Vector Calculus · Computational Laboratory, Integrative Problems, and Curriculum Organization · Introduction

Introduction

What this guide covers

Implementation in Python of multivariate visualization, symbolic and automatic differentiation, first and second order numerical optimizers and Monte Carlo integration. Four major integrative problems with step-by-step mathematical deduction and complete curricular organization in 24 study blocks.

Overview

Topics covered

Introduction
Computational Laboratory, Integrative Problems and Curriculum
Multivariate Computational Laboratory with Python
30.0. Reproducible Environment and a House Rule
30.1. Visualization of Surfaces, Contours and Gradient Fields
30.2. Symbolic and Automatic Differentiation

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

\iint_D f(\mathbf{x}) d\mathbf{x} \approx \frac{|\Omega|}{N} \sum_{i=1}^N f(\mathbf{X}_i) \mathbb{I}_{\{\mathbf{X}_i \in D\}}.

View LaTeX source

\iint_D f(\mathbf{x}) d\mathbf{x} \approx \frac{|\Omega|}{N} \sum_{i=1}^N f(\mathbf{X}_i) \mathbb{I}_{\{\mathbf{X}_i \in D\}}.