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nemenman>Ilya at 13:51, 21 February 2017

2017-02-21T13:51:50Z

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{{PHYS212-2017}}

Here we start a new module, where we will explore how to model and solve dynamical systems in more detail. In this lecture we discussed a few important concepts in programming, some specific to Python, and some not.

# We discussed the importance of encapsulating the code that you use repeatedly into either a script or a function.
# We discussed the difference between scripts (no inputs and no outputs) and functions (have inputs and outputs).
# We did the book section 5.1 -- Writing your own functions, and we wrote our first functions -- various growth rates for bacterial growth and solvers of the corresponding differential equations.
# We started talking about variable types, and importance of type checking, and how Python figures out which type is a variable that has been passed to a function; we will return to this later.
# We wrote our own loadable modules, and discussed the important of using the reload function.
# Finally, we discussed some common coding mistakes that we all do when working with python, and specifically:
:# Appending list or arrays instead of pre-allocating arrays -- appending arrays causes creation of new arrays, and then copying numbers, which takes time.
:# Doing loops instead of vectorizing your math and operating on arrays -- doing loops causes Python to do type checking of variables at every step of the way, which is costly.
# Finally, we talked about <math>O(dt^n)</math> notation, and we saw, by writing the scripts that I have uploaded below that the simple Euler method of solving differential equations has an error of <math>O(dt)</math>

:Scripts for this Module:
::[[media:GrowthFunctions_v2.txt | GrowthFunctions]] -- module defining different growth functions.
::[[media:Integrators_v2.txt | Integrators]] -- module defining different integrators (Euler and Runge-Kutta second order).
::[[media:Module2_v2.txt | Module 2]] -- catch-all scripts I used during the class.

I also asked you to show that the numerical error is dependent largely (but not fully) on the solving method, not the equation being solved. For this you needed to define a different growth function, solvee the growth equation, and [https://docs.google.com/forms/d/e/1FAIpQLSeNvrPddCgvMfHdlSA8uYDddBFqLK81Rrr4l7jfozud6J7iww/viewform submit your work].

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Physics 212, 2017: Lecture 7 - Revision history

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nemenman>Ilya at 13:51, 21 February 2017