# Tutorial Series

This package comes with a set of Jupyter notebooks designed as a structured tutorial series in **numerical methods**, both mathematically rigorous and hands-on with code.

## Core Tutorials

1. [Tutorial 1: Vectors and Matrices](tutorial1_vectors.ipynb)

   - Definitions of vectors and matrices.
   - Vector operations: addition, scalar multiplication, dot product, norms.
   - Matrix operations: addition, multiplication, transpose, inverse.
   - Matrix and vector norms.
   - Examples with `numethods.linalg`.

2. [Tutorial 2: Linear Systems of Equations](tutorial2_linear_systems.ipynb)

   - Gaussian elimination and Gauss–Jordan.
   - LU decomposition.
   - Cholesky decomposition.
   - Iterative methods: Jacobi and Gauss-Seidel.
   - Examples with `numethods.solvers`.

3. [Tutorial 3: Orthogonalization and QR Factorization](tutorial3_orthogonalization.ipynb)

   - Inner products and orthogonality.
   - Gram–Schmidt process (classical and modified).
   - Householder reflections.
   - QR decomposition and applications.
   - Examples with `numethods.orthogonal`.

4. [Tutorial 4: Root-Finding Methods](tutorial4_root_finding.ipynb)

   - Bisection method.
   - Fixed-point iteration.
   - Newton’s method.
   - Secant method.
   - Convergence analysis and error behavior.
   - Trace outputs for iteration history.
   - Examples with `numethods.roots`.

- [Polynomial Regression Demo](./polynomial_regression.ipynb)

- Step-by-step example of polynomial regression.
- Shows how to fit polynomials of different degrees to data.
- Visualizes fitted curves against the original data.

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