![]() The key to understanding tensor calculus at a deep level begins with understanding linear and multilinear functions between vector spaces. If you haven't taken an advanced linear algebra class, dealing not just with matrices and row reduction, but with vectors, bases, and linear maps, do that. Is my current knowledge in calculus and physics + dynamics enough, or do I need to first learn a few more concepts in mathematics in order to begin attacking tensor calculus problems?ĭROP EVERYTHING AND GO STUDY LINEAR ALGEBRA How should I approach tensor calculus? through a physics or through a mathematics perspective?įrom what I've seen, tensor calculus seems very abstract and more towards the proving side of the spectrum (like a pure mathematics subject), it doesn't look "practicable" as appose to other calculus courses where I could go to any chapter in the textbook and find many problems to practice and become familiar with the concept. All of these sources seem quite different and seem like I require much more advanced topics in mathematics in order to understand. I've also seen many other textbooks on continuum mechanics and tensor analysis for mathematicians/physicists. I want to learn tensor calculus in order to study more advanced mathematics and physics such as General Relativity, Differential Geometry, Continuum Mechanics etc. I don't know what I should take from these lectures and notes and what part of the work to focus on in order to start practicing as soon as possible. I have been through the first 3 chapters and watched the first 5 videos, but I don't seem to understand the content. ![]() ![]() Other textbooks go much more in depth in advanced math topics. I've started self studying tensor calculus, my sources are the video lecture series on the YouTube channel "MathTheBeautiful" and the freeware textbook/notes "Introduction to Tensor Calculus" by Kees Dullemond & Kasper Peeters. I have completed a course in dynamics, calculus I, calculus II and calculus III. If you have studied the book thoroughly, you will be prepared to start working on the physics of gravitation as described by general relativity.I am currently a 3rd year undergraduate electronic engineering student. This book serves as a good basis for mastering tasks. For exercises, there are enough examples in the relevant textbooks that can be used to deepen a topic. For this purpose, many examples and detailed extra introductions have been made. And it is thus the stage on which the physical processes and procedures show themselves.Ĭalculation tasks have been deliberately omitted. Space is a component of the representation of the physical real. Therefore, the emphasis in this textbook has been placed on understanding space in its geometric configuration. General relativity is in its deeper sense a geometric theory. ![]() Great importance is always attached to the clarity of the explanations and derivations of the topics. This textbook starts with basic topics such as vector space and vectors (chapter 1), dual space and covectors (chapter 2), tensors (chapter 3), etc. Some knowledge of linear algebra and analysis are required. This book is intended for physics students who want to prepare for lectures on general relativity. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” Albert Einstein Start learning the foundations of General Relativity today… “Imagination is more important than knowledge.
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