updated readme

README.md

@@ -1,6 +1,6 @@
 # Welcome to AnaFlow
 
-[![DOI](https://zenodo.org/badge/116264578.svg)](https://zenodo.org/badge/latestdoi/116264578)
+[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.1135723.svg)](https://doi.org/10.5281/zenodo.1135723)
 [![PyPI version](https://badge.fury.io/py/anaflow.svg)](https://badge.fury.io/py/anaflow)
 [![Documentation Status](https://readthedocs.org/projects/docs/badge/?version=latest)](https://anaflow.readthedocs.io/en/latest/)
 [![Code style: black](https://img.shields.io/badge/code%20style-black-000000.svg)](https://github.com/ambv/black)
@@ -34,7 +34,35 @@ Have a look at: https://github.com/scikit-umfpack/scikit-umfpack
 You can find the documentation under [geostat-framework.readthedocs.io][doc_link].
 
 
-## Provided Functions
+### Example
+
+In the following the well known Theis function is called an plotted for three
+different time-steps.
+
+```python
+import numpy as np
+from matplotlib import pyplot as plt
+from anaflow import theis
+
+
+time = [10, 100, 1000]
+rad = np.geomspace(0.1, 10)
+
+head = theis(rad=rad, time=time, T=1e-4, S=1e-4, Qw=-1e-4)
+
+for i, step in enumerate(time):
+    plt.plot(rad, head[i], label="Theis(t={})".format(step))
+
+plt.legend()
+plt.show()
+```
+
+<p align="center">
+<img src="https://raw.githubusercontent.com/GeoStat-Framework/AnaFlow/master/docs/source/pics/01_call_theis.png" alt="Theis" width="600px"/>
+</p>
+
+
+### Provided Functions
 
 The following functions are provided directly
 
@@ -48,6 +76,17 @@ anaflow.ext_theis3D  # extended Theis solution in 3D
 ```
 
 
+### Laplace Transformation
+
+We provide routines to calculate the laplace-transformation as well as the
+inverse laplace-transformation of a given function
+
+```python
+anaflow.get_lap      # Get the laplace transformation of a function
+anaflow.get_lap_inv  # Get the inverse laplace transformation of a function
+```
+
+
 ## Requirements
 
 - [NumPy >= 1.10.0](https://www.numpy.org)