Today’s Goals

Day 03 - Getting Started with VS Code

\[v_i \approx \frac{x_{i+1} - x_i}{\Delta t}\]

Today we'll set up VS Code for scientific computing and practice numerical differentiation.

PHY 321 Classical Mechanics I - Spring 2026

Today’s Goals#

After this session, you should be able to:

Set up VS Code for Python scientific computing
Use Jupyter notebooks in VS Code
Perform numerical differentiation using finite difference methods
Compare numerical results with analytical solutions

Step 1: Download VS Code#

Go to: https://code.visualstudio.com/download

Choose your operating system:

macOS: Universal download (Intel + Apple Silicon)
Windows: User Installer
Linux: .deb, .rpm, or .tar.gz

The download is ~200 MB and takes just a minute or two.

Step 2: Install VS Code#

On macOS:

Open the downloaded .zip file
Drag Visual Studio Code.app to Applications
Launch from Applications

On Windows:

Double-click the .exe installer
Follow the wizard (default settings are fine)
VS Code launches automatically

Step 3: Install Required Extensions#

Click the Extensions icon (4 squares) on the left sidebar

Or press Ctrl+Shift+X (Windows/Linux) or Cmd+Shift+X (Mac)

Install these two extensions:

Jupyter by Microsoft
Python by Microsoft

Click Reload when prompted.

Step 4: Verify Python#

Open VS Code’s Terminal: View → Terminal (or Ctrl+`)

Type:

python --version

or

python3 --version

You should see something like Python 3.10.0 or newer.

If not, install Python from: https://www.python.org/downloads/

Download Today’s Activity#

Open the notebook for today’s activity:

https://dannycaballero.info/phy321msu/resources/vscode-setup-numerics-activity.html

Or find it in the course website under Resources.

Download the .ipynb file and open it in VS Code.

Libraries We’ll Use#

import numpy as np          # Numerical computations
import matplotlib.pyplot as plt  # Plotting
import pandas as pd         # Data manipulation

Run the first code cell to load these libraries.

If you get an error, you may need to install them:

pip install numpy matplotlib pandas

The Physics: Numerical Derivatives#

In experiments, we measure positions at different times.

To get velocities or accelerations, we numerically differentiate our data.

\[v_i \approx \frac{x_{i+1} - x_i}{\Delta t}\]

This is the forward difference method.

Finite Difference Methods#

Three common methods:

Forward: \(f'(x_i) \approx \dfrac{f(x_{i+1}) - f(x_i)}{\Delta x}\)
Backward: \(f'(x_i) \approx \dfrac{f(x_i) - f(x_{i-1})}{\Delta x}\)
Central: \(f'(x_i) \approx \dfrac{f(x_{i+1}) - f(x_{i-1})}{2\Delta x}\)

Central difference is more accurate but uses both neighboring points.

The Synthetic Data#

We’ve generated position data for a ball tossed with air resistance:

\[\mathbf{F}_{\text{net}} = -m\mathbf{g} - C_D |\mathbf{v}|\mathbf{v}\]

Run the data generation cells in the notebook to create:

t - time array (seconds)
x - x-position array (meters)
y - y-position array (meters)

Your Task#

Using only finite difference methods:

Compute and plot the numerically-derived velocities (\(v_x\), \(v_y\))
Compute and plot the numerically-derived accelerations (\(a_x\), \(a_y\))
Compare your numerical derivatives with the “true” values
What do you notice about the accuracy?

Work through the notebook with your neighbors!

Hints#

To compute velocity from position:

dt = t[1] - t[0]  # time step
vx = (x[1:] - x[:-1]) / dt  # forward difference

Note: Your derivative arrays will be one element shorter than the original!

To plot against the right time values:

plt.plot(t[:-1], vx)  # use t[:-1] not t

Exporting Notebooks to PDF#

For homework submissions on Gradescope:

Option A: VS Code Extension

Install “Jupyter PDF Export” extension
Right-click notebook → Export as PDF

Option B: Command Line

jupyter nbconvert --to pdf your_notebook.ipynb