What do you wish you had done before?

[integration]

Hi,

I am about to go to college and study engineering physics. I am studying calc based physics and Calculus BC, and some vector calculus (From the Stewart's textbook).

I think I am going to enroll in a introductory physics class that is more advanced than the usual intro for engineers and scientists this fall. My intro mechanics class will use Kleppner&Kolenkow, and my intro electricity will use math tools like Divergence, Grad, Curl to apply Maxwell's equations.

For those of you who went through that big jump between the rather easy high school physics and the more difficult college theoretical physics, what preparation did you wish you had done? I'm specifically interested in the math preparation, but physics advices are more than welcome.

I often hear that the big jump lies in the math. It's weird for me because setting up and solving integrals in calculus BC seems so easy, but when I have to use the same integrals for things like charge distributions, kinematics problems/momentum/acceleration, I often mess up the limits of integration, or forget a cosine component (I desperately working on Irodov's problems in physics right now, quite in vain actually), or I'm completely clueless on how to set the integrals with so many freaking confusing variables to deal with at the same time. Do you think that problem lies mainly in my lack of knowledge in vector calculus (and deep understanding of chain rule) and differential equations?

Do you have any suggestions for my preparation?

Thanks so much :D

PS: Keep in mind I have an intro textbooks for DiffE, linear algebra and vector calc that I am able to use.

 

[ZapperZ]

Somewhere in this forum are a few threads that discussed mathematical preparations, and in particular, a discussion of Mary Boas's valuable book "Mathematical Methods in the Physical Sciences". You might want to seriously look for either those threads, or that book.

I have also talked about it in my "So You Want To Be A Physicist" essay.

Zz.

 

[integration]

Thanks for responding. I looked over some threads, even the Mary Boas's thread, but it seems to me that those threads don't really address what I wanted to know.

I think I should reformulate my question.

1. I have books for Linear algebra (standard one), Ordinary differential equation (an easy one, and a proof based book by Petrovsky), multivariate calculus (last part of Stewart's calculus), and Feynman lectures (and Irodov problems to accompany it)

Considering my aspirations_ to ace my first year "honors" physics and math_ what are the "hot" topics from the books above that I am advised to prioritize and learn?

here is an example: should I prioritize

1st: vector calculus, grad/curl/div, Green's/Stokes' theorems
2nd: 1st/2nd Order ODE, homogeneous, Bernouilli
3rd: Laplace Transform, Fourier Series
3rd: proof-based ODE
Last: Linear Algebra.

I am currently have started on Differential equations (1st,2nd ODE+ homogenous, bernouilli finished), vector calculus (up to gradient of scalar fields), but it seems to me slightly counterproductive becomes some topics I learn seem not of absolute need for my physics. Since I'm going to college next year, I need to prioritize because I won't get everything done in 1/2 year. If you could guide me to skip around and master the necessary topics for 1st year mechanics/E&M, that would be very helpful.

Thanks.

 

[j93]

That isn't a very practical order for physics preparation
Quantum has two formulations
-Schrödinger's - Differential Equations intensive
-Heisenberg's - Linear Algebra Intensive
Both are mathematically equivalent
yet you have linear algebra last.


1st: vector calculus, grad/curl/div, Green's/Stokes' theorems
2nd: 1st/2nd Order ODE, homogeneous, Bernouilli
3rd: Linear Algebra.
4th: Laplace Transform, Fourier Series
Last: proof-based ODE

I am not sure exactly what the engineering part adds in but I would imagine it would make 4th more like 3.1