What Math Should I Know for Classical and Quantum Mechanics?

AI Thread Summary
To prepare for Classical and Quantum Mechanics courses without completing all prerequisite math classes, a solid foundation in several key mathematical concepts is essential. Important topics include linear algebra, particularly focusing on scalar products, dual space vectors, and Hilbert spaces, as well as variational calculus and operators with their eigenfunctions. Additionally, understanding Lagrange multipliers, commutators, and Lie brackets will be beneficial. Resources such as textbooks and online materials that thoroughly explain these concepts are recommended for effective self-study. Mastering these areas will significantly aid in grasping the complexities of both mechanics disciplines.
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I'm interested in taking Classical and Quantum Mechanics courses next year at my university; however, I won't be able to take the prerequisite mathematics courses due to scheduling conflicts. I have taken differential calculus, integral calculus, and vector calculus and I will be taking an Ordinary Differential Equations course over the summer. If anyone could supply me or direct me to a list of suggested concepts, it'd be extremely beneficial. Books, websites, etc - whatever will explain the concepts thoroughly. A detailed, sequential list would be highly appreciated.

Thanks!
 
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Linear Algebra for quantum.
 
nnnm4 said:
Linear Algebra for quantum.

Thank you, but I was wondering if you could be a little more specific. I understand that large-scale concepts such as linear algebra and partial differential equations are necessary, but what specific concepts should I note to help me with Classical and Quantum Mechanics?
 
Lagrange multipliers, scalar products, dual space vectors, commutators, lie brackets, variational calculus, principal value decomposition, Hilbert spaces, operators and their eigenfunctions

That should cover your bases.
 

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