TENSORS FOR PEDESTRIANS

Tensor for Pedestrians is an accessible aid for physics and engineering undergraduates who seek a deeper understanding of tensors at an intuitive level. The book is intended as a self-study introduction to differential geometry, curvature, and Cartan moving frames. The subjects treated are planned to transit the student from the standard vector calculus taught in introductory courses towards modern differential geometry with its various applications. Presentation of the material is leisurely paced — as befits pedestrian learners. Chapters are self contained and equations in the text are fully explained without obscure and annoying gaps. The book is richly supplemented by many examples and detailed problems and solutions at the end of each chapter. All in all, the book will enable a beginner or an intermediate learner to explore and appreciate the beauty of the fundamental concepts presented.

Contents:

• Prelude to Tensors
• The One-Form Space
• Curvilinear Coordinates
• General Tensors
• Tensor Variants
• Parallel Transport
• Tensor Derivatives
• Differential Forms
• Derivatives of Forms
• Integrating Forms
• Gaussian Curvature
• Riemannian Curvature
• Curvature via Cartan

Readership: Undergraduates of mathematics and engineering disciplines. Also physics undergraduates, especially those interested in particle physics and quantum fields, continuum physics, astrophysics and other disciplines of physics requiring differential geometry.