Tensor Calculus and Differential Forms: From Vector Calculus to the Geometry of Forms

Vector calculus is often taught as a collection of formulas and techniques. Yet behind the operators grad, curl, and div lies a deeper unity.

This book presents calculus through the geometry of differential forms, showing that its core concepts arise from a few fundamental principles: orientation, antisymmetry, and change. Through a gradual and structured development, the reader is guided from vectors to a unified theory that connects algebra, geometry, and physics.

It is intended for those who seek not only to compute, but to understand in depth the structure of space and the nature of calculus.