```python
%pylab inline
import sympy
sympy.init_printing()
```

    Populating the interactive namespace from numpy and matplotlib



```python
t, sigma, omega = sympy.symbols('t, sigma, omega')
s = sympy.symbols('s', complex=True)
```


```python
def my_laplace_transform(f):
    return sympy.Integral(f*sympy.exp(-s*t), (t, 0, sympy.oo))

my_laplace_transform(t)
```


```python
def my_laplace_transform_double_sided(f):
    return sympy.Integral(f*sympy.exp(-s*t), (t, -sympy.oo, sympy.oo))

my_laplace_transform_double_sided(1).doit()
```


```python
sympy.integrate(sympy.exp(-s*t), t)
```


```python
my_laplace_transform(sympy.sin(2*t)).doit().simplify()
```


```python
my_laplace_transform(t).doit()
```


```python
sympy.laplace_transform(sympy.sin(t), t, s)
```


```python
omega = sympy.symbols('omega')
my_laplace_transform(sympy.sin(omega*t)).doit().simplify()
```

# Unit Step


```python
sympy.laplace_transform(1, t, s)
```


```python
y = sympy.exp(-2*t)
sympy.laplace_transform(y, s, t)
```


```python
sympy.plot(y, (t, 0, 5))
```


```python
Y = sympy.laplace_transform(y, t, s)[0]
Y
```

8223ff510a647fadbdccdd45a9fa51c3e276494a
ipynb
Jupyter Notebook
02.Laplace.ipynb
jgoppert/aae364_notebook
bc77866860e6bdb7d59467ce9817a604c7f26e20
BSD-3-Clause
2020-01-18T03:46:08.000Z
2020-01-18T03:46:08.000Z
02.Laplace.ipynb
jgoppert/aae364_notebook
bc77866860e6bdb7d59467ce9817a604c7f26e20
BSD-3-Clause
02.Laplace.ipynb
jgoppert/aae364_notebook
bc77866860e6bdb7d59467ce9817a604c7f26e20
BSD-3-Clause
2019-03-30T19:32:13.000Z
2020-07-09T07:18:17.000Z
Qwen/Qwen-72B
1. YES
2. YES