Studying How Can I Improve My Vector Calculus Skills for Classical Mechanics?

AI Thread Summary
A third-year physics undergraduate is seeking advice on improving vector calculus skills to better engage with classical mechanics coursework. The student feels out of place in class and has identified a lack of confidence in their mathematical abilities, particularly in visualizing force fields and setting up line integrals. They are currently using Taylor's classical mechanics textbook, which does not extensively cover vector calculus. Suggestions from other forum members include resources like Griffith's "Introduction to Electromagnetism" for its vector calculus review, online notes from Paul, and standard texts like Marsden's "Vector Calculus" and Phillips' "Vector Analysis." The discussion also highlights a potential gap in the student's physics background, as they have only taken introductory mechanics and a semester of modern physics, raising questions about their prior coursework and understanding of electricity and magnetism.
camc03
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Hello to all, I am looking for a little bit of advice/guidance here.

I am a third year physics undergraduate. Just beginning to take classical mechanics, and I do feel a bit out of place in the class. I feel like my vector calculus skills are far too underdeveloped/rusty for the course I am in. I am wondering if there are any good resources (preferably a book / text) that covers vector calculus with depth for going forward in my Physics courses?

I am taking a math methods course also.
 
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camc03 said:
I am a third year physics undergraduate. Just beginning to take classical mechanics, and I do feel a bit out of place in the class. I feel like my vector calculus skills are far too underdeveloped/rusty for the course I am in

It would probably help to tell us which textbook you're using for classical mechanics.

Have you had a course in electricity and magnetism beyond the first year course? In my experience, intermediate/advanced E&M uses far more vector calculus than does classical mechanics.

Griffith's Introduction to Electromagnetism has a decent review of vector calculus in the first chapter or two, which I think could probably be used on a stand-alone basis.
 
jtbell said:
It would probably help to tell us which textbook you're using for classical mechanics.

Have you had a course in electricity and magnetism beyond the first year course? In my experience, intermediate/advanced E&M uses far more vector calculus than does classical mechanics.

Griffith's Introduction to Electromagnetism has a decent review of vector calculus in the first chapter or two, which I think could probably be used on a stand-alone basis.
Sorry, I didn't. I haven't had an upper division course in electricity and magnetism. And I mean, I think my calculus skills are just rusty in general. I am using Taylor's classical mechanics, which doesn't really do too much vector calculus except for the line integrals with calculating work and some other topics that I haven't thought of. Overall, I am just struggling to even start some problems even after trying to read through the sections multiple times and attempting to recall on my own. Thanks

Cam
 
camc03 said:
Sorry, I didn't. I haven't had an upper division course in electricity and magnetism. And I mean, I think my calculus skills are just rusty in general. I am using Taylor's classical mechanics, which doesn't really do too much vector calculus except for the line integrals with calculating work and some other topics that I haven't thought of. Overall, I am just struggling to even start some problems even after trying to read through the sections multiple times and attempting to recall on my own. Thanks

Cam
Paul's online notes are a good resource for all things calculus:

https://tutorial.math.lamar.edu
 
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Marsden Vector Calculus is a standard text.
I have always been fond of the more applied Vector Analysis by Phillips.
 
OP: I'm a bit confused with your scenario. What physics and math courses (and what textbooks did you use) in your freshman and sophomore years?
 
CrysPhys said:
OP: I'm a bit confused with your scenario. What physics and math courses (and what textbooks did you use) in your freshman and sophomore years?
Calculus 1-3 with Stewart's calculus, DiffEQ with Jiri Lebl's notes, and I took introductory mechanics using University Physics by Hugh D Young and Freedman.
 
camc03 said:
Overall, I am just struggling to even start some problems even after trying to read through the sections multiple times and attempting to recall on my own.
Why do you think your issue is due to rusty math skills? Can you give us an example of a problem you struggled with?
 
vela said:
Why do you think your issue is due to rusty math skills? Can you give us an example of a problem you struggled with?
I think a big problem I have is visualizing and identifying force fields and how they work ; especially in relation to setting up line integrals when given some vector field and parametrizing it to solve for work done. Thanks for asking these questions as well; you are assisting me in ways I didn't think about
 
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camc03 said:
I am a third year physics undergraduate.

CrysPhys said:
OP: I'm a bit confused with your scenario. What physics and math courses (and what textbooks did you use) in your freshman and sophomore years?

camc03 said:
Calculus 1-3 with Stewart's calculus, DiffEQ with Jiri Lebl's notes, and I took introductory mechanics using University Physics by Hugh D Young and Freedman.

This doesn't add up. You're a third yr physics major. But in your first and second yrs, you've taken only intro mechanics. No intro E&M? No intro modern physics? No other physics?

Is there a back story here? Your profile says US. Are you in a US university, or elsewhere? Have you recently switched majors?
 
  • #11
CrysPhys said:
This doesn't add up. You're a third yr physics major. But in your first and second yrs, you've taken only intro mechanics. No intro E&M? No intro modern physics? No other physics?

Is there a back story here? Your profile says US. Are you in a US university, or elsewhere? Have you recently switched majors?
Sorry, I made a mistake lol. We just call the entire first year sequence mechanics here. And I took one semester of Modern Physics which included Special Relativity and quantum mechanics. I have also taken a few labs.
 
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