Are Differential Equations Essential for Waves and Oscillations in Physics?

[Howers]

For this second year course, my school reccommends Differential Equations and Calc II. Are they neccessary?

Description: Complex notation; free, damped and forced harmonic oscillations; resonance; AC circuits; coupled oscillators; normal modes; traveling waves; simple harmonic wave; wave equation; wave impedance; transverse and longitudinal waves; flow of energy in waves; reflection and transmission at interfaces; group and phase velocity; Fourier series and Fourier transforms.

 

[G01]

I would say that both Calc II and DiffEQ are necessary for the course you have described. Fourier Transforms involve integration (Calc II) and the wave equation is a differential equation, so if your going to be solving the wave equation with different boundary condition etc., knowing how to solve differential equations will also be necessary. The study of damped and forced oscillations will also require differential equations if covered quantitatively. If you know the basics of Calc II and DiffEQ, you might be able to teach yourself the math as you go, but if you don't know much about either, I'd recommend taking Calc II and DiffEQ.

 

[Howers]

Alright. I am definitely taking calc II, but was hoping to postpone DiffEq until summer. The course is very quantitative I've read. The book we're using is The Physics of Vibrations and Waves by H.J Pain.

 

[momentum_waves]

Pain's book is excellent. Lot's of reading, but a very worthwhile reference.

 

[proton]

Alright. I am definitely taking calc II, but was hoping to postpone DiffEq until summer. The course is very quantitative I've read. The book we're using is The Physics of Vibrations and Waves by H.J Pain.

DE's course shouldn't be quantitative, if that's what you are referring to by 'quantitative'. You can take it right after calc II with no worries

 

[user101]

DE is absolutely necessary. DE's rule the world, really.

 

[Howers]

No, I mean W&O are very quantitative. Or in other words, very rigorous.

I am taking calc II but was wondering if I can take DE later on, because as it stands I already have 4 math and physics courses and would rather do DE in the summer so I can replace my fifth course with some writing like philosophy. The only problem is I don't want to suffer in Waves and Oscillations, becasue the prof reccommends we take DE now. However, it is not REQUIRED. In the end, I will definitely take DiffEqn, I just want to know if I can get by this course, physical chem, thermal, and E&M without taking it along side them.

If I can't, I have no choice but to do it now.

 

[^_^physicist]

I just want to know if I can get by this course, physical chem, thermal, and E&M without taking it along side them.

All of those classes will require a degree of fluency with diff. eqs.
P. Chem, Thermal, and Waves & Oscillations will all need an intro level or higher diff. eq knowledge to be enjoyable or, in my opinion, pass-able. E&M, depends on the way the course is directed, I have seen some syallibus's that have designed the course to be more integral equation based than differential equation based, but if the course is attempting to work at very general levels, than differential equations are necessary (and if you are looking for the most general than you need Tensor Anaylsis and Differential Geometry!).

Take the Diff. Eq course, pospone taking Physical Chemistry or Thermo, and try to learn as much as you can in the Waves course in terms of techiques to solve differential equations, as it coupled with diff. eq. would be a great learning experance (albet a bit painful).