Choose First: Theoretical Mechanics I or Methods of Theoretical Physics?

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The discussion revolves around choosing between two physics courses: Theoretical Mechanics I and Methods of Theoretical Physics. Theoretical Mechanics I focuses on Newtonian mechanics, oscillations, and Lagrangian mechanics, while Methods of Theoretical Physics covers advanced techniques like complex numbers and partial differential equations (PDEs). Participants suggest that taking Theoretical Mechanics I first is beneficial, as it lays a strong foundation for understanding physics concepts. There is a consensus that PDEs are not heavily utilized in Theoretical Mechanics, with more emphasis on ordinary differential equations (ODEs) and Fourier series. Some participants recommend delaying the Methods of Theoretical Physics course, suggesting it could be taken before Electromagnetism (E&M) instead. Additionally, there is a preference for numerical methods over PDEs for practical applications in physics.
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So, I have to choose between these two, on which to take first.

Here are descriptions:

Theoretical Mechanics I
An intermediate study of mechanics, including the study of Newtonian mechanics of a single particle and multiple-particle systems, oscillations, motion in noninertial reference frames, gravitation and central-force motion, and Lagrangian mechanics.
Credits: 3.0
Lec-Rec-Lab: (3-0-0)
Semesters Offered: Fall
Pre-Requisite(s): (PH 2200 or PH 2260) and (MA 3520 or MA 3521 or MA 3530 or MA 3560)[\quote]Or, this one, which I think would help out for theoretical mechanics.
Methods of Theoretical Physics
Introduction to the techniques and methods frequently encountered in advanced physics with a particular emphasis on application to physical problems. Topics include, but are not limited to, complex numbers, vector analysis, partial differential equations, and integral transforms.
Credits: 3.0
Lec-Rec-Lab: (3-0-0)
Semesters Offered: Fall
Pre-Requisite(s): MA 3160 and (MA 3520 or MA 3521 or MA 3530 or MA 3560)
[\quote]

So, any opinions on which first?
 
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I took these classes together and it was perfect. If I had to pick 1 it would be mechanics. The math methods class can be delayed a bit... Though I would suggest it before taking E&M.
 
Alright, I don't have to take them technically until next year, and this year I'm taking Thermo and stat mechanics in the spring. So PDEs aren't used heavily in theo mech.? Because I'm also planning on taking an intro to either PDEs or numerical solutions to PDEs in the spring as well. Can't decide between these two as well.
 
Nope PDE's shouldn't be used much at all in mechanics. Though you will see a lot of ODE's and maybe some Fourier series. I took PDE's alongside E&M and it complimented quite nicely.
 
Hmm alright, well between the two I think numerical solving would be more helpful. Any thoughts?
 
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Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...
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