Sponsored links: Algebra eBooks
 

Help Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

The Maxima on-line user's manual

Algebra Calculator

Search:

Ilt Calculator

Ilt

Function: ilt (<expr>, <s>, <t>) Computes the inverse Laplace transform of <expr> with respect to <s> and parameter <t>. <expr> must be a ratio of polynomials whose denominator has only linear and quadratic factors. By using the functions laplace and ilt together with the solve or linsolve functions the user can solve a single differential or convolution integral equation or a set of them.

atvalue(y(x),x=0,4);
l:laplace(y(x),x,s);
eq:

          (%i1) integrate (sinh(a*x)*f(t-x), x, 0, t) + b*f(t) = t**2;
                        t
                       /
                       [                                    2
          (%o1)        I  f(t - x) sinh(a x) dx + b f(t) = t
                       ]
                       /
                        0
          (%i2) laplace (%, t, s);
                                         a laplace(f(t), t, s)   2
          (%o2)  b laplace(f(t), t, s) + --------------------- = --
                                                 2    2           3
                                                s  - a           s
          (%i3) linsolve ([%], [laplace(f(t), t, s)]);
                                                  2      2
                                               2 s  - 2 a
          (%o3)     [laplace(f(t), t, s) = --------------------]
                                              5         2     3
                                           b s  + (a - a  b) s
          (%i4) ilt (rhs (first (%)), s, t);
          Is  a b (a b - 1)  positive, negative, or zero?

pos; sqrt(a b (a b - 1)) t 2 cosh(---------------------) 2 b a t

          (%o4) - ----------------------------- + -------
                        3  2      2               a b - 1
                       a  b  - 2 a  b + a

2 + ------------------ 3 2 2 a b - 2 a b + a

There are also some inexact matches for ilt. Try ?? ilt to see them.

(%o1)                                true
(%i2) 

Ilt Example

Related Examples

ilt-invert-matrix

A:matrix([8+5*s,4],[4...

invA:invert(matrix([8...

E:matrix([24/s],[24/s]);

Calculate

ilt-plot2d
plot2d(f(t),[t,0,1]);

f(t):=ilt( (s*(0.0012...

f(t);

plot2d(f(t),[t,0,1]);

Calculate

ilt

f(p):=2/(p*(p -1) *(p...

ilt(f(p), p, t);

Calculate

ilt

ilt((Kp*s+Ki)/s, s, t);

Calculate

ilt

ilt(1/(k*s+1)/s,s,t);

Calculate

ilt

ilt(s^0.5,s,t);

Calculate

ilt

f=ilt(s/((s^2+1)*((s-...

g=ilt((s-2)/(s^2-2*s+...

Calculate

ilt

ilt(((s+2)^2)/s^3,s,t);

ilt((1)/(5*s-2),s,t);

ilt((2*s-6)/((s^2)+9)...

Calculate

ilt

F(s)=L[f(t)];

f:t;

F:Laplace*(f,t,s);

Calculate

ilt-plot2d
plot2d(f, [t, 0, 5]);

f: ilt((1)/s^2, s, t);

plot2d(f, [t, 0, 5]);

Calculate