Python

Apr 15, 2024 ODE Foundations 24 min read

Ordinary Differential Equations (18): Frontiers and Series Finale

The series finale. Survey four research frontiers reshaping how we model dynamics -- Neural ODEs, delay equations, stochastic differential equations, and fractional calculus -- then take stock of the entire 18-chapter …

Mar 29, 2024 ODE Foundations 22 min read

Ordinary Differential Equations (17): Physics and Engineering Applications

See ODEs in action across physics and engineering. Walk through the nonlinear pendulum, RLC circuit and resonance, Kepler orbits and conservation laws, multi-DOF structural vibration with tuned mass dampers, and fluid …

Mar 12, 2024 ODE Foundations 22 min read

Ordinary Differential Equations (16): Fundamentals of Control Theory

Learn how differential equations power control systems. Cover transfer functions, PID controllers, root locus, Bode plots, state-space methods, controllability, observability, pole placement, LQR optimal control, and …

Feb 24, 2024 ODE Foundations 26 min read

Ordinary Differential Equations (15): Population Dynamics

Mathematical ecology from single-species to spatial: Malthus, logistic, Allee, Lotka-Volterra predator-prey and competition, age-structured Leslie matrices, metapopulations, and Fisher-KPP traveling waves.

Feb 7, 2024 ODE Foundations 22 min read

Ordinary Differential Equations (14): Epidemic Models and Epidemiology

Mathematical epidemiology from first principles. Build the SIR and SEIR models, derive R0 and the herd-immunity threshold, fit COVID-style scenarios with asymptomatic transmission and time-varying interventions.

Jan 21, 2024 ODE Foundations 24 min read

Ordinary Differential Equations (13): Introduction to Partial Differential Equations

Step from ODEs into partial differential equations. Classify PDEs into parabolic, hyperbolic, and elliptic types. Solve the heat, wave, and Laplace equations using separation of variables and finite differences.

Jan 4, 2024 ODE Foundations 26 min read

Ordinary Differential Equations (12): Boundary Value Problems

Boundary value problems specify the solution at both ends of an interval. Master shooting, finite differences, collocation, and Sturm-Liouville eigenproblems -- with applications from beam deflection to the quantum …

Dec 18, 2023 ODE Foundations 26 min read

Ordinary Differential Equations (11): Numerical Methods

From Euler's tangent step to Dormand-Prince adaptive integrators: a working numerics toolkit. Convergence orders, A-stability, stiffness, and when to reach for Radau or BDF instead of RK45.

Dec 1, 2023 ODE Foundations 32 min read

Ordinary Differential Equations (10): Bifurcation Theory

Bifurcation theory explains how smooth parameter changes cause dramatic qualitative shifts in system behavior. Master saddle-node, transcritical, pitchfork, and Hopf bifurcations through normal forms, stability …

Jul 1, 2023 ODE Foundations 30 min read

Ordinary Differential Equations (1): Origins and Intuition

Why do differential equations exist? Starting from cooling coffee and swinging pendulums, build your first ODE intuition and solve one in Python.

Apr 27, 2022 Python Engineering 36 min read

Python Engineering (8): Performance — Profiling, Caching, and Knowing When to Stop

Profile Python code to find real bottlenecks, apply caching and vectorization where they matter, and avoid the trap of premature optimization.

Apr 24, 2022 Python Engineering 28 min read

Python Engineering (7): Packaging — From pip install to PyPI

Package your Python code for distribution via pip, publish to PyPI, create Docker images, and manage versioning. The complete guide from local project to installable package.

Apr 21, 2022 Python Engineering 38 min read

Python Engineering (6): Concurrency — Threads, Processes, and asyncio

Understand the GIL, master threading, multiprocessing, and asyncio. Learn which concurrency model to use for I/O-bound vs CPU-bound workloads.

Apr 19, 2022 Python Engineering 34 min read

Python Engineering (5): I/O, Serialization, and Data Formats

Handle files, paths, encodings, and data formats in Python. Compare JSON, YAML, TOML, CSV, pickle, and Parquet with practical examples.

Apr 17, 2022 Python Engineering 34 min read

Python Engineering (4): Type Hints, Linting, and Code Quality

Add type safety with mypy, enforce style with ruff and black, and automate checks with pre-commit hooks. Make code reviews about logic, not formatting.

Apr 14, 2022 Python Engineering 34 min read

Python Engineering (3): Testing — pytest, Fixtures, and the Confidence Loop

Build confidence in your code with pytest fixtures, parametrize, mocking, and coverage. Learn debugging techniques that save hours.

Apr 12, 2022 Python Engineering 32 min read

Python Engineering (2): Project Structure — From Script to Package

Learn how to organize Python code into proper packages with imports, entry points, and CLI tools. Build a real command-line application from scratch.

Apr 10, 2022 Python Engineering 30 min read

Python Engineering (1): Environment Setup — pyenv, venv, and Dependency Hell

Master Python environment management with pyenv, virtual environments, and modern dependency tools. Escape dependency hell for good.