Matlab基础之符号表达式
前言：
为了计算更方面
一、表达式化简
1化简：
syms x y;%定义符号变量
f=x^2*y+x*y-x^2-2*x;
f(x)=collect(f) %合并同类项
g=-1/4*x*exp(-2*x)+3/16*exp(-2*x);
g(x)=collect(g,exp(-2*x))
h(x)=expand(f(x)*g(x))%相乘展开升幂排列
q(x)=factor(x^2-y^2)%
p(x)=simplify(x^2-y^2)%系统尽可能的去化简
>>Untitled
f(x) =
(y - 1)*x^2 + (y - 2)*x
g(x) =
(3/16 - x/4)*exp(-2*x)
h(x) =
(5*x^2*exp(-2*x))/16 - (3*x*exp(-2*x))/8 + (x^3*exp(-2*x))/4 + (3*x*y*exp(-2*x))/16
- (x^2*y*exp(-2*x))/16 - (x^3*y*exp(-2*x))/4
q(x) =[ x - y, x + y]
p(x) = x^2 - y^2
limit Limit of an expression.
limit(F,x,a) takes the limit of the symbolic expression F as x -> a. %指定变量求极限
limit(F,a) uses symvar(F) as the independent variable.
limit(F) uses a = 0 as the limit point.
limit(F,x,a,'right') or limit(F,x,a,'left') specify the direction %分段函数左右极限
of a one-sided limit.
Examples:
syms x a t h;
limit(sin(x)/x) returns 1
limit((x-2)/(x^2-4),2) returns 1/4
limit((1+2*t/x)^(3*x),x,inf) returns exp(6*t)
limit(1/x,x,0,'right') returns inf
limit(1/x,x,0,'left') returns -inf
limit((sin(x+h)-sin(x))/h,h,0) returns cos(x)
v = [(1 + a/x)^x, exp(-x)];
limit(v,x,inf,'left') returns [exp(a), 0] diff(S) differentiates a symbolic expression S with respect to its
free variable as determined by SYMVAR.
diff(S,'v') or diff(S,sym('v')) differentiates S with respect to v.
diff(S,n), for a positive integer n, differentiates S n times. %求n次微分
diff(S,'v',n) and diff(S,n,'v') are also acceptable. %对指定变量求n次微分
Examples;
syms x t
diff(sin(x^2)) is 2*x*cos(x^2)
%%%%%%%%%%%%
syms x y;
f=sin(x^2+y-1);
f1=diff(f)
f2=diff(f,x)
f3=diff(f,y)
f4=diff(f,x,2)
>> Untitled
f1 =2*x*cos(x^2 + y - 1)
f2 =2*x*cos(x^2 + y - 1)
f3 =cos(x^2 + y - 1)
f4 =2*cos(x^2 + y - 1) - 4*x^2*sin(x^2 + y - 1)
4.符号积分
nt Integrate
int(S) is the indefinite integral of S with respect to its symbolic variable as defined by SYMVAR. S is a SYM (matrix or scalar).
If S is a constant, the integral is with respect to 'x'. %默认求积分
int(S,v) is the indefinite integral of S with respect to v. v is a scalar SYM. %对符号V求积分
int(S,a,b) is the definite integral of S with respect to its
symbolic variable from a to b. a and b are each double or
symbolic scalars. The integration interval can also be specified
using a row or a column vector with two elements, i.e., valid
calls are also int(S,[a,b]) or int(S,[a b]) and int(S,[a;b]).
int(S,v,a,b) is the definite integral of S with respect to v from a to b. The integration interval can also be specified
using a row or a column vector with two elements, i.e., valid calls are also int(S,v,[a,b]) or int(S,v,[a b]) and
int(S,v,[a;b]).
syms x y;
f=x+2*y+1;
f1=int(f,x)%对x积分,把y当成常数
f2=int(f,x,2,4)%对x做2到4的定积分,把y当成常数
%%%%%%%%%%%%%
>> Untitled
f1 =x^2/2 + (2*y + 1)*x
f2 =4*y + 8
二、方程组求解
对方程和求解。
syms x y z ;
[x y z]=solve('x+y+z=10','3*x+2*y+z=14','2*x+3*y-z=1')
%g=solve('x+y+z=10','3*x+2*y+z=14','2*x+3*y-z=1', x,y,z);
%X=g.x
%Y=g.y
%Z=g.z;syms x y sina a b;
[x y]=solve('x*cos(sina)-y*sin(sina)=a','x*sin(sina)+y*cos(sina)=b',x,y)
>> Untitled
x = (a*cos(sina) + b*sin(sina))/(cos(sina)^2 + sin(sina)^2)
y = (b*cos(sina) - a*sin(sina))/(cos(sina)^2 + sin(sina)^2三、符号积分变换
傅里叶正（反）Fourier(iFourier)变换、拉普拉斯）、拉氏变换l正（反) aplace(ilaplace)变换等。（待更）