title	Applied Mathematics - Collaboration Guide
description	Contributing guide for Applied Mathematics course content
tableOfContents	true
sidebar	order 999

Applied Mathematics

Read this course at: https://siliconwit.com/education/applied-mathematics/

Nine lessons covering the mathematics engineers use most often: modeling, calculus, linear algebra, complex numbers, probability, differential equations, Fourier analysis, numerical methods, and feedback control. Every topic starts with a real problem, introduces the math as the tool to solve it, and includes Python code where it helps.

Lessons

#	Title
1	Spherical Cows and the Art of Model Building
2	Calculus for Engineers
3	Linear Algebra: Vectors, Matrices, and Transforms
4	Complex Numbers and Phasors
5	Probability, Statistics, and Noise
6	Differential Equations and Real Systems
7	Fourier Analysis and the Frequency Domain
8	Numerical Methods: Math in Code
9	Feedback and Control Systems

File Structure

applied-mathematics/
├── index.mdx
├── spherical-cows-model-building.mdx
├── calculus-for-engineers.mdx
├── linear-algebra-vectors-matrices.mdx
├── complex-numbers-and-phasors.mdx
├── probability-statistics-noise.mdx
├── differential-equations-real-systems.mdx
├── fourier-analysis-frequency-domain.mdx
├── numerical-methods-computation.mdx
├── feedback-control-systems.mdx
└── README.md

How to Contribute

All commands below work on Linux, macOS, and Windows (using Git Bash, PowerShell, or Command Prompt with Git installed).

For Team Members (with push access)

First time setup (clone the repo once):

git clone https://github.com/SiliconWit/applied-mathematics.git
cd applied-mathematics

Every time you start working:

git pull origin main

Always pull before making changes. This avoids conflicts with other contributors.

After making your changes:

git add .
git commit -m "Brief description of what you changed"
git push origin main

If you get a push error (someone pushed before you):

git pull origin main

Git will merge the changes automatically in most cases. If there is a conflict, Git will mark the conflicting lines in the file. Open the file, choose which version to keep, then:

git add .
git commit -m "Resolve merge conflict"
git push origin main

Tips to avoid conflicts:

• Always git pull origin main before you start working
• Push your changes as soon as you are done, do not hold onto uncommitted work for long
• Coordinate with other contributors so two people are not editing the same file at the same time

For External Contributors (without push access)

1. Fork the repository: SiliconWit/applied-mathematics
2. Clone your fork:

   git clone https://github.com/YOUR-USERNAME/applied-mathematics.git
   cd applied-mathematics

3. Make your changes and commit:

   git add .
   git commit -m "Brief description of what you changed"
   git push origin main

4. Open a Pull Request against main on the original repository
5. Describe what you changed and why in the PR description

Content Standards

• All lesson files use .mdx format
• Do not use <BionicText> in this course
• Code blocks should include a title attribute:

  ```python title="matrix_operations.py"
  import numpy as np
  A = np.array([[1, 2], [3, 4]])
  ```

• Use ASCII diagrams in text code blocks where they help visualize circuits, signals, or systems
• Use Starlight components (<Tabs>, <TabItem>, <Steps>, <Card>) where appropriate
• Every formula should be preceded by intuition (explain what it means before showing the equation)
• Include working Python examples that readers can run directly
• Mathematical notation uses LaTeX in MDX

Local Development

Clone the main site repository and initialize submodules:

git clone --recurse-submodules <main-repo-url>
cd siliconwit-com
npm install
npm run dev

To test a production build:

npm run build

License

This course content is released under the MIT License.