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Example: Laplace transforms with Maxima

Maxima

takeover MaximaControl int(), diff(), sum() and lim() now use Maxima

2 t * a + exp t sin * t * t s laplace Maxima e a^2 s * 4 - (s 2^4 s * - 5 + (2^/ *

This example reveals some translation issues (diff(f,x,1) -> diff(f,x) and at() function):

t delta t 2 diff t s laplace Maxima t delta t 1 diff t 0 ≡ ?at - s 2^+ 0 delta s * -

12 / t gamma_incomplete t s laplace factor Maxima π sqrt s sqrt s 1 + (s / sqrt * 1 - (s 32 / (^s 1 + (s / sqrt * (/ *

1 - (n^t n π * - unit_step * t sin * (n 0 ∞ sum t s laplace Maxima e π s *^e π s *^1 - (s i - (* s i + (* /

Integral equation (example from Maxima handbook)

eq a x * sinh t x - f * x 0 t int b t f * + t 2^≡ (:

Laplace transform

L eq t s laplace Maxima :

L t f t s laplace a b s a - (* s a + (* + (* s a - (s a + (* / 2 s 3^/ ≡

Solve for Laplace transform of unknown function

L L t f t s laplace LinSolve :

L 1 el t f t s laplace 2 s a - (* s a + (* s 3^b s 2^* a 1 a b * - (* + (* / ≡

Inverse transformation of the solution

L 1 el rhs s t ilt Maxima 2 a b * a b * 1 - (* sqrt t b / * cosh a 3^b 2^* 2 a 2^* b * - a + (/ * - a t 2^a b * 1 - (/ * + 2 a 3^b 2^* 2 a 2^* b * - a + (/ +