Unit 7 Symbolic Processing

中華技術學院電子系 副教授 蔡樸生 副教授 林盈灝

Algebraic and Math. Operator

 syms : Create Symbolic Variables  expand : expands the expression by carrying out power  simplify : simplifies the expression E  factor : factors the expression E  >> syms x y  >> expand ((x+y)^3)  >> expand (sin(x+y))  >> factor(x^2-1)

Algebraic and Math. Operator

 >> E1=x^2+5;  >> E2=y^3-2;  >> S1=E1+E2 : S1=x^2+3+y^3  >> S2=E1*E2 : S2=(x^2+5)*(y^3-2)  >> expand(S2)  >> E3=x^3+2*x^2+5*x+10  >> S3=E3/E1  >> simplify(S3)

Evaluating Expressions

   subs(E,old,new): To replace old with a numeric value to new in the expression E ezplot(E,[xmin xmax]) poly2sym([a,b,c…….],’v’)   >> syms x >> E=x^2+6*x+7   >> G=subs(E,x,2) >> ezplot(E,[-2 6])  >> poly2sym([2,5,-3],’x’)

Test Your Understanding (I)

  Given the expressions:

E

1 

x

3  15

x

2  75

x

 125

E

2  (

x

 5) 2  20

x

Find the product E1*E2 and express it in its simplest form  Find the quotient E1/E2 and express it in its simplest form  Evaluate the sum E1+E2 at x=7.1

Differentiation

 syms n x y  diff(f(x,y),y,n) : 對於f(x,y)中的 y 作偏微 n 次   2 

y

2

xy

)]  [ sin(

xy

)] 

y

 [ln( )] 

x

Integration

 (

x n

) 

x

int(f(x,y),y,a,b) : 對於f(x,y)由 a 到 b 作定積分  0 5 2

xy dy t



e t

sin

xdx



n x dn



a b

5

x dx

Test Your Understanding (II)

    Given that , use MATLAB to find at x=0.2.

dx

Given that , use MATLAB to find

dz dy

Given that ,use MATLAB to 

ydx

Use MATLAB to evaluate  5  2

x

find