If you're studying physics and looking for a book to learn tensors for the first time, here are a few recommendations that provide an introduction to tensors with a focus on physics applications:
"A Student's Guide to Vectors and Tensors" by Daniel Fleisch: This book offers a gentle introduction to vectors and tensors, specifically designed for students of physics and engineering. It covers the basics of vectors, matrices, tensors, and their applications in physics. The explanations are clear, and the book includes numerous worked examples and exercises to reinforce understanding.
"Tensor Calculus Made Simple" by Taha Sochi: This book provides a concise and accessible introduction to tensors, focusing on their use in physics and engineering. It covers the essential concepts, notation, and operations of tensor calculus, along with applications in classical mechanics, general relativity, and electromagnetism. The explanations are intuitive, and the book includes worked examples and exercises.
"A Brief on Tensor Analysis" by James G. Simmonds: This book provides a concise introduction to tensors with a focus on mathematical physics. It covers the basics of tensors, including tensor algebra and calculus, and explores applications in continuum mechanics, elasticity theory, and general relativity. The book strikes a balance between mathematical rigor and physics applications, making it suitable for a physics student.
"Tensor Geometry: The Geometric Viewpoint and its Uses" by Dodson and Poston: This book presents tensors from a geometric viewpoint, emphasizing the geometric interpretation of tensors and their applications in physics. It covers tensor algebra, differential forms, and Riemannian geometry, providing a solid foundation for understanding tensors in a geometric context. While it requires some mathematical background, the book is well-suited for physics students interested in the geometric aspects of tensors.
Remember that learning tensors can be challenging, so it's beneficial to work through the examples and exercises in these books actively. Additionally, consulting your course materials and seeking guidance from your professors can provide valuable insights and support in understanding tensors in the context of your physics studies.