Multivariable differential calculus refresher?

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SUMMARY

This discussion focuses on resources for refreshing multivariable differential calculus, particularly for physicists. The recommended texts include "Div, Grad, Curl and All That: An Informal Text on Vector Calculus" by H.M. Schey, which is ideal for vector calculus, and "Mathematical Methods in the Physical Sciences" by George B. Arfken and Hans J. Weber, which covers coordinate systems, partial derivatives, the multivariable chain rule, Taylor series, and Lagrange multipliers. Both books are noted for their abundance of exercises and suitability for self-study, targeting undergraduate students.

PREREQUISITES
  • Understanding of basic calculus concepts
  • Familiarity with vector calculus
  • Knowledge of coordinate systems
  • Basic proficiency in mathematical methods used in physical sciences
NEXT STEPS
  • Explore "Div, Grad, Curl and All That: An Informal Text on Vector Calculus" by H.M. Schey
  • Study "Mathematical Methods in the Physical Sciences" by George B. Arfken and Hans J. Weber
  • Practice exercises on partial derivatives and the multivariable chain rule
  • Research Lagrange multipliers and their applications in optimization problems
USEFUL FOR

Students and professionals in physics, mathematics, and engineering who seek to strengthen their understanding of multivariable differential calculus and vector calculus concepts.

Euclid
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I need a refresher on my multivariable differential calculus. Does anyone know of something brief with lots of exercises (maybe something geared towards physicists)?
 
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there are no exercises but posts 115-116 of my thread who wants to be a mathematician summarizes basic several variable differential calculus.
 
Since you are a physicist, I presume you are mostly interested in vector calculus and the book for that is:

div, grad, curl and all that: an informal text on vector calculus

the author is h.m. Schey

If you want to review the other things, like coordinate systems, partial derivatives, multivar chain rule, taylor series, lagrange multipliers, then I recommend to you the book by Boas, Mathematical Methods in the Physical Sciences.

Edit: both books have loads of exercises, and are especially well suited towards self-study (the target audience is undergraduates).
 

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