```python
from sympy import symbols, laplace_transform, \
                  DiracDelta, Heaviside, exp, sin, cos

s, t, a, n, b = symbols('s t a n b')

laplace_transform(DiracDelta(t), t, s)
```




    (1 - Heaviside(0), -oo, True)




```python
laplace_transform(Heaviside(t), t, s, noconds=True)
```




$\displaystyle \frac{1}{s}$




```python
laplace_transform(1, t, s, noconds=True)
```




$\displaystyle \frac{1}{s}$




```python
laplace_transform(t, t, s, noconds=True)
```




$\displaystyle \frac{1}{s^{2}}$




```python
laplace_transform(t**n, t, s, noconds=True)
```




$\displaystyle \frac{s^{- n} \Gamma\left(n + 1\right)}{s}$




```python
laplace_transform(exp(-a*t), t, s, noconds=True)
```




$\displaystyle \frac{1}{a + s}$




```python
laplace_transform(sin(b*t), t, s, noconds=True)
```




$\displaystyle \frac{b}{b^{2} + s^{2}}$




```python
laplace_transform(cos(b*t), t, s, noconds=True)
```




$\displaystyle \frac{s}{b^{2} + s^{2}}$




```python
laplace_transform(exp(-a*t)*sin(b*t), t, s, noconds=True)
```




$\displaystyle \frac{b}{b^{2} + \left(a + s\right)^{2}}$




```python
laplace_transform(exp(-a*t)*cos(b*t), t, s, noconds=True)
```




$\displaystyle \frac{a + s}{b^{2} + \left(a + s\right)^{2}}$



21885c04c5fb74ae05ae0b7b38f0d40ea28871cd
ipynb
Jupyter Notebook
Laplace transform.ipynb
mfkiwl/GMPE340
3602b8ba859a2c7db2cab96862472597dc1ac793
MIT
2021-09-07T09:36:36.000Z
2021-09-07T09:36:36.000Z
Laplace transform.ipynb
mfkiwl/GMPE340
3602b8ba859a2c7db2cab96862472597dc1ac793
MIT
Laplace transform.ipynb
mfkiwl/GMPE340
3602b8ba859a2c7db2cab96862472597dc1ac793
MIT
2021-09-20T18:48:20.000Z
2021-09-20T18:48:20.000Z
Qwen/Qwen-72B
1. YES
2. YES