forked from denizdonmez/numethods
48 lines
1.6 KiB
Markdown
48 lines
1.6 KiB
Markdown
# Tutorial Series
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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.
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## Core Tutorials
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1. [Tutorial 1: Vectors and Matrices](./tutorial1_vectors.ipynb)
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- Definitions of vectors and matrices.
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- Vector operations: addition, scalar multiplication, dot product, norms.
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- Matrix operations: addition, multiplication, transpose, inverse.
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- Matrix and vector norms.
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- Examples with `numethods.linalg`.
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2. [Tutorial 2: Linear Systems of Equations](./tutorial2_linear_systems.ipynb)
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- Gaussian elimination and Gauss–Jordan.
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- LU decomposition.
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- Cholesky decomposition.
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- Iterative methods: Jacobi and Gauss-Seidel.
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- Examples with `numethods.solvers`.
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3. [Tutorial 3: Orthogonalization and QR Factorization](./tutorial3_orthogonalization.ipynb)
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- Inner products and orthogonality.
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- Gram–Schmidt process (classical and modified).
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- Householder reflections.
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- QR decomposition and applications.
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- Examples with `numethods.orthogonal`.
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4. [Tutorial 4: Root-Finding Methods](./tutorial4_root_finding.ipynb)
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- Bisection method.
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- Fixed-point iteration.
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- Newton’s method.
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- Secant method.
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- Convergence analysis and error behavior.
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- Trace outputs for iteration history.
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- Examples with `numethods.roots`.
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- [Polynomial Regression Demo](./polynomial_regression.ipynb)
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- Step-by-step example of polynomial regression.
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- Shows how to fit polynomials of different degrees to data.
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- Visualizes fitted curves against the original data.
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