# 15.3. Analyzing real-valued functions
https://ipython-books.github.io/153-analyzing-real-valued-functions/

## Ref

* SymPy integral transforms - http://docs.sympy.org/latest/modules/integrals/integrals.html
* Real analysis on Wikipedia, at https://en.wikipedia.org/wiki/Real_analysis#Bibliography
* Calculus on Wikibooks, at http://en.wikibooks.org/wiki/Calculus
* Real analysis on Awesome Math, at https://github.com/rossant/awesome-math/#real-analysis


```python
from sympy import *
init_printing()
```


```python
var('x z')
```


```python
f = 1 / (1 + x**2)
```


```python
type(f)
```




    sympy.core.power.Pow




```python
v = f.subs(x, 1)
v, type(v)
```




    (1/2, sympy.core.numbers.Half)




```python
diff(f, x)
```


```python
limit(f, x, oo)   # "oo" for infinity
```


```python
ts = series(f, x0=0, n=9)
ts
```


```python
type(ts)
```




    sympy.core.add.Add



How to remove higher order terms:
* https://stackoverflow.com/questions/25001896/sympy-drop-higher-order-terms-in-polynomial


```python
ts = series(f, x0=0, n=9).removeO()   # remove Big-O
ts
```


```python
type(ts)
```




    sympy.core.add.Add




```python
integrate(f, (x, -oo, oo))
```


```python
integrate(f, x)
```


```python
fourier_transform(f, x, z)
```


```python

```

e3aebec8de37b10c6a32486fe7d963ed3a68a3fd
ipynb
Jupyter Notebook
chapter15_symbolic/03_function.ipynb
wgong/cookbook-2nd-code
8ca2e5b3c90fee6605f4155e6b9dfb783ce46807
MIT
chapter15_symbolic/03_function.ipynb
wgong/cookbook-2nd-code
8ca2e5b3c90fee6605f4155e6b9dfb783ce46807
MIT
chapter15_symbolic/03_function.ipynb
wgong/cookbook-2nd-code
8ca2e5b3c90fee6605f4155e6b9dfb783ce46807
MIT
Qwen/Qwen-72B
1. YES
2. YES