What Math Should I Know for Classical and Quantum Mechanics?

[intwo]

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!

 

[nnnm4]

Linear Algebra for quantum.

 

[intwo]

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?

 

[0xDEADBEEF]

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.

 

[pmacias]

I understand the importance of having a strong foundation in mathematics in order to fully grasp the concepts of Classical and Quantum Mechanics. While it may be unfortunate that your scheduling conflicts prevent you from taking the prerequisite mathematics courses, it is great that you have already taken differential calculus, integral calculus, and vector calculus, and will be taking an Ordinary Differential Equations course over the summer. These courses will provide you with a solid understanding of the fundamental mathematical concepts needed for Classical and Quantum Mechanics.

In terms of additional resources, I would recommend looking into textbooks such as "Mathematical Methods in the Physical Sciences" by Mary L. Boas, "Mathematical Methods for Physicists" by George B. Arfken and Hans J. Weber, and "Mathematical Physics: A Modern Introduction to Its Foundations" by Sadri Hassani. These books cover the necessary mathematical concepts in a clear and thorough manner.

Additionally, there are many online resources available such as Khan Academy, MIT OpenCourseWare, and Coursera that offer free courses and tutorials on various mathematical topics. It may also be helpful to seek out online forums or study groups where you can discuss and practice these concepts with other students.

In terms of a sequential list, I would suggest focusing on the following topics: linear algebra, complex analysis, partial differential equations, and Fourier analysis. These concepts are essential for understanding Classical and Quantum Mechanics and will also be useful in other areas of physics.

I hope this helps and I wish you all the best in your studies. With dedication and determination, I have no doubt that you will be able to successfully tackle the mathematical prerequisites and excel in your Classical and Quantum Mechanics courses.