Vector Analysis: Bridging Math and Physics with Rigor and Visuals

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Discussion Overview

The discussion revolves around finding suitable resources for understanding vector analysis, particularly for individuals who have an interest in both mathematics and physics. Participants explore various textbooks and materials that provide rigorous content complemented by visuals and examples.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants suggest specific textbooks, including works by Marsden and Bamberg & Sternberg, as potential resources for vector analysis.
  • One participant expresses skepticism about the quality of the suggested books, citing poor reviews and questioning their suitability for the intended audience.
  • Another participant defends the value of the suggested books, attributing negative reviews to unprepared students rather than the quality of the texts.
  • Additional recommendations include Spivak's "Calculus on Manifolds," Munkres' "Analysis on Manifolds," and H. M. Edwards' "Advanced Calculus: A Differential Forms Approach," with a note that the last one may align closely with the original request.
  • A participant mentions a specific resource by Bowen, highlighting its usefulness despite some typographical issues.
  • There is a reference to Marsden & Tromba's "Vector Calculus" as a typical book on the subject, which one participant realizes has already been mentioned.
  • A later reply introduces a paper on differential forms that has been adapted into a book, suggesting it as an additional resource for those interested in that area.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best resources, with differing opinions on the quality and suitability of the suggested textbooks. Multiple competing views remain regarding the effectiveness of the materials discussed.

Contextual Notes

Some participants express concerns about the preparedness required to tackle the recommended texts, suggesting that familiarity with vector calculus and related concepts may be necessary.

ice109
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something for a mathematician that likes physics or a physicist that likes math. rigorous but with pictures and examples and the such?
 
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I like them both...especially the Bamberg&Sternberg one.
 
ice109 said:
the first one is a calc book apparently and has terrible reviews and the second one is a math methods book with terrible reviews but thanks anyway
I would take terrible reviews on Amazon.com with a grain of salt. Many of those reviews are by lazy, underprepared, or unprepared students who are looking to vent their frustrations with a book that they were not willing, ready or able to tackle. If none of those suggestions appeal to you, some standard textbooks for a second course in vector calculus / calculus on manifolds include Spivak, Calculus on Manifolds; Munkres, Analysis on Manifolds; C. H. Edwards, Advanced Calculus of Several Variables; and H. M. Edwards, Advanced Calculus: A Differential Forms Approach. Of those, the last book by H. M. Edwards is probably the closest to what you're looking for. But I would warn you that, since you cannot identify that vector analysis is the same as vector calculus or that it would likely be covered fairly extensively in a math methods book, you may not be adequately prepared to tackle any of these books.
 
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You might like
http://www1.mengr.tamu.edu/rbowen/
 
Last edited by a moderator:
Bowen's book posted by robphy is really good, if you're willing to deal with ugly typesetting and some typos. Edwards' book on advanced calculus with differential forms is a current project of mine, so I'll let you know how it goes. A more typical book on vector analysis though,is Marsden & Tromba's Vector Calculus. EDIT: which I just realized has already been posted. Sorry.

YET ANOTHER EDIT: If you'd like to learn about differential forms, here's a paper on the arXiv which was turned into a book: A Geometric Approach to Differential Forms
 
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