VECTOR CALCULUS: FORMULATIONS, APPLICATIONS AND PYTHON CODES

This unique compendium deals with the differentiation and integration of vector functions. It examines critical effects and extracts important features using powerful tools of differentiation and integration. Techniques and codes for computing the divergence, curl, and gradients of a given field function, which reveal the mathematical behavior of the vector field, are discussed. Green's theorem, Stokes's theorem, and Gauss's formula, along with their novel extensions, are presented in detail with applications such as the smoothed gradient method.

Written in Jupyter notebook format, the book offers a unified environment for theory description, code execution, and real-time interaction, making it ideal for reading, practicing, and further exploration.

Contents:

• Introduction
• Preliminaries: Vectors and Operators
• Integration of Vector Fields along Curves
• Green's Theorems and Applications
• Surface Integrals
• The Divergence Theorem
• Stokes' Theorem
• Gauss's Formula and Beyond
• Conservative and Divergence-Free Fields
• Gradient Smoothing Methods

Readership: Researchers, professionals, academics and graduate students in engineering mechanics, mechanical engineering and calculus of variations.