An open computational learning module on the three mathematical tools behind introductory circuit analysis — complex numbers, matrix algebra and calculus — taught through executable Jupyter notebooks with biomedical examples.
Why this module¶
Complex numbers, linear systems and differential equations are taught in first-year mathematics as abstract tools, and reappear in electronics courses as assumed knowledge. This module closes that gap by computing: you verify numerically what the textbook derives analytically, change a parameter and see what happens.
It complements the open textbook Electrónica en Ingeniería Biomédica — Volumen I Miguel-Medina, 2026, whose appendices A–C develop the theory. The textbook explains; the notebooks let you experiment.
What it covers¶
| Block | Tool | You will |
|---|---|---|
| A | Complex numbers | draw phasors, compute impedances, sweep frequency and build a first Bode plot |
| B | Matrix algebra | turn a circuit into a matrix, write your own mini-SPICE, study tolerances and conditioning, fit a model by least squares |
| C | Calculus | compute RMS, power and energy, differentiate and integrate signals, solve first- and second-order transients |
Each block can be used on its own. Biomedical examples run through all three: electrode–skin models, ECG filtering, EMG activation, bioimpedance.
How each notebook works¶
Every notebook follows the same sequence:
Learning objectives: three or four.
Key idea: brief, pointing to the textbook section.
Predict: a question to answer before running anything.
Explore: guided code with parameters to change.
Explain: interpretation questions.
Exercises: basic, applied, and a biomedical challenge.
Summary and link to the next notebook.
Licence¶
Code is released under BSD-3-Clause and content (text, figures) under CC BY 4.0. You are free to reuse and adapt both, with attribution.
- Miguel-Medina, T. (2026). Electrónica en Ingeniería Biomédica — Volumen I. Autopublicación. 10.5281/zenodo.22913382