# Numerical methods
```{sidebar} Numerical methods
Source: [Wikipedia](https://en.wikipedia.org/wiki/Mathematics)
```
### Table of contents:
0. {ref}`mm1_intro_to_modelling`
1. {ref}`nm_interpolation_curve_fitting`
* {ref}`nm_interpolation`
* {ref}`nm_curve_fitting`
* {ref}`nm_extrapolation`
2. {ref}`nm_num_differentiation`
* {ref}`nm_forward_difference`
* {ref}`nm_central_difference`
* {ref}`nm_second_derivative`
3. {ref}`nm_solving_diff_eq`
* {ref}`timestepping_ode`
* {ref}`nm_euler_method`
* {ref}`nm_heun_method`
* {ref}`runge_kutta_method`
* {ref}`successive_over_relaxation`
* {ref}`ftcs_scheme`
* {ref}`nm_btcs_scheme`
4. {ref}`nm_num_integration`
* {ref}`nm_midpoint_rule`
* {ref}`nm_trapezoid_rule`
* {ref}`nm_simpsons_rule`
* {ref}`nm_composite_simpsons_rule`
* {ref}`nm_weddles_rule`
5. {ref}`nm_roots_of_equations`
* {ref}`nm_picards_method`
* {ref}`nm_root_bracketing`
* {ref}`nm_bisection_method`
* {ref}`nm_newton_method`
* {ref}`nm_quasi_newton_method`
* {ref}`nm_secant_method`
6. {ref}`Numerical linear algebra `
* {ref}`nm_gaussian_elimination`
* {ref}`nm_gauss_jordan_elimination`
* {ref}`nm_lu_decomposition`
* {ref}`nm_ill_conditioning_roundoff_errors`
* {ref}`nm_iterative_methods_matrix`
* {ref}`nm_sparse_matrices`
## References
* Material used in this notebook was based on lecture content of Numerical Methods 1 (by Prof. Matthew Piggott) and Numerical Methods 2 (by Prof. Stephen Neethling) at Earth Science and Engineering Department at Imperial College London