Engineering_Analysis

A curated set of small, focused numerical methods and applied-physics mini-projects—each living in its own folder with a notebook and/or Python script. The emphasis is on clarity of methods (discretizations, transforms, estimators) and reproducible figures.

Folders in this repo include: Fourier_Series_Gibbs_Analysis/, Diffusion_Constant_Evaluation/, Finite_Differences/, Finite_Element_Method/, Interpolation_Methods/, Topography/, X-Ray_Diffraction/, rPPG/.
Most content is Jupyter notebooks with some Python scripts. (GitHub reports this repo as ~95% Jupyter Notebook, ~5% Python.)

Last verified from the repo tree.

What’s inside (one-liners)

• Fourier_Series_Gibbs_Analysis/ — Explore Fourier partial sums and quantify Gibbs overshoot near discontinuities (step/square-like test functions). Typical outputs: partial-sum plots, error vs. N.

• Diffusion_Constant_Evaluation/ — Simple estimators for diffusion/transport parameters from synthetic or provided data; sanity checks against analytic solutions where available.

• Finite_Differences/ — Canonical FD stencils (1D/2D) for Poisson/heat/wave toy problems; boundary conditions, stability/CFL notes, and convergence demos.

• Finite_Element_Method/ — Minimal FEM examples (triangular meshes, assembly of K, handling of Dirichlet BC) for Laplace on a disk.

• Interpolation_Methods/ — Interpolation vs. approximation: piecewise linear/cubic, polynomial pitfalls, and residual visualization.

• Topography/ — DEM download + resampling + basic rendering. Handy for turning real terrain data into meshes and shaded relief (used with OpenTopography APIs).

• X-Ray_Diffraction/ — Bragg’s law mini-utilities, peak finding, and simple structure-factor illustrations for teaching/demo purposes.

• rPPG/ — Remote photoplethysmography signal extraction from face video.
  This is the most in-depth subproject in the repo: it evolved from basic FFT/wavelet/band-pass pipelines into a full stack pipeline that integrates

  • ROI detection with edge-model AI
  • Forward–backward Lucas–Kanade optical flow for ROI stabilization
  • Standard-deviation motion metrics for robust segment weighting/rejection
  • Camera consistency checks (aperture, exposure, white balance)
  • Multiple spectral estimators (FFT, wavelet, Butterworth) on the stabilized signals

  Outputs include synchronized BPM time series, confidence measures, and debug visualizations. See rPPG/Full_Stack for the complete integrated workflow.

Each folder is intentionally self-contained: read the notebook top cell (or README.md inside the folder, if present) for exact inputs/outputs.

Quickstart

1) Environment

# a. create a clean environment (conda or venv)
conda create -n eng-analysis python=3.10 -y
conda activate eng-analysis
# or: python -m venv .venv && source .venv/bin/activate

# b. install common essentials (safe defaults for most folders)
pip install numpy scipy matplotlib jupyter pandas

License

This project is licensed under the MIT License.