Vector Calculus: Multivariable Integral Calculus · Rigorous Theory and Advanced Methods · Introduction

Introduction

What this guide covers

A rigorous, geometric and analytical exposition on the theory of integration in Euclidean spaces , vector fields, parametrization of boundary varieties, Green, Gauss and Stokes integral theorems, and their definitive unification through the calculation of exterior differential forms.

Overview

Topics covered

Introduction
Vector Calculus: Multivariable Integral Calculus
Riemann Measurement and Integration in
Zero Measure Sets and Lebesgue-Vitali Characterization
Integration on General Limited Sets and Jordan's Measurability
Multiple Integrals and the Fubini Theorem

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

I = [a_1, b_1] \times [a_2, b_2] \times \cdots \times [a_n, b_n] = \left\{ \mathbf{x} = (x_1, \dots, x_n) \in \mathbb{R}^n \mid a_i \le x_i \le b_i, \; \forall i=1,\dots,n \right\}.

View LaTeX source

I = [a_1, b_1] \times [a_2, b_2] \times \cdots \times [a_n, b_n] = \left\{ \mathbf{x} = (x_1, \dots, x_n) \in \mathbb{R}^n \mid a_i \le x_i \le b_i, \; \forall i=1,\dots,n \right\}.