Education

Random goodies and visualizations to help understand mathematical and other concepts.

This repository contains interactive SageMath applets and Python visualizations for teaching and learning fundamental concepts in calculus and linear algebra. Each topic includes the original SageMath code, a Python 3 translation (using matplotlib and numpy), generated visualization images, and a detailed explanation.

Contents

Calculus

Single-Variable Calculus

• Newton's Method -- Iterative root-finding using tangent line approximations

  

• Newton's Method (Animated) -- Step-by-step visual breakdown of each iteration

  

• Taylor Expansion -- Successive polynomial approximations converging to sin(x) and e^x

  

• Partial Fraction Decomposition -- Step-by-step decomposition of rational functions with optional row reduction (SageMath)

  

Multivariable Calculus

• 3D Surface with Level Curves -- Paraboloid x^2 + y^2 with horizontal level curve slices and contour plot

  

• 3D Surface with Cross Sections -- Paraboloid x^2 + y^2 with vertical cross-section slices

  

• Gradient Descent for Linear Regression -- Gradient descent optimization with regression line and cost convergence plots

  

Linear Algebra

• Linearization via Jacobian -- Comparing a nonlinear R^2 -> R^2 map with its Jacobian linear approximation

  

How to Run

Python Visualizations

All Python scripts require Python 3 with matplotlib, numpy, and scipy:

pip install matplotlib numpy scipy

Then run any visualization:

python3 calculus/newtons_method/newtons_method.py
python3 calculus/taylor_expansion_animated_dir/taylor_expansion.py
python3 linear_algebra/linearize_jacobian/linearize_jacobian.py
# etc.

SageMath Code

The original SageMath code can be run without installation on SageMathCell. Simply copy the contents of any sage_code file and paste it into the cell server.

License

GNU General Public License v3.0 -- see calculus/LICENSE.

Author

Keivan Hassani Monfared (k1monfared)