Computational and Writing Primer

Computational and Writing Primer#

This short primer introduces the tools you will use throughout this course to write, compute, and verify physics problems. It is not a programming course, and you are not expected to become a software developer. Instead, the goal is to give you just enough structure to use computation as a thinking and verification tool.

You should return to this chapter whenever you need a refresher.

Working in Google Colab#

What Is a Jupyter Notebook?#

A Jupyter notebook is a document that combines explanatory text, mathematical equations, executable code, and output in a single place. In this course, notebooks serve the same role as a lab notebook or worked-solution sheet: they record what you did, why you did it, and how you checked it.

Notebooks are made of cells, which come in two main types:

  • Markdown cells, used for explanations and equations

  • Code cells, used for calculations and verification

Mini Exercise#

Create a new notebook cell and change it to a Markdown cell. Write one sentence describing what a Jupyter notebook is used for in this course.

Solution

A Jupyter notebook is used to combine written explanations, mathematical equations, and executable code in a single document so that physical reasoning and calculations can be recorded together.

Opening the Book in Google Colab#

Each chapter of this book can be opened directly in Google Colab by clicking the rocket icon at the top of the page and selecting Google Colab. This opens a copy of the notebook in your browser without requiring any local software installation.

Mini Exercise#

Open any chapter in Google Colab and run one existing code cell.

Solution

If the code cell executes without errors and produces output, the notebook is running correctly in the Colab environment.

Python Basics for Physics#

Variables#

A variable stores a value so that it can be reused later. Variables allow us to name physical quantities and keep track of them symbolically.

distance = 80      # meters
time = 4           # seconds
speed = distance / time
print(speed)

Mini Exercise#

Define variables for a distance of 120 m and a time of 6 s. Compute and print the speed.

Solution

distance = 120
time = 6
speed = distance / time
print(speed)

Comments#

Comments explain why a calculation is being performed. They are ignored by Python but essential for readability.

# Convert meters to kilometers
distance_km = distance / 1000

Mini Exercise#

Add a comment explaining what a calculation represents physically.

Solution

# This calculation determines the average speed of the object
speed = distance / time

Importing Libraries#

Scientific calculations commonly rely on external libraries. The most frequently used library in this course is NumPy.

import numpy as np

NumPy provides mathematical constants, array operations, and numerical functions.

Mini Exercise#

Use NumPy to compute the area of a circle with radius 3.5 m.

Solution

import numpy as np

r = 3.5
area = np.pi * r**2
print(area)

Lists and Arrays#

A list stores multiple values, while a NumPy array allows mathematical operations to be applied to all values at once.

measurements = [4.8, 5.3, 4.9, 5.4]
weights = np.array(measurements)

Mini Exercise#

Create a list of four measurements, convert it to a NumPy array, and compute the average.

Solution

import numpy as np

measurements = [4.8, 5.3, 4.9, 5.4]
weights = np.array(measurements)
print(np.mean(weights))

For Loops#

A for loop repeats an action for each item in a collection.

for value in measurements:
    print(value)

Mini Exercise#

Write a loop that prints each measurement multiplied by 2.

Solution

for value in measurements:
    print(2 * value)

Functions#

Functions package calculations so they can be reused and clearly named.

def percent_uncertainty(A, dA):
    return (dA / A) * 100

Mini Exercise#

Write a function that computes speed given distance and time.

Solution

def speed(distance, time):
    return distance / time

Writing in Markdown#

Markdown cells are used for clear scientific writing, not for computation.

Headings, Emphasis, and Lists#

# Section Title
## Subsection Title

*italic text*  
**bold text**

- first item
- second item

Mini Exercise#

Create a Markdown cell with a heading and a bulleted list describing a problem-solving strategy.

Solution

## Strategy
- Identify known quantities
- Choose appropriate equations
- Solve the math
- Verify the result

Inline Code#

Use backticks to refer to code inside text, such as np.sqrt().

Mathematics with LaTeX#

LaTeX is used to typeset mathematical expressions.

Inline Mathematics#

The area is $A = \pi r^2$.

Rendered: The area is \(A = \pi r^2\).

Displayed Equations#

$$ A = \pi r^2 $$

Rendered:

\[ A = \pi r^2 \]

Aligned Equations#

\begin{align*}
v &= \frac{d}{t} \\
  &= \frac{80\ \text{m}}{4\ \text{s}} \\
  &= 20\ \text{m/s}.
\end{align*}

Rendered:

(1)#\[\begin{align} v &= \frac{d}{t} \\ &= \frac{80\ \text{m}}{4\ \text{s}} \\ &= 20\ \text{m/s}. \end{align}\]

Mini Exercise#

Write the LaTeX expression for average speed.

Solution

The average speed is given by \(\displaystyle v = \frac{d}{t}\).

How Python Fits into Problem Solving#

In this course, Python is used after the physics reasoning is complete. It serves as a verification tool, not a substitute for understanding.

The typical workflow is:

  1. Build a physical model

  2. Solve the math analytically

  3. Verify the result using Python

Example Verification#

distance = 80    # meters
time = 4         # seconds

speed = distance / time
print(f"Speed = {speed:.1f} m/s")

Mini Exercise#

Change the distance and time values and observe how the speed changes.

Solution

Increasing the distance increases the speed, while increasing the time decreases the speed, consistent with the definition \(v = d/t\).

Common Mistakes to Avoid#

  • Writing explanations in code cells

  • Using Python without understanding the physics

  • Dropping units during calculations

  • Treating Python as a formula lookup tool

Python should support your reasoning, not replace it.

What You Are Expected to Know#

By the end of the semester, you should be comfortable with:

  • creating and editing Jupyter notebooks,

  • defining variables and functions,

  • importing NumPy,

  • writing Markdown explanations,

  • typesetting equations in LaTeX,

  • using Python to verify results.

Final Advice#

A Jupyter notebook is a record of your thinking. Someone reading your notebook later should be able to follow your reasoning without additional explanation.

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