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

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

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

Test Your Understanding (I) Given the expressions: Given the expressions: Find the product E1*E2 and express it in its simplest form Find the product E1*E2 and express it in its simplest form Find the quotient 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 Evaluate the sum E1+E2 at x=7.1

Differentiation syms n x y syms n x y diff(f(x,y),y,n) : 對於 f(x,y) 中的 y 作偏微 n 次 diff(f(x,y),y,n) : 對於 f(x,y) 中的 y 作偏微 n 次Integration int(f(x,y),y,a,b) : 對於 f(x,y) 由 a 到 b 作定積分 int(f(x,y),y,a,b) : 對於 f(x,y) 由 a 到 b 作定積分

Test Your Understanding (II) Given that, use MATLAB to find at x=0.2. Given that, use MATLAB to find at x=0.2. Given that, use MATLAB Given that, use MATLAB to find Given that,use MATLAB to find Given that,use MATLAB to find Use MATLAB to evaluate Use MATLAB to evaluate