I am currently a 3rd year undergraduate electronic engineering student. I have completed a course in dynamics, calculus I, calculus II and calculus III.
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. Other textbooks go much more in depth in advanced math topics. I have been through the first 3 chapters and watched the first 5 videos, but I don't seem to understand the content. 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 want to learn tensor calculus in order to study more advanced mathematics and physics such as; General Relativity, Differential Geometry, Continuum Mechanics etc. I've also seen many other textbooks on continuum mechanics and tensor analysis for mathematicians/physicists. All of these sources seem quite different and seem like I require much more advanced topics in mathematics in order to understand. How should I approach tensor calculus? through a physics or through a mathematics perspective?
From 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.
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?