineers10Notice : (.*, ./ and .^) (*,/,^) .Sym : E=sym('m*c^2')

E m c E m c . .MATLAB for Engineers11

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ideal_gas_law=sym('P*V=n*R*Temp')

MATLAB for Engineers12This is an algebraic equationThis is an assignment statement

: :

= .

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Working with Equation & Expression .

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Numden : (numerator) & (denomicator)MATLAB for Engineers17

.Expanding, factoring and collecting terms expandfactorcollectWhen used with equations, each side is treated separately

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w is an equation

w is an equationnum is an expressionMATLAB for Engineers20

The factor function , den The factor function w The collect function is similar, .SimplifyingExpand, factor, collect . . simplify .MATLAB for Engineers21MATLAB for Engineers22

simplify used on an expressionsimplify used on an equationSimple Simple simplify .!Simple .Poly2Sym Sym2poly MATLAB for Engineers23MATLAB for Engineers24

All of the possibilities evaluated are reported, however there is only one actual answerBoth simple and simplify work on expressions and equationsHintPoly2Sym : Sym2poly :

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11.2 Solve ( 0 ) . / .MATLAB for Engineers26

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Solve .

x .Solve .MATLAB for Engineers29

. a solve .Solve MATLAB for Engineers30

Solve MATLAB for Engineers31

Solve : .MATLAB for Engineers32

This result is a structure array. MATLAB for Engineers33There are several different approaches to find the actual values of x, y, and z

Specify the field name inside the structure array to retrieve the values for x, y, and zMATLAB for Engineers34

Assign individual variable names. Notice that x, y and z are symbolic variablesExample 11.1 D = D0*exp(-Q/RT)Solve for Q

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MATLAB Solution

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Substitution()MATLAB for Engineers37

E4 x 3 . Subs : , , .MATLAB for Engineers38

{ } .Example 7.2 .

5 . ? : ( ) : : , / : , /

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11.3 ezplot()

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, . .Explot(): , MATLAB for Engineers46

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Peaks() MATLAB for Engineers48

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Example 11.3 MATLAB for Engineers53

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11.4 MATLABs symbolic toolbox supportsSymbolical differentiationSymbolic integration This makes it possible to find analytical solutions for many problems, instead of numeric approximations.

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11.5 , ( ) . ) MATLAB for Engineers59

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, . .

() MATLAB for Engineers64

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Diff : () . diff() . .!MATLAB for Engineers66

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, MATLAB for Engineers68

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SummaryMatlab array! Data Type & Array type NumericdoublesingleintegersCharacterSymbolicLogical

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+ .Num2str() . .

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