EulerFoldComputational Physics Basics
“An intensive two-week path from numerical foundations to verified simulations in computational physics. It emphasizes Python, NumPy, SciPy, error analysis, ODE/PDE solvers, Monte Carlo sampling, and reproducible verification artifacts.”
Numerical Computing Foundations and Error Analysis
By the end of this module you will be able to construct vectorized numerical experiments, quantify floating-point and discretization error, and produce reproducible diagnostic plots with dimensionally consistent physical quantities.
Linear Algebra, Interpolation, and Nonlinear Solvers
By the end of this module you will be able to formulate computational physics problems as linear or nonlinear systems, select appropriate solvers, diagnose conditioning, and validate numerical solutions against analytic or benchmark results.
Ordinary Differential Equations and Dynamical Systems
By the end of this module you will be able to implement and compare explicit, adaptive, and symplectic ODE integrators for physical systems, evaluate stability and conservation properties, and interpret phase-space diagnostics.
Monte Carlo Sampling and Statistical Estimation
By the end of this module you will be able to implement Monte Carlo integration and Markov-chain sampling, quantify statistical uncertainty, diagnose autocorrelation, and compare sampled distributions with analytic statistical-physics targets.
Partial Differential Equations and Finite-Difference Simulation
By the end of this module you will be able to discretize one-dimensional PDEs using finite differences, enforce common boundary conditions, analyze stability constraints, and perform grid-convergence studies for time-dependent simulations.
Verification, Validation, Performance, and Reproducible Reporting
By the end of this module you will be able to verify numerical solvers with manufactured solutions, validate them against benchmarks, profile and optimize computational kernels, and package results into a reproducible computational physics report.
References
Week 1: Numerical Computing Foundations and Error Analysis
Week 2: Linear Algebra, Interpolation, and Nonlinear Solvers
Week 3: Ordinary Differential Equations and Dynamical Systems
Week 4: Monte Carlo Sampling and Statistical Estimation
Week 5: Partial Differential Equations and Finite-Difference Simulation
Week 6: Verification, Validation, Performance, and Reproducible Reporting
Community Insights
0Join the discussion
Sign in to share your thoughts and technical insights.
Loading insights...