In which order should I take these (or more) courses?

[Aayam]

Hi,

I recently graduated from high school and am planning on taking studying physics in college(im taking a gap year).

Until them, I am trying to spend whatever free time I might get, studying and basically getting better at physics.

Here is my background, I have taken math up to Calculus BC(roughly equal to second semester calculus). I have taken two algebra based physics courses(ap physics 1&2), however, took the Ap Physics C exams(5 on both, roughly equal to first two semester of calculus based mechanics and E&M).

Ok, so my question is, from here on out, how should I proceed math and physics courses to make the most of my time? The college I plan on going to, allows for students to get credit for a class by taking an exam, which is one of the reasons I am pursuing this route.

So basically, one issue I had when I was studying physics before was I would always tend to stretch whatever I was working on beyond the scope of the course, so i would try to solve something but get lost, mainly because of my mathematical limitations. This is why I would like to revisit both mechanics and E&M (after expanding my mathematical toolbox), except with new textbook, the Feynman lectures.

Here are the math/Physics courses that come to mind, but if there are more, please let me know.
Calculus 3 (multi-variable Calculus)
Differential Equations (1 semester)
Linear Algebra
Vector Calculus
A course on Waves( differential equations is a prereq)

In what order should I take the courses(basically meaning courses from most to least importance), and are there more course that are perhaps more useful/necessary?

Also, other than just learning whatever I've learned more thoroughly, i would like to get good preparation to begin junior level mechanics and E&M course. This is where I would like to start when I enter college. Thats not to say I am preparing simply just for these two courses, just saying, this is where I will begin. The math courses are intended to give me a good grounding for most of undergraduate(and possibly graduate) physics.

And yes, i plan to continuously review everything I've learned so I remember it when I enter college.

Thanks.

 

[MidgetDwarf]

Retake Calculus 1 at the university. A large majority of these AP calculus courses are not the full material one sees at the University.
Maybe try Spivak or Apostol Calculus. You can also try Moise, which is between Calculus of the level of Stewart and Spivak, but closer to Spivak.

 

[Aayam]

Retake Calculus 1 at the university. A large majority of these AP calculus courses are not the full material one sees at the University.
Maybe try Spivak or Apostol Calculus. You can also try Moise, which is between Calculus of the level of Stewart and Spivak, but closer to Spivak.

I am currently Reviewing calculus. I am using the textbook by Briggs and Cochran, just to make sure I have solid grounding. Spivak, from what I've read, is too "mathy" while I am mostly interested in math I can apply to physics. Mainly because I am not interested in abstract material. Is my choice wrong?

 

[MidgetDwarf]

No, Briggs is to basic. Get a copy of Moise, he uses the calculus motivate physics.

 

[jtbell]

Calculus 3 (multi-variable Calculus)
[...]
Vector Calculus

Are Calculus 3 and Vector Calculus different courses at your (future) university? Usually multi-variable calculus is the same thing as vector calculus. One might be more "applied", for physics and engineering majors, and the other more rigorous or "proofy", for math majors.

 

[Aayam]

Are Calculus 3 and Vector Calculus different courses at your (future) university? Usually multi-variable calculus is the same thing as vector calculus. One might be more "applied", for physics and engineering majors, and the other more rigorous or "proofy", for math majors.

well, there is a vector calculus course. but also a Multi variable calculus course. (but now you mention it, i think they cover the same stuff). In a different university's course sequence, they were separate courses. So i assumed that they could be treated as such.

 

[jtbell]

Different universities do things differently. In a large university, different departments may do things differently. I appreciate that you may not want to say which university, because of concerns about privacy, but if people here can't look things up on the university's web site, it's hard for them to give informed advice.

 

[Aayam]

Different universities do things differently. In a large university, different departments may do things differently. I appreciate that you may not want to say which university, because of concerns about privacy, but if people here can't look things up on the university's web site, it's hard for them to give informed advice.

Thanks for the reply. This should help.

http://catalog.utexas.edu/undergraduate/natural-sciences/courses/mathematics/

 

[Aayam]

Thanks for the reply. This should help.

http://catalog.utexas.edu/undergraduate/natural-sciences/courses/mathematics/

also, I just realized the difference between the two different multivariable calc courses offered. So, thanks, i think I get it now.

 

[jtbell]

Wow, UT has a lot of different versions of calculus courses. Anyway, it looks like they use "multivariable calculus" in the names of some courses, and "vector calculus" is listed as one of the topics in those courses. So they consider vector calculus as a subset of multivariable. I'm used to smaller schools that have a simple Calculus I, II, III sequence, with III being multivariable/vector.

There's a pair of upper-division courses named "Vector and Tensor Analysis" (1 & 2) but I'm pretty sure those are "proofy" courses intended for math majors who have already been through one of the other calculus sequences.

Over on the physics side, the upper division Classical Electrodynamics courses are the ones that use a lot of vector calculus, and they have Math 427L (Advanced Calculus for Applications II) as prerequisite. Another way to satisfy the prerequisite is Vector & Tensor Analysis, but I think this is probably to allow for math majors who want to take a physics course on the side.

 

[Student100]

Is UT on the quater system? That could explain why they have an independent vector calculus course. UCSD was the same way, all incoming transfer students had to take it even though at community college it was covered in our calculus three course.

Supposedly there was an exam you could take to try to earn previous credit, although I'm told it was nearly impossible to pass. I just redid the course myself, it was a softer introduction into the difficultly levels between CC and university anyway.

To OP you're going to have take all these classes anyway for your major, just follow the prerequisites. The only thing I can think to recommend possibly out of normal order is to take linear algebra before calculus three.

Saw MD mentioned Apostol, great book and about as rigorous as the majority of physics students would ever need in my opinion. Highly recommended since you've already been exposed in AP course work.

Maybe an unpopular opinion here, but FL aren't textbooks. To gain a deeper understanding than your ap courses look into both Kleppner and Kolenkow (first or second edition okay, second edition is a bit better in SR sections) and Purcell third edition. If you're really rusty or feel intimated by these texts, physics 5th edition by H&R are the best mid range intro texts, also in my opinion. FL are good reads, but lack some of things a good textbook needs.

Another opinion, don't skip courses via an exam. That to me seems sketchy. If you've never had a waves or optics course, calculus three course, linear course, etc., to exam out of it would be a foolish decision. I can't think of a realistic way to come in as a freshman taking the junior level (Griffiths type level?) E&M.

But this is just my view on all of it.

 

[Aayam]

Is UT on the quater system? That could explain why they have an independent vector calculus course. UCSD was the same way, all incoming transfer students had to take it even though at community college it was covered in our calculus three course.

Supposedly there was an exam you could take to try to earn previous credit, although I'm told it was nearly impossible to pass. I just redid the course myself, it was a softer introduction into the difficultly levels between CC and university anyway.

To OP you're going to have take all these classes anyway for your major, just follow the prerequisites. The only thing I can think to recommend possibly out of normal order is to take linear algebra before calculus three.

Saw MD mentioned Apostol, great book and about as rigorous as the majority of physics students would ever need in my opinion. Highly recommended since you've already been exposed in AP course work.

Maybe an unpopular opinion here, but FL aren't textbooks. To gain a deeper understanding than your ap courses look into both Kleppner and Kolenkow (first or second edition okay, second edition is a bit better in SR sections) and Purcell third edition. If you're really rusty or feel intimated by these texts, physics 5th edition by H&R are the best mid range intro texts, also in my opinion. FL are good reads, but lack some of things a good textbook needs.

Another opinion, don't skip courses via an exam. That to me seems sketchy. If you've never had a waves or optics course, calculus three course, linear course, etc., to exam out of it would be a foolish decision. I can't think of a realistic way to come in as a freshman taking the junior level (Griffiths type level?) E&M.

But this is just my view on all of it.

Hi, thanks for the reply

The feynman lectures were suppose to basically be an addition to what i have already learned, not necessarily replacement. This is because freshman lvl material turned out simple enough that I thought I would now just do FL first and then move on to something that's beyond freshman level. But, I kinda see what you are trying to say.

Also, is Apostol's calculus the best text in this scenario? Is there one better? I have read about Spivak but people also say its also an introduction to analysis(don't really know what that means) and is unnecessarily "pure"(or rigorous), so it looks kinda unappealing. Is there a better book or is Apostol the way to go?

 

[MidgetDwarf]

Apostol is similar to Spivak. However, it has a mixture of proof, plug and chug, and goes into multi variable calculus. This book is difficult. I found Spivak to be easier to read.

There is a step down as mentioned previously. Please make it habit to read all the replies, or you make people not want to answer your questions in the future. The step down from Apostol and Spivak would be the book by Edwin E. Moise: Calculus. It is like a mixture of Stewart and Spivak/Apostol. It uses a lot of physics explanations to motivate the calculus. You can also try Thomas: Calculus with Analytical Geometry 3rd ed. Both are great books. Both are cheap, so get them both.

Ideally, Apostol would have all the Calculus you need to know, but it can be overkill for most physics students. I am not a physics major, I am a math major, but have completed the typical 3 semester introductory physics sequence.

 

[MidgetDwarf]

Here is a review of Moise found on Amazon:

This book deserves to be recognized as one of the best calculus texts ever written and gets my
highest possible recommendation. Moise was a world famous geometer and professor of mathematics at Harvard.
It is a crime that Stewart's book is on everyone's shelf these days and this
book (if you are lucky) exists only as a single worn dusty copy on the shelf of your local university library (and as a point of reference the Cal Tech library no longer has a copy of this book).

There are two branches of calculus texts, the first is the applied branch
consisting of books such as Strang and Thomas and the second branch consists of the texts that encroach on real analysis such as Spivak, Apostol, or Courant.
Where does this book fit in the mix? Its center of mass is closer to the second branch but it is quite a bit
more elementary than Spivak and is more focused on using the techniques of calculus to solve physical problems. It not only covers all the usual Calculus 101 topics but also wanders through
territory outside the
mainstream and discusses the relationship between polynominals/partial fraction decomposition and the integers, mathematical induction, linear algebra and matrices, complex numbers, Fourier series, and basic ideas of multivariable calculus. Surprisingly, given its depth and extent of coverage, it is also much shorter and
lighter (under 800 pages and about 2 lbs) than
your modern 5 pound multi-colored 1200+ page calculus book. If your goal is to obtain a deep understanding of calculus this book is an absolute must have. This book would also be
appreciated by those who already know calculus but want to see how the subject was presented by a master of mathematics.

 

[Aayam]

For everyone, is it at all possible for you to compare these texts to the level of Calculus BC? This is because I have fairly limited exposure so I am unaware of most things beyond the BC curriculum. So how are the texts relative to AP coursework?