第四章 MATLAB 的符号计算功能

第四章 MATLAB 的符号计算功能

4.1 符号变量与符号表达式

MATLAB 中用 sym 来定义一个符号或者符号表达式。

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代码

syms a b t x y 
f = sin(a*x) + cos(b*t)
g = diff(f)
gg = diff(f, t)

syms a b t x y 
f = sin(a*x)+cos(b*t);
f = sin(a*x*t)+cos(b*t*x^2)-2*x*t^3;
diff(f,2)
diff(f,t,2)

syms a x 
a = [sin(a*x), cos(a*x); -cos(a*x), -sin(a*x)]
dy = diff(a)

syms a x
f = sin(a*x)
g = int(f)
gg = int(f, a)

syms x t a 
f = sin(x)/x
g = limit(f)
limit((cos(x+a)-cos(x))/a,a,0)
limit((1+x/t)^t, t, inf)

syms x k
symsum(1/x, 1, 3) %级数和

taylor(sin(x)) %泰勒多项式

syms a b x c
f = a*x^2+b*x+c
s = solve(f) %解代数方程
ss = solve(f, b)

dsolve('Dy=1+y^2') %解微分方程

A = [a b c; b c a; c a b]
B = [1 1 1]'
x = A\B
A1 = triu(A) %提取上三角矩阵
L = eig(A) %计算A的全部不特征值，构成向量

syms x t y
collect(x^3+2*x^2-5*x^2+4*x-3*x+12-3) %合并同类项
expand((x-1)*(x-2)*(x-3)) %将乘积展开为和式
horner(x^3-6*x^2+11*x-6) %把多项式转换为嵌套形式
simplify((1-x^2)/(1-x))  %利用各种恒等式化简代数式
factor(x^3-6*x^2+11*x-6) %因式分解
simple(1/x^3+6/x^2+12/x+8)

subs(x+y, x, 4) %x换为4

ezplot(sin(2*x))
ezplot(sin(2*x), -pi/2, pi/2)