Computational Mathematics — Assignments (AITU)

Six Jupyter notebooks covering root-finding, linear-system solvers, matrix inversion, curve fitting, interpolation, and numerical differentiation.

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Overview

This repository contains six graded assignments from the Computational Mathematics course at Astana IT University. Each notebook implements numerical algorithms from scratch (using NumPy) and verifies results against analytical or library-based references.

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What it covers

Assignment	Numerical methods implemented
1	Graphical root localization; bisection method; absolute error analysis
2	Jacobi iterative method for linear systems; diagonal-dominance check; convergence plots
3	Iterative matrix inversion (Schulz / Newton–Schulz iteration); comparison with numpy.linalg.inv
4	Linear, polynomial (quadratic), and exponential curve fitting; three-parameter law fitting; forward difference table
5	Newton's forward interpolation; Newton's backward interpolation; central difference interpolation
6	First and second derivatives via Newton's forward/backward difference formulas

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Notebooks

File	Description
Assignment_1_CM.ipynb	Root finding: graphical method + bisection; absolute error
Assignment_2_CM.ipynb	Jacobi method for 3×3 system; convergence analysis
Assignment_3_CM.ipynb	Iterative matrix inversion; convergence check vs NumPy
Assignment_4_CM.ipynb	Curve fitting (linear, quadratic, exponential, 3-constant law); finite difference table
Assignment_5_CM.ipynb	Newton forward/backward/central interpolation formulas
Assignment_6_CM.ipynb	Numerical differentiation (1st and 2nd derivatives) via finite differences

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Getting started

# 1. Create and activate a virtual environment
python -m venv .venv
source .venv/bin/activate   # Windows: .venv\Scripts\activate

# 2. Install dependencies
pip install jupyter numpy scipy matplotlib

# 3. Open any notebook
jupyter lab Assignment_1_CM.ipynb

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Adil Ormanov — GitHub