Advanced & Applied Topics · Numerical Optimization & Scientific Methods

Numerical methods: numerical differentiation and integration

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction // Advanced Numerical Methods · Theory and Practice

Overview

Topics covered

  • Introduction
  • Differentiation and Numerical Integration
  • Introduction and Epistemological Foundations
  • Taylor Series and the Origin of Finite Differences
  • Forward difference (forward difference)
  • Backward difference (backward difference)

Related concepts

Main connections

  • Calculus & differentiation
  • Maximum likelihood estimation
  • Normal (Gaussian) distribution
  • Linear algebra & matrices
  • Monte Carlo simulation
  • Bayes' theorem & priors

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

f(x+h)=f(x)+hf'(x)+h22f''(x)+h36f'''(x)+h424f(4)(ξ1),ξ1∈[x,x+h]
View LaTeX sourcef(x+h) = f(x) + hf'(x) + \frac{h^2}{2}f''(x) + \frac{h^3}{6}f'''(x) + \frac{h^4}{24}f^{(4)}(\xi_1), \quad \xi_1 \in [x, x+h]