Vector Calculus · Multivariable Integral Calculus, Probability, and Fundamental Theorems · Introduction

Introduction

What this guide covers

From double and triple integrals to the change of variable by Jacobian transformations, polar, cylindrical and spherical coordinates. Fundamentals of joint probability, marginal and conditional densities, covariance, multivariate normal and the Box-Muller algorithm. Vector fields, divergence, curl and the great unification of Green, Stokes and Gauss.

Overview

Topics covered

Introduction
Multivariate Integral Calculus, Probability and Theorems of Vector Analysis
Double Integrals over Rectangles and General Regions of the Plane
15.1 and 15.2. Definition by Riemann Sums and Geometric Interpretation
15.3 and 15.4. Fubini's Theorem and Factorizable Integrals
15.5 and 15.6. General Regions and Reversal of Order

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

\iint_R f(x,y) dA = \lim_{\|P\| \to 0} \sum_{i=1}^m \sum_{j=1}^k f(x_{ij}^*, y_{ij}^*) \Delta A.

View LaTeX source

\iint_R f(x,y) dA = \lim_{\|P\| \to 0} \sum_{i=1}^m \sum_{j=1}^k f(x_{ij}^*, y_{ij}^*) \Delta A.