Best Multivariable Calc Textbook for self teaching

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SUMMARY

The discussion centers around recommended textbooks for self-teaching multivariable calculus, specifically for physics majors who have completed proof-based calculus courses. The top recommendation is "Vector Calculus" by Marsden and Tromba, noted for its aesthetic quality and effective "vectors first" approach. Other suggestions include "Intermediate Calculus" by Murray & Protter, which is deemed too basic for those with prior proof experience, and "Advanced Calculus" by Friedman, which is considered more suitable for advanced learners.

PREREQUISITES
  • Understanding of proof-based calculus concepts
  • Familiarity with vector calculus fundamentals
  • Ability to solve complex mathematical problems
  • Basic knowledge of multivariable functions
NEXT STEPS
  • Explore "Vector Calculus" by Marsden and Tromba for a comprehensive understanding of multivariable calculus
  • Review "Intermediate Calculus" by Murray & Protter for supplementary concepts
  • Study "Advanced Calculus" by Friedman for deeper insights into advanced topics
  • Practice solving problems from recommended textbooks to reinforce learning
USEFUL FOR

Students majoring in physics, mathematics enthusiasts, and anyone seeking to deepen their understanding of multivariable calculus through self-study.

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So i did fairly well in both calc I and II, both being proof based (for math majors, and I got an A in both). I am working a job that allows me to read at work this summer, and would like to teach myself some multivariable/vector calc. I am a physics major, but my school requires me to take the proof based version for math majors. What textbook would you recommend? Thanks
 
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Marsden and Tromba, Vector Calculus.

This is probably the most beautiful book ever written.
 
MarcusAgrippa said:
Marsden and Tromba, Vector Calculus.

This is probably the most beautiful book ever written.

That's actually not a bad suggestion. It has problems that really test the material and it uses a "vectors first" approach which is nice. Reading it at work though, that would be difficult IMHO, you would need to do the problems and be quite focused.

One that you could read through but that still contains proofs is Murray & Protter - Intermediate Calculus. I think it's too low level for you because you have done two proof courses already, but if you are reading it in your spare time between phone calls or whatever, it would suffice.

I think you can choose something more grown up though. Advanced Calculus by Friedman for example.
 

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