From fcd63fa1b2455248b6843e02bdc7faf526fab0c1 Mon Sep 17 00:00:00 2001 From: Deniz Date: Wed, 17 Sep 2025 11:25:56 +0300 Subject: [PATCH] Update README.md --- README.md | 41 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 41 insertions(+) diff --git a/README.md b/README.md index a6f5f3c..15bbfdd 100644 --- a/README.md +++ b/README.md @@ -12,6 +12,47 @@ A lightweight, from-scratch, object-oriented Python package implementing classic --- +## 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](tutorials/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](tutorials/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](tutorials/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](tutorials/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`. + +--- + ## Features ### Linear system solvers