Part 1

Introduction

• Python is a programming language that has become very popular.
  • there are literally thousands of libraries written for Python
• It is simple and powerful (like Gnuplot).
  • used for automating tasks that would be difficult or “messy” in shell scripts.
  • used to process “big data”, machine learning, and build physics simulations.
  • used to write professional quality software (Google, YouTube, Spotify, etc)

Installing

Python usually comes installed by default on Linux machines. But, if not, on Ubutnu we would run

$ sudo apt install python3 python-is-python3

• We want Python version 3.
• We want python to be an alias for python3.

First “Program”

• Python is an “interpreter”.
• That means we can write a script and tell Python to run the commands in the script.
  • It also means anything we can do in a python script we can do at the command line.
• We can also tell Linux run the script with Python using the shebang.

Demo: Hello World

demos/02-helloworld.sh

Part 2

Python as a Calculator

• We can use python as a powerful calculator.

Part 3

Python as a Calculator

Variables

What will the gravitational force between a 500 kg and a 200 kg mass placed 0.01 meter apart?

. . .

• Variables are a way for us to store a number and give it a name.
• We don’t want to type 6.67430e-11 every time we do a new calculations.
• We can use a variable to store the number, and then use the name.

Variables in Python are different than bash:

• We can store the actual number, not just the text.
• We don’t have to use a $ to get the variables value.

demos/04-variables.py

Python as a Calculator

Functions

What will the gravitational force between a 5000 kg and a 2500 kg mass placed 0.2 meter apart?

. . .

• Functions are a way for us to store a calculation and give it a name.
• We don’t want to type out G*m1k*m2/r**2 every time we want to do a calculation (see a pattern?)

Functions are different in Python than Gnuplot:

• We have to declare the function using def functionname(args):
• Then we “return” the functions value.

Python as a Calculator

Part 4

Python as a Calculator

Modules

The torque generated by a force is given by the cross product of the lever arm and the force \[ \vec{\tau} = \vec{r} \times \vec{F} \]

The magnitude of the torque will be \[ \tau = \left| \vec{r} \times \vec{F} \right| = r F \sin\theta \]

. . .

Python as a Calculator

Modules

• Python libraries are called “modules”
• Modules are just pieced (sometimes large) of code that somebody else has already written to do something useful.
• The trigonometry functions are in the math module has functions for evaluating trig functions.

./demos/06-modules.sh

Standard Library

The “Python Standard Library” is a collection of modules (like the math module) that are included with Python.

There are dozens of librarys…

https://docs.python.org/3/library/

Part 5

Useful Modules: pint

• Pint is a python module for doing unit conversions and dimensional analysis.
• It can do unit conversions, and check that the dimensions of a quantity are correct.
• This makes python very useful as a calculator.
• But we need to install it…

Local installs and virtual environments

• Python supports installing modules into a “system” directory or a “local” directory.
• “Virtual environments” are a way to install modules into a local, self-contained, environment.
• In Ubuntu 24.04, there was a change. You can no longer install packages into the system directory without using apt.

Local installs and virtual environments

Steps to create and use a virtual environment:

• python -v venv venv Create a new virtual environment in a directory named venv
• venv/bin/pip install <module> Install modules into the virtual environment
• venv/bin/python my_script.py Use the environment to to run a script
• source venv/bin/activeate Setup shell to use the environment by default

Part 6

A better interpreter

• When we run python3 with no arguments, we get a command prompt.
• The python interpreter starts reading text from standard input and running the python code we type in.
• This is fine, but there are more advanced interfaces…

./demos/08-ptpython.sh

Part 7

Useful Modules: pyErrorProp

• In physics, we often need to perform some calculation with measured values that have uncertainty.
• We need to quantity the uncertainty in our calculated values.
• We do this by “propagating error”.

pyErrorProp is a python module for doing error propagation.

• Given a user-defined function, pyErrorProp will compute the uncertainty in the returned value of the function based on the uncertainty of the arguments passed in.

Error Propagation Example

If you measure the length of a table to be 150 centimeter, plus or minus 0.5 centimeter, and the width to be 80 centimeter, plus or minus 0.5 centimeter, what is the area of the table top?

Error Propagation Example

Straight out of the Physics Lab Error Analysis Reference:

You drop a ball bearing 10 times from a height of 3 meter, plus or minus 0.5 cm, and measure the fall time to be 0.79 s, plus or minus 0.02 s. What is \(g\)? Recall: \(g = \frac{2h}{t^2}\)

Another group performs the same experiment and computes \(g = 10.6 \pm 0.4\) meter per second squared. Are your measurements consistent?

Useful Modules: numpy

Numerical Python (numpy) is a (large) collection of tools for doing numerical calculations in python.

For us, it provides tools for doing vector operations (compute the dot product, cross product, etc), matrix-vector operations (multiply a vector by a matrix), and matrix operations (invert matrix, compute eigen values and eigen vectors, etc)

Useful Modules: numpy

Vector operations

1. How much work is done by a force \(\vec{F} = 5 N \hat{x}\) if the object that the force is exerted on is displaced \(\Delta \vec{r} = 2 m \hat{x} + 4 m \hat{y}\).

   Recall: \(W = \vec{F} \cdot \Delta\vec{r}\)

2. Compute the torque generated by a for \(\vec{F} = 5 N \hat{x}\) exerted on a lever arm \(r = 10 cm \hat{x} + 10 cm \hat{y}\)

   Recall: \(\vec{\tau} = \vec{r} \times \vec{F}\)

   Also: \(\tau = r F \sin\theta\)

Useful Modules: numpy

Work Calculation

Useful Modules: numpy

Torque Calculation

Useful Modules: numpy

Matrix-vector operations

Matrix-vector multiplication is as simple as creating a matrix and “dotting” it with a vector.

Useful Modules: numpy

Matrix operations

Systems of equations can be represented as matrix equations.

1. Jack goes out for a run and plans to run 2 miles. He starts out running at a brisk 10 mile/hour pace, but soon tires and ends up walking the rest of the way at 2 mile per hour. It takes Jack 45 minutes to travel the two miles. At what time did Jack stop running?

Useful Modules: numpy

System of Equations

1. Jack goes out for a run and plans to run 2 miles. He starts out running at a brisk 10 mile/hour pace, but soon tires and ends up walking the rest of the way at 2 mile per hour. It takes Jack 45 minutes to travel the two miles. At what time did Jack stop running?

Useful Modules: numpy

System of Equations

1. Jack goes out for a run and plans to run 2 miles. He starts out running at a brisk 10 mile/hour pace, but soon tires and ends up walking the rest of the way at 2 mile per hour. It takes Jack 45 minutes to travel the two miles. At what time did Jack stop running?

Useful Modules: numpy

System of Equations

1. Jack goes out for a run and plans to run 2 miles. He starts out running at a brisk 10 mile/hour pace, but soon tires and ends up walking the rest of the way at 2 mile per hour. It takes Jack 45 minutes to travel the two miles. At what time did Jack stop running?

Useful Modules: numpy

System of Equations

1. Jack goes out for a run and plans to run 2 miles. He starts out running at a brisk 10 mile/hour pace, but soon tires and ends up walking the rest of the way at 2 mile per hour. It takes Jack 45 minutes to travel the two miles. At what time did Jack stop running?