Mathematical Foundations · Multivariable Calculus

Vector Calculus: Specific Applications to Probability and Mathematical Statistics

Public introduction · full guide in Eikos

Introduction

What this guide covers

An integral and mathematically rigorous treatise on the theory of differential operators and multivariate integrals, density analysis on varieties, stochastic quadratic forms, Fisher-Rao metrics and the geometric foundations of asymptotic theory.

Overview

Topics covered

  • Introduction
  • Vector Calculus in Probability and Statistics
  • Fundamentals and Differential Operators in
  • Taylor Multivariable Development with Quadratic Form
  • Random Vectors and Multivariable Transformations
  • Polar and Hyperbolic Coordinates in Probability

Related concepts

Main connections

  • Linear algebra & matrices
  • Calculus & differentiation
  • Variance & standard deviation
  • Maximum likelihood estimation
  • Normal (Gaussian) distribution
  • Conditional probability & independence

Compatible notation

Mathematical sample in LaTeX

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

∇≡(∂∂x1,∂∂x2,…,∂∂xn)T.
View LaTeX source\nabla \equiv \left( \frac{\partial}{\partial x_1}, \frac{\partial}{\partial x_2}, \dots, \frac{\partial}{\partial x_n} \right)^T.