Introduction To Einstein S Summation Notation
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Introduction to Einstein's Summation Notation
Author: Hans-Friedrich Pfeiffer
language: en
Publisher: BoD – Books on Demand
Release Date: 2023-02-20
This book is about Einstein's Summation Notation (ESN). It explains the rules for correct use of ESN-notation, covering the Kronecker-symbol and the Levi-Civita-symbol. Examples are taken from Linear Algebra (vector - and matrix - calculation) as well as functional analysis (diferential operators gradient, curl, divergence). The book aims at students of physics who want to deal with the Special - and General Theory of Relativity by Albert Einstein, as the correct use of ESN in this area is essential.
A Visual Introduction to Differential Forms and Calculus on Manifolds
This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.
Practical Guide to Coordinate Transformations
Author: Hans-Friedrich Pfeiffer
language: en
Publisher: BoD – Books on Demand
Release Date: 2025-05-16
This practical and comprehensive guide is designed for students, engineers, and scientists who wish to deepen their understanding of coordinate transformations in Euclidean space. With a clear focus on curvilinear coordinate systems and tensor calculus, the book builds from foundational concepts to advanced mathematical tools essential for theoretical and applied physics. Key topics include the Einstein Summation Convention, vector calculus in index notation, the role of the metric tensor and Christoffel symbols, and the transition from Cartesian to curvilinear coordinates. Readers are introduced to differential operators (gradient, divergence, curl, Laplacian) and their generalizations, as well as the principles of tensor algebra and calculus. The guide features: Over 60 fully solved exercises and numerous worked examples. A structured introduction to covariant/contravariant vectors and dual bases. Detailed treatment of the Jacobi matrix, tensor operations, and coordinate transformations. Applications in integration using polar, cylindrical, and spherical coordinates. A reference section listing more than 15 coordinate systems with their metric properties and transformation tools. Supplementary SageMath notebooks are available for download, providing interactive support for key calculations and visualizations. Written in a clear and pedagogical style, this volume lays the groundwork for further study in differential geometry and General Relativity, to be explored in Part II.