Numerical Analysis

The "Mathematical Python" website covers most (~60%) of this page in the best form possible. There's a series of lectures for computational physicists that mostly covers theoretical information related to Numerical Analysis.

The three core things in Numerical Analysis that you will need are: Numerical Differentiation, Numerical Integration, and Numerical Root Finding. There's one more thing, however, which is way less popular Numerical Linear Algebra.

1. Numerical Differentiation

Numerical Differentiation means finding the derivative of a function numerically. The basic methods are constructed by approximating the derivative directly from its definition. A subclass of methods for doing numerical differentiation is automatic differentiation (AD for short), which is a way more intelligent approach. In general, numerical differentiation is a very big field itself.

Basic Methods for Numerical Differentiation.
Forward-Mode Automatic Differentiation via High Dimentional Algebras

2. Numerical Integration

Analogous to the previous subtopic, this one is about computing a function's integral numerically.

Basic Numerical Integration Rules mentioned by R. Feynman
Riemann Sums
Trapezoid Rule
Simpson's Rule
A Paper on Automatic Integration

3. Numerical Root Finding

In a nutshell, this subtopic is about solving equations of the form f(x) = 0 for x numerically.

Bisection Method
Secant Method
Newton's Method (important)

4. Numerical Linear Algebra

Matrix Methods for Signal Processing by MITOCW
Matrix Calculus and the Julia Programming Language
Computational Linear Algebra

Numerical Methods for Differential Equations

This topic is too distinct to put it as a 5th subtopic of Numerical Analysis, thus it has been made a separate one for the purposes of logic. I am only going to cover the classic methods of solving DEs numerically, while there are other, more advanced methods (see Differential Equations & ML).

Numerical Solution of Ordinary Differential Equations by R. Sureshkumar Euler's Method
Euler's Method (Video Example)
First Order Equations (short)
Runge-Kutta Methods (Wikipedia)