What are basis vectors, one forms, and basis one forms?

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Homework Help Overview

The discussion revolves around the concepts of basis vectors, one forms, and basis one forms, with a particular focus on understanding their definitions and relationships. The original poster expresses confusion regarding these topics, especially in relation to covariance and contravariance.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to clarify their understanding of basis vectors and their role in coordinate systems, while also seeking insights into covariance and contravariance. Participants inquire about the original poster's mathematical background to gauge their familiarity with relevant concepts.

Discussion Status

The discussion is ongoing, with the original poster receiving suggestions for resources to further their understanding. There is an acknowledgment of the original poster's current level of study and the complexity of the topics at hand, indicating a productive exchange of information.

Contextual Notes

The original poster is transitioning into more advanced topics in mathematics, including tensor calculus, and is balancing their studies with other academic responsibilities.

Varnick
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I'm not sure this is the correct forum section for this question, if not, please move me. Essentially, I'm looking for help understanding what basis vectors, one forms, and basis one forms are. I'm fairly sure I get basis vectors, I would describe them as a description of a co-ordinate system, and also function similar to unit vectors. One of the main areas related to this that confuses me is covariance and contravariance, could anyone shed some light on this? Many thanks,

V
 
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What's your mathematical experience? Do you know elementary linear algebra and calculus?
 
I'm going into my A2 year (UK education system, just before college for you USers). I've completed work in linear algebra and calculus, and have looked at very basic vector calculus, partial differentiation, matrices, and some tensor analysis (now starting to look at tensor calculus, when my mind isn't exploding). I'm starting to understand what the geometries I listed are mathematically, but not qualitatively. Any help appreciated,

V
 
OK, you should be able to handle the following reference with no problem then.

A Geometric Approach to Differential Forms.

It's a free textbook on differential forms aimed at students who have studied multivariable calculus and a little linear algebra.
 
Thanks, I'll get reading that next week, got to finish a paper for Tuesday.

V
 

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