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01 展开：展开因式：expand(f)
--- 幂函数：则根据次数从高到低
--- 三角函数：展开角部分
--- 指数：展开指数部分
>> z=(x+y+3)*(2*x-4*y+7)+sin(x+y)+exp(x+y)+log(x*y)
z =
exp(x + y) + log(x*y) + sin(x + y) + (2*x - 4*y + 7)*(x + y + 3)
>> expand(z)
ans =
13*x - 5*y + log(x*y) + exp(x)*exp(y) + cos(x)*sin(y) + cos(y)*sin(x) - 2*x*y + 2*x^2 - 4*y^2 + 21
>>
>> z=(x+y+3)*(2*x-4*y+7)
z =
(2*x - 4*y + 7)*(x + y + 3)
>> expand(z)
ans =
2*x^2 - 2*x*y + 13*x - 4*y^2 - 5*y + 21
>>
02 合并：因式分解：factor(f)
>> z1=3*x^3+2*x^2+x+2
z1 =
3*x^3 + 2*x^2 + x + 2
>> factor(z1)
ans =
[ x + 1, 3*x^2 - x + 2]
>>
>> z1=x^2+2*x*y+y^2
z1 =
x^2 + 2*x*y + y^2
>> factor(z1)
ans =
[ x + y, x + y]
>>
03 合并同类项：collect(f)
>> z2=x^2+x*y*7-x^2+y+x-8
z2 =
x + y + 7*x*y - 8
>> collect(z2)
ans =
(7*y + 1)*x + y - 8
>> collect(z2,y)
ans =
(7*x + 1)*y + x - 8
>> collect(z2,x)
ans =
(7*y + 1)*x + y - 8
>>
04 化简：simplify(f)
>> z3=x^2+y^2-2*x*y+sin(x)^2+cos(x)^2
z3 =
cos(x)^2 + sin(x)^2 - 2*x*y + x^2 + y^2
>> simplify(z3)
ans =
x^2 - 2*x*y + y^2 + 1
>>
05 解方程：solve(f,x)
>> z=x^3+x-6
z =
x^3 + x - 6
>> solve(z,x)
ans =
root(z^3 + z - 6, z, 1)
root(z^3 + z - 6, z, 2)
root(z^3 + z - 6, z, 3)
>> z=x^2+x-2
z =
x^2 + x - 2
>> solve(z,x)
ans =
-2
1
>>
06 级数求和：symsum(f,n,a,b)
--- 级数求和：symsum(f,n,a,b)：f为一个级数的通项，是一个符号表达式，求自变量n为从a到b的通项和；
其中inf可表示无穷大
>> f=n
f =
n
>> symsum(f,n,1,n)
ans =
(n*(n + 1))/2
>> symsum(f,n,1,10)
ans =
55
>> f=1/n^2
f =
1/n^2
>> symsum(f,n,1,inf)
ans =
pi^2/6
>>
07 求极限：limit(f,x,a)
--- 某点极限： limit(f,x,a)
--- 某点左极限：limit(f,x,a,'left')
--- 某点右极限：limit(f,x,a,'right')
--- 无穷极限： limit(f,x,inf)
--- 正无穷极限：limit(f,x,inf,'right')
--- 负无穷极限：limit(f,x,inf,'left')
>> f=sin(x)/x
f =
sin(x)/x
>> limit(f,x,0)
ans =
1
>> limit(f,x,0,'right')
ans =
1
>> limit(f,x,0,'left')
ans =
1
>> limit(f,x,inf)
ans =
0
>> limit(f,x,inf,'right')
ans =
0
>> limit(f,x,inf,'left')
ans =
0
>>
>> help limit
--- sym/limit 的帮助 ---
limit Limit of an expression.
limit(F,x,a) takes the limit of the symbolic expression F as x -> a.
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
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]
08：求导数：diff(f,x,n)
--- diff(f,x,n) 表示函数f对自变量x求n阶导数
>> f=x^2+exp(x)+log(x)+sin(x)+cos(x)
f =
cos(x) + exp(x) + log(x) + sin(x) + x^2
>> diff(f,x,2)
ans =
exp(x) - cos(x) - sin(x) - 1/x^2 + 2
>>
09 泰勒展开：taylor(f,x,a,'Order',n)
--- taylor(f,x,a,'Order',n) 表示函数f在自变量x=a处的泰勒展开式，n为展开的阶数
>> f=exp(x)
f =
exp(x)
>> taylor(f,x,0,'Order',3)
ans =
x^2/2 + x + 1
>> taylor(f,x,1,'Order',3)
ans =
exp(1) + exp(1)*(x - 1) + (exp(1)*(x - 1)^2)/2
>>
10 求积分：int(f,x,a,b)
--- int(f,x) 表示函数f对自变量x的不定积分
--- int(f,x,a,b) 表示函数f对自变量x从a到b的定积分,a和b可以为正负inf
>> f=sin(x)
f =
sin(x)
>> int(f,x,0,pi)
ans =
2
>> int(f,x)
ans =
-cos(x)
>>
美化符号表达式：pretty(f)
>> f=sin(pi/3)
f =
0.8660
>> pretty(f)
未定义与 'double' 类型的输入参数相对应的函数 'pretty'。
>> f=sin(sym(pi/3))
f =
3^(1/2)/2
>> pretty(f)
sqrt(3)
-------
2
>>
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