From 05ba5da27205905e5adf8b59bfe1bf5327e7b0d6 Mon Sep 17 00:00:00 2001
From: Deniz Donmez <deniz.donmez_03@metu.edu.tr>
Date: Mon, 15 Sep 2025 10:32:07 +0300
Subject: [PATCH] new module 'differentiation'

---
 README.md | 27 +++++++++++++++++++++++----
 1 file changed, 23 insertions(+), 4 deletions(-)

diff --git a/README.md b/README.md
index 755a6ea..e671d2a 100644
--- a/README.md
+++ b/README.md
@@ -1,8 +1,17 @@
 # numethods
 
-A small, from-scratch, object-oriented Python package implementing classic numerical methods.  
+A lightweight, from-scratch, object-oriented Python package implementing classic numerical methods.  
 **No NumPy / SciPy solvers used**, algorithms are implemented transparently for learning and research.
 
+## Why this might be useful
+
+- Great for teaching/learning numerical methods step by step.
+- Good reference for people writing their own solvers in C/Fortran/Julia.
+- Lightweight, no dependencies.
+- Consistent object-oriented API (.solve() etc).
+
+---
+
 ## Features
 
 ### Linear system solvers
@@ -25,7 +34,7 @@ A small, from-scratch, object-oriented Python package implementing classic numer
 - **Newton** (divided differences): `NewtonInterpolation`
 - **Lagrange** polynomials: `LagrangeInterpolation`
 
-### Orthogonalization, QR, and Least Squares (NEW)
+### Orthogonalization, QR, and Least Squares
 
 - **Classical Gram-Schmidt**: `QRGramSchmidt`
 - **Modified Gram-Schmidt**: `QRModifiedGramSchmidt`
@@ -33,13 +42,23 @@ A small, from-scratch, object-oriented Python package implementing classic numer
 - **QR-based linear solver** (square systems): `QRSolver`
 - **Least Squares** for overdetermined systems (via QR): `LeastSquaresSolver`
 
+### Numerical Differentiation
+
+- **Forward difference**: `ForwardDiff`
+- **Backward difference**: `BackwardDiff`
+- **Central difference (2nd order)**: `CentralDiff`
+- **Central difference (4th order)**: `CentralDiff4th`
+- **Second derivative**: `SecondDerivative`
+- **Richardson extrapolation**: `RichardsonExtrap`
+
 ### Matrix & Vector utilities
 
 - Minimal `Matrix` / `Vector` classes
-- `@` operator for **matrix multiplication** (NEW)
-- `*` for **scalar**-matrix multiplication
+- `@` operator for **matrix multiplication**
+- `*` for **scalar**–matrix multiplication
 - `.T` for transpose
 - Forward / backward substitution helpers
+- Norms, dot products, row/column access
 
 ---