Taking derivative of a time based function?

58 次查看（过去 30 天）
Len
Len 2013-12-6
编辑： Wayne King 2013-12-6
I'm new to MatLab and want to plot out some time based functions.
As an example, I have a function y = ((t/T).^n).*exp(-t/T). I want to plot the function vs time (t), along with the derivative of the function vs t.
I'm trying to use the diff function, but it's not working right. Any suggestions? Below is my actual code:
T = 8;
n = 1;
t = 0:0.1:100;
y = ((t/T).^n).*exp(-t/T);
x = diff(y,t);
plot(t,y,t,x)

请先登录，再回答此问题。

回答（3 个）

Azzi Abdelmalek
Azzi Abdelmalek 2013-12-6
编辑：Azzi Abdelmalek 2013-12-6
T = 8;
n = 1;
t = 0:0.1:100;
y = ((t/T).^n).*exp(-t/T);
x = diff(y)./diff(t);
plot(t,y,t(1:end-1),x)
% or use gradient
T = 8;
n = 1;
t = 0:0.1:100;
y = ((t/T).^n).*exp(-t/T);
x=gradient(y,t)
plot(t,y,t,x)
Wayne King
Wayne King 2013-12-6
编辑：Wayne King 2013-12-6
Are you trying to differentiate symbolically or numerically?
T = 8;
n = 1;
t = 0:0.1:100;
y = ((t/T).^n).*exp(-t/T);
x = diff(y)./diff(t);
subplot(211)
plot(t,y); title('y(t)');
subplot(212)
plot(t(2:end),x); title('dy/dt')
Symbolically
syms t; % requires symbolic toolbox
g(t) = t/8;
h(t) = exp(-t/8);
y = g(t)*h(t);
x = diff(y,t);
subplot(211)
ezplot(y,[0 100])
subplot(212)
ezplot(x,[0 100])
Roger Stafford
Roger Stafford 2013-12-6
The 'diff' function serves two purposes, one to take derivatives and the other to take finite differences. To make it take derivatives you have to declare the variables involved as type 'sym'. To use the numeric form as you have as an approximation you will need to divide the 'diff' output by the length of the 't' interval which in your case is 0.1 .

类别

在 Help Center 和 File Exchange 中查找有关 Calculus 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by