Understanding Vector Calculus & Trigonometry for Physics

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SUMMARY

This discussion centers on the challenges faced by individuals in understanding vector calculus and trigonometry as they apply to physics. The user expresses difficulty in grasping the combination of derivatives with vectors, specifically in the context of particle motion represented by the vector equation r(t) = r(i*coswt + j*sinwt). Recommendations for clear and intuitive textbooks include "Trigonometry" by I. M. Gelfand and Mark Saul, as previous attempts with "Calculus: An Intuitive and Physical Approach" by Morris were unsatisfactory.

PREREQUISITES
  • Basic understanding of trigonometry
  • Fundamental knowledge of vectors
  • Familiarity with calculus concepts, particularly derivatives
  • Ability to interpret vector equations in physics
NEXT STEPS
  • Research "Vector Calculus for Engineers" to understand applications in physics
  • Study "Calculus: Early Transcendentals" by James Stewart for a comprehensive calculus foundation
  • Explore online resources for visualizing vector motion and derivatives
  • Investigate "Physics for Scientists and Engineers" by Serway for practical applications of calculus in physics
USEFUL FOR

This discussion is beneficial for students in physics, particularly those struggling with the integration of vector calculus and trigonometry, as well as educators seeking effective teaching resources.

christian0710
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Hi.

Every time i read physics I feel so discouraged by my lack of understanding in terms of vector calculus and trigonometry. I do understand basic trigonometry and basic vectors but when professors or textbooks move onto combining derivatives with vectors i lack understanding of which rules apply to vectors when combined with calculus, and also how to interprete it. I really need some good book recomendations for brushing up on this and understanding it clearly and intuitively.

And example would be the motion of a particle where r(t) is a vector and i,j are unit vectors.
r(t) = r(i*coswt + j*sinwt)

The professor says "we can see from this that the length of the vector is one" But for me this does not make sense, how can we see this, and how do we apply the length formyla |r|=sqrt(a^2 + b^2) on the r(t) equation?

Please help me with some good physics/calculus math books, that are easy and clear to understand and explain the subjects in detail.

I did try Calculus: An Intuitive and Physical Approach by Morris, but i don't find that it explains trigonometry very well and had to quit after the first 100 pages.
 
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Try to get I. M. Gelfand and Mark Saul "Trigonometry".
 

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