Quick introduction to tensor analysis

TL;DR

This book offers a concise, DIY-style introduction to tensor analysis, focusing on core definitions and theorems with exercises for self-study, aiming for quick and effective learning.

Contribution

It presents a minimal, exercise-based approach to tensor theory, emphasizing understanding through active engagement rather than exhaustive proofs.

Findings

Provides a quick, self-guided learning method for tensor analysis

Includes numerous exercises to reinforce understanding

Focuses on core concepts and formulas without detailed proofs

Abstract

I wrote this book in a "do-it-yourself" style so that I give only a draft of tensor theory, which includes formulating definitions and theorems and giving basic ideas and formulas. All other work such as proving consistence of definitions, deriving formulas, proving theorems or completing details to proofs is left to the reader in the form of numerous exercises. I hope that this style makes learning the subject really quick and more effective for understanding and memorizing.