This repository contains two Jupyter notebooks developed as part of the Mathematics for Natural Sciences module (NSCI0006) in my first year at UCL. Both notebooks explore environmental systems using mathematical modelling and data analysis.
This notebook models historical US oil production data by fitting a logistic function to capture resource-limited growth. The model is used to estimate the timing of "peak oil" — the point at which oil production reaches its maximum before declining. The notebook evaluates the model's predictive power and discusses its assumptions and limitations.
This notebook investigates the possibility of multiple stable climate equilibria by modeling the balance between global energy input (from the Sun) and energy output (via thermal radiation). It simulates how feedback loops, particularly those involving polar ice melt and albedo changes, could push the Earth’s climate over a tipping point into a new equilibrium state. The notebook visualizes how small changes in parameters can lead to large shifts in system behavior.
- Python (via Google Colab)
numpy,matplotlib- Analytical and numerical techniques for solving and visualizing differential equations and equilibrium models
- These notebooks were written for coursework and are shared here for demonstration purposes.
- External 'US Oil' data file is required for 'Peak_Oil.ipynb'.
- The models are simplified and educational in nature, but aim to illustrate important real-world dynamics.