Seite - 216 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python

216 A GettingAccesstoPython A.5.1 ASimpleProgramintheNotebook Start the IPythonnotebook locally by the commandipython notebookor go to SageMathCloudorWakari as described above. Thedefault input area is a cell for Pythoncode. Type g = 9.81 v0 = 5 t = 0.6 y = v0*t - 0.5*g*t**2 in a cell and run the cellbyclickingonRun Selected (notebookrunning locallyon yourmachine)oron the“play”button(notebookrunningin thecloud). Thisaction will execute the Python code and initialize the variablesg, v0, t, andy. You can thenwriteprint y in anewcell, execute that cell, andsee theoutputof this state- ment in thebrowser. It is easy togoback toacell, edit thecode, and re-execute it. To download the notebook to your computer, choose the File – Download as menu and select the type of file to be downloaded: the original notebook format (.ipynbfileextension)oraplainPythonprogramversionof thenotebook(.pyfile extension). A.5.2 MixingText,Mathematics,Code,andGraphics The real strength of IPython notebooks ariseswhen youwant towrite a report to document how a problem can be explored and solved. As a teaser, open a new notebook,click in thefirst cell, andchooseMarkdownas format(notebookrunning locally) or switch fromCode to Markdown in the pull-downmenu (notebook in the cloud). The cell is nowa textfieldwhereyoucanwrite textwithMarkdown17 syntax.MathematicscanbeenteredasLATEXcode. Trysometextwith inlinemath- ematicsandanequationonaseparate line: Plot the curve $y=f(x)$, where $$ f(x) = e^{-x}\sin (2\pi x),\quad x\in [0, 4] $$ Execute thecell andyouwill seenicely typesetmathematics in thebrowser. In the newcell, addsomecode toplotf.x/: import numpy as np import matplotlib.pyplot as plt %matplotlib inline # make plots inline in the notebook x = np.linspace(0, 4, 101) y = np.exp(-x)*np.sin(2*pi*x) plt.plot(x, y, ’b-’) plt.xlabel(’x’); plt.ylabel(’y’) 17http://daringfireball.net/projects/markdown/syntax