1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
|
/*
* rtest_ilt.mac -- test cases for Inverse Laplace Transform.
*/
(assume(a>0), 0);
0;
/* 0 */
ilt(0, s, t);
0;
/* constants */
ilt(a, s, t);
a*delta(t);
ilt(1/s, s, t);
1;
ilt(7/s, s, t);
7;
/* powers */
ilt(1/s^2, s, t);
t;
ilt(1/s^4, s, t);
t^3/6;
/* exp */
ilt(1/(1 + s), s, t);
exp(-t);
ilt(1/(7 + s), s, t);
exp(-7*t);
ilt(1/(a + s), s, t);
exp(-a*t);
ilt(exp(-b)/(a + s), s, t);
exp(-a*t-b);
ilt(1/s/(s+a), s, t);
1/a-exp(-a*t)/a;
ilt(s/(s+a)^2, s, t);
exp(-a*t)-a*t*exp(-a*t);
/* sin */
ilt(1/(1 + s^2), s, t);
sin(t);
ilt(a/(a^2 + s^2), s, t);
sin(a*t);
ilt(1/((s+b)^2+a^2), s, t);
exp(-b*t)*sin(a*t)/a;
/* cos */
ilt(s/(1 + s^2), s, t);
cos(t);
ilt(s/(49 + s^2), s, t);
cos(7*t);
ilt(s/(a^2 + s^2), s, t);
cos(a*t);
ilt(s/((s+b)^2+a^2), s, t);
%e^-(b*t)*(cos(a*t)-(b*sin(a*t))/a);
/* sinh */
ilt(1/(s^2 - 1), s, t);
exp(t)/2-exp(-t)/2;
ilt(a/(s^2 - a^2), s, t);
exp(a*t)/2-exp(-a*t)/2;
/* cosh */
ilt(s/(s^2 - 1), s, t);
exp(t)/2+exp(-t)/2;
ilt(s/(s^2 - 49), s, t);
exp(7*t)/2+exp(-7*t)/2;
ilt(s/(s^2-a^2), s, t);
exp(a*t)/2+exp(-a*t)/2;
/* delta */
ilt(1, s, t);
delta(t);
ilt(1/7, s, t);
delta(t)/7;
ilt(1/a, s, t);
delta(t)/a;
/* Miscellaneous rational functions */
ilt(1/(s^3+a^3), s, t);
%e^((a*t)/2)*(sin((sqrt(3)*a*t)/2)/(sqrt(3)*a^2)-cos((sqrt(3)*a*t)/2)/(3*a^2))
+%e^-(a*t)/(3*a^2)$
ilt(s/(s^2+a^2)^4, s, t);
(-(t^3*sin(a*t))/(48*a^3))+(t*sin(a*t))/(16*a^5)-(t^2*cos(a*t))/(16*a^4);
forget(a > 0);
[a > 0];
|
