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numerical-analysis-notebooks

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Jupyter notebooks used in the course Numerical Analysis (MAST 334 and MATH 354) at Concordia University

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# Numerical analysis notebooks
This is a collection of Jupyter notebooks developed for the course Numerical Analysis (MAST 334 and MATH 354) at Concordia University. The purpose of these notebooks is to illustrate the most important numerical analysis concepts using simple Python examples and complement theoretical lectures.

For any comments or suggestions, please [contact me](mailto:simone.brugiapaglia@concordia.ca).

## Notebooks

### Preliminaries
1. [Know your (computer's) limits: Floating point arithmetic](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/01_floating_point.ipynb)
2. [A visual tour of algorithms' convergence](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/02_convergence.ipynb)

### Root-finding methods
3. [Bisection: divide et impera](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/03_bisection.ipynb)
4. [Fixed-point iteration: keep calm and apply g(·)](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/04_fixed_point.ipynb)
5. [Going off on a tangent with Newton's method](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/05_Newton.ipynb)
6. [Getting the most out of linear convergence with Aitken's method](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/06_Aitken.ipynb)

### Function approximation
7. [Three ways to perform polynomial interpolation](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/07_interpolation.ipynb)
8. [Cubic splines and Runge's phenomenon](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/08_Splines.ipynb)
9. [Discrete least squares to understand climate change](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/09_Discrete_Least_Squares.ipynb)
10. [Continuous least squares: from the Hilbert matrix to Legendre polynomials
](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/10_Orthogonal_polynomials.ipynb)
11. [The FFT and its application to signal denoising](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/11_Fourier.ipynb)

### Numerical differentiation and integration
12. [Numerical differentiation and Richardson's extrapolation](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/12_differentiation.ipynb)
13. [Efficient numerical integration via composite and Gaussian quadrature rules](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/13_quadrature.ipynb)
14. [Solving differential equations with Euler's method(s)](https://github.com/simone-brugiapaglia/numerical-analysis-notebooks/blob/main/14_Euler.ipynb)

## Acknowledgements

I would like to thank Ben Hersey (Concordia) for providing feedback on these notebooks.

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