- #1
galois427
- 16
- 0
whats a good intro book to tensors and manifolds?
Tide said:THE book on tensor calculus is by Synge and Schild (Tensor Calculus) but I don't know whether it's still in print.
Tensors and manifolds are mathematical objects used to describe and analyze geometric phenomena. Tensors are multi-dimensional arrays or matrices that represent the relationships between different quantities, while manifolds are abstract spaces that have curvature and can be described using coordinates.
Tensors and manifolds have many applications in physics, engineering, and computer science. They are used to model and understand complex physical systems, such as fluid dynamics and general relativity. Additionally, they are essential for advanced topics in machine learning and data analysis.
There are many great introductory books on tensors and manifolds, but one highly recommended book for beginners is "Tensor Calculus Made Simple" by Taha Sochi. It provides a clear and concise explanation of the fundamentals of tensors and manifolds, with many examples and exercises to reinforce concepts.
A basic understanding of linear algebra and calculus is necessary for understanding tensors and manifolds. It is also helpful to have some familiarity with differential geometry and multivariable calculus, but many introductory books provide a review of these topics.
Tensors and manifolds have a wide range of applications in various fields, such as physics, engineering, and computer science. For example, they can be used to model the behavior of materials under stress, analyze the movement of particles in fluid flow, or improve the accuracy of machine learning algorithms. By understanding tensors and manifolds, you can gain valuable skills that can be applied in many different industries and research areas.