Interesting book explaining the principle of least action in detail

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SUMMARY

The discussion centers on the principle of least action, a fundamental concept in mechanics, and its mathematical foundations. A recommended resource for understanding this principle is Taylor's book on classical mechanics, specifically the chapters on Variational Calculus and Lagrangian Mechanics. To comprehend Taylor's material, a solid understanding of vector calculus is essential, which can be learned from the suggested text by Marsden and Tromba. Additionally, a foundational knowledge of single variable calculus is necessary, although no specific beginner resources were provided for that topic.

PREREQUISITES
  • Single Variable Calculus
  • Vector Calculus
  • Variational Calculus
  • Lagrangian Mechanics
NEXT STEPS
  • Read Taylor's book on classical mechanics, focusing on Variational Calculus and Lagrangian Mechanics.
  • Study Marsden and Tromba's text to gain a solid understanding of vector calculus.
  • Explore introductory resources on single variable calculus to build foundational knowledge.
  • Research the historical context and applications of the principle of least action in physics.
USEFUL FOR

Students pursuing mathematics or physics, particularly those interested in mechanics and the mathematical principles underlying physical theories.

Isolde
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Hi, I'm doing further maths and I would like to study maths at university. I have been asked to read a number of books to put on my personal statement, and as I am finding it difficult coming to terms with the fact that mechanics is taught as maths and not physics, a maths don at Oxford suggested that I should look into the principle of least action, apparently what all mechanics is based on (I'm sure that it's fairly obvious that I know nothing about this, so forgive me if I'm wrong). I was wondering if anyone knew of a readable book that explains the concept and the history surrounding it that I could read. Thanks!
 
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I would highly recommend Taylor's book on classical mechanics:

https://www.amazon.com/gp/product/189138922X/?tag=pfamazon01-20

You'll have to read the chapter on Variational Calculus and then the chapter on Lagrangian Mechanics. Once you understand those, the variational principle will make sense.

However, keep in mind that you'll need to have a solid grasp of vector calculus in order to understand the material in Taylor. Personally I learned vector calculus from this text:

https://www.amazon.com/gp/product/1429215089/?tag=pfamazon01-20

Naturally, in order to understand vector calculus you first need to understand regular old single variable calculus. Though on that subject I know of no good introductory books, because personally I was taught basic calculus by a weekly private tutor, and then I skipped straight to advanced texts like Spivak:

https://www.amazon.com/gp/product/0914098918/?tag=pfamazon01-20

But Spivak definitely isn't for beginners.
 
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