Vector Calculus · Differential Calculus, Optimization, and Matrix Calculus · Introduction

Introduction

What this guide covers

Of the partial derivatives and the tangent plane to the Jacobian matrix, the Hessian and the multivariate Taylor expansions. Rigorous structural connections with the Delta method, Fisher Information, Laplace approximation, maximum likelihood estimation, least squares (OLS), Lagrange multipliers and numerical optimization.

Overview

Topics covered

Introduction
Multivariate Differential Calculus, Optimization and Matrix Calculus
Scalar Functions of Various Variables, Domains and Level Curves
3.1. Multivariate Scalar Functions
3.2. Analytical and Topological Determination of Domains
3.3. Graphic Representation: Surfaces, Sections and Projections

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

f: D \subset \mathbb{R}^n \to \mathbb{R}.

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f: D \subset \mathbb{R}^n \to \mathbb{R}.