Prerequisites needed to grasp analytical mechanics.

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A solid understanding of calculus, including vector calculus, and linear algebra is essential for grasping analytical mechanics. While knowledge of differential geometry, topology, and manifolds can enhance comprehension, they are not strictly necessary for an initial encounter with the subject. It is advisable to focus on the physical concepts first before delving into advanced mathematical frameworks. Familiarity with the physics will provide a foundation for later studies in more complex mathematical areas. Ultimately, the approach should align with individual goals and current understanding.
amjad-sh
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1.What are the mathematical prerequisites needed to grasp analytical mechanics conceptually and technically?

2.To understand the very concept of analytical mechanics, do I need to train my self in Euclidean and Riemannian manifolds, and do I need to have good knowledge in topology and differential geometry?

Hope I would get good answers, and thanks in advance!
 
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I think it depends a lot on your goals and your current level of understanding. For a first encounter with analytical mechanics, I believe you can learn a lot without differential geometry, but with a good understanding of calculus (including vector calculus) and linear algebra. In fact, I would recommend that you focus on the physics first and, after you have familiarised yourself with this and are interested, proceed to learn more about formulations using modern differential geometry and topology.
 
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