Calculus: One and Several Variables by Salas, Etgen, Hille

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Discussion Overview

The discussion revolves around the textbook "Calculus: One and Several Variables" by Salas, Etgen, and Hille, focusing on its suitability for undergraduate mathematics and its application in theoretical physics, particularly in quantum field theory (QFT). Participants evaluate the book's content, clarity, and pedagogical approach.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants appreciate the book's exercises for progressively teaching section concepts but criticize the dense jargon and brevity of explanations.
  • One participant suggests that mathematics texts should be more accessible to students rather than relying heavily on jargon, proposing that popular calculus texts could benefit from being split into multiple volumes.
  • Another participant notes that while the book has a decent treatment of multivariate concepts and proves most theorems, it falls short in introducing fundamental properties, such as the least upper bound property of R, until later chapters.
  • There are inquiries about the book's adequacy for theoretical physics undergraduates, with some arguing that it may not be sufficient for advanced topics like QFT, suggesting that students should seek additional resources beyond this text.

Areas of Agreement / Disagreement

Participants express mixed opinions about the book's effectiveness, with some agreeing on its limitations while others find it acceptable for introductory calculus. The discussion remains unresolved regarding its suitability for advanced theoretical physics studies.

Contextual Notes

Some participants highlight the book's reliance on dense language and delayed introduction of key concepts, which may affect comprehension and learning outcomes. The discussion reflects varying expectations for undergraduate calculus texts.

For those who have used this book

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micromass
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This book is good in that the exercises clearly teach the section concepts in a progressive fashion. It is not so good in that the explanations of the material seem to aim to use as few words as possible, and rely on some VERY dense jargon to save paper.

A few extra words per sentence would make this a great book. It's a failing I find common to 90% of mathematics texts. Popular calc texts should be split into 3 separate volumes, IMO. The explanations need to be fleshed out and accessible and understandable to students - not just math professors.
 
salas and hille was a classic, o do not remember the other guy.
 
Book isn't bad but isn't great either. Seems to straddle an unfortunate line in level of material between something like Apostol or Spivak and Stewart. Much better IMO to just sit down and work through Spivak etc. But it has an okay treatment of multivariate concepts and actually proves most of the theorems.

Although, looking back on it, I am shocked to say they didn't introduce the least upper bound property of R until chapter 11. Which is terrible...
 
Hi micromass, I just want to ask if Calculus by Salas is enough for theoretical physics undergraduates? I am curious because I want to do research in QFT in grad school and I'm thinking if my investment for Salas is enough.
 
shinobi20 said:
Hi micromass, I just want to ask if Calculus by Salas is enough for theoretical physics undergraduates? I am curious because I want to do research in QFT in grad school and I'm thinking if my investment for Salas is enough.
Salas, Hille, Etgen's Calculus is okay but if you want to do QFT, you pretty much need to go beyond this text. I have used this book for my elementary calculus classes only.
 

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