Differential Equations Are Eating Me Alive

[galaxywanderer]

So I am a sophomore physics major at a university near my hometown. I have always been fascinated by the way studying physics makes me think about the world, and I have struggled with but enjoyed my other undergraduate physics and math classes.

This semester, however, I am taking multivariable calculus and differential equations in addition to my modern physics classes, and a terrible thing has happened; the further along I go with math and physics, the more I find I dislike it. Calc I was great, Calc II was hard, and now I get a pit in my stomach every single time I sit down to do my math homework. I hate it. I hate spending hours and hours working on extremely complicated math problems. I absolutely cannot stand solving differential equations and doing vector calculus and Laplace transforms and all of it. I am capable of solving the problems, but I find every minute of it to be laborious and painful and dull. My physics classes are definitely slightly more interesting, and I like the way they make me think about the world and about problem solving, but when it really comes down to it it is all of course just applied mathematics.

Okay so I just spent the entire last paragraph ranting, but to get to the point I am wondering if I should change my major to another field of study. I am looking at Chem/Biochem as a possible alternative but not sure if I would really enjoy either of these more. I just find the concepts of physics so interesting, but in practice I really dislike doing physics for any considerable amount of time. I feel kind of lost like I really don't know what I enjoy doing now.

Any and all advice would be appreciated.

 

[phyzguy]

What do you want us to say? If you dislike doing mathematics so much then clearly physics and math are not the place for you. The question you need to answer is, just what do you enjoy doing? Nobody can answer that for you.

 

[berkeman]

I am wondering if I should change my major to another field of study. I am looking at Chem/Biochem as a possible alternative but not sure if I would really enjoy either of these more. I just find the concepts of physics so interesting, but in practice I really dislike doing physics for any considerable amount of time.

It does sound like you should look at other majors to decide which one turns you on the most. I used to get goosebumps at the start of each semester in uni when I looked through my brand new textbook purchases and saw what I was going to learn soon. Physics was my first love in school, but I ended up pursuing EE.

What other interests do you have that may turn into promising areas of study?

 

[dlgoff]

I am wondering if I should change my major to another field of study.

After doing all the math work, why would you want to change now? Isn't this what's important?

I have always been fascinated by the way studying physics makes me think about the world, ...

 

[dlgoff]

Physics was my first love in school, but I ended up pursuing EE.

At my university, the School of Engineering offered a BS in Engineering Physics. All the Math and Physics courses required by the College of Liberal Arts, but with all their other required courses being Engineering electives. I loved all those electives (In my case, all were EE courses).

 

[symbolipoint]

galaxywanderer,

Do like studying and learning Mathematics?
Do you dislike studying and learning Mathematics?

Do you like USING Mathematics?
Do you dislike USING Mathematics?

To what extent so far have you studied, which other courses of Science, Engineering, Technology?

Your honest answers to those five questions can be helpful to you yourself, and for people or members here who could offer guidance.

 

[galaxywanderer]

galaxywanderer,

Do like studying and learning Mathematics?
Do you dislike studying and learning Mathematics?

Do you like USING Mathematics?
Do you dislike USING Mathematics?

To what extent so far have you studied, which other courses of Science, Engineering, Technology?

Your honest answers to those five questions can be helpful to you yourself, and for people or members here who could offer guidance.

Thank you for these questions as a guideline to better express some of my thoughts. I think in answering these I will include replies to some of the other excellent questions/answers that you all have posted above.

1. As to whether I like/dislike studying mathematics, I would say that this is definitely the thing I dislike the most. Some of my peers (obviously especially the math majors) can sit and work on math problems for hours at a time. I find this very dull and tedious, and to be honest even if I do it for a long time (~25-30 hours) each week I still struggle with doing well in class.

2. Now as to using math, I admittedly have less experience. dlgoff mentioned doing engineering physics above, and I've only taken one introductory engineering classes (just because at my university there aren't any required for my degree). As far as applying math to physics problems, I still find a lot of my physics homework to be about the same as most of my math homework.

Talking to dlgoff's other point about the fact that I've already made it through most of my pure math classes already, the biggest thing that made me question my major the most wasn't actually one of the pure math classes, it was one of my classmates' E&M homework, the very sight of which probably increased my blood pressure 10 points.

As far as what else I've studied/what else interests me as mentioned in a few replies above, I did take that Introduction to Engineering Design class I mentioned above. As I recall we mostly just did a lot of CAD modeling, and that was about all. I've done some geology/environmental science, which was okay but probably not for a long term career.

I also took some chemistry while I was doing my general ed classes and I found it very interesting, more so than most of my other classes. The only thing is that when I look at some of the material that I will be studying (especially PChem unsurprisingly), it still looks about the same as most of my physics textbooks. Has anybody taken Physical Chemistry? How does it compare in mathematical rigor to your sophomore/junior level undergraduate modern physics classes? I don't want to uproot everything and change majors just to realize that I'm still in the same boat I was before.

 

[dlgoff]

Talking to dlgoff's other point about the fact that I've already made it through most of my pure math classes already, the biggest thing that made me question my major the most wasn't actually one of the pure math classes, it was one of my classmates' E&M homework, the very sight of which probably increased my blood pressure 10 points.

bold by me.

Oh yea, the homework is difficult. At least it was for me; my hardest course. It was difficult for everyone in the class. So much so, that many of us formed study groups just to do the homework. I remember some problems taking a whole ream of paper. But you can get through it, then you can feel like you've really accomplished something.

 

[symbolipoint]

galaxywanderer,
I do not yet have much of anything to add; but the question possibility of RESTUDYING something on your own or by course repetition is valuable to ponder and sometimes to do.

 

[dlgoff]

Has anybody taken Physical Chemistry? How does it compare in mathematical rigor to your sophomore/junior level undergraduate modern physics classes?

For me, there was very little mathematics.

 

[symbolipoint]

galaxywanderer asks

Has anybody taken Physical Chemistry? How does it compare in mathematical rigor to your sophomore/junior level undergraduate modern physics classes?

dlgoff responded

For me, there was very little mathematics.

The amount of Mathematics used in Physical Chemistry is very significant. A bit of limited use of multivariable calculus. Reaction rate kinetics will use some cumbersome algebra and the course will have use some simple differential equations; maybe some not too complicated linear algebra.

 

[Delta2]

Seems to me you have two options:
1. You devote yourself and do some hard study to learn the hard math even though it seems you don't like them a lot. See it is a sacrifice you must make in order to become good at physics (and if I can judge from your avatar, Astrophysics).
2. You choose a major that does not require a lot of math. There must be physics majors that do not require heavy math, but then again your physics degree is going to be treated as light weight and this might affect your career options.

 

[valenumr]

So I am a sophomore physics major at a university near my hometown. I have always been fascinated by the way studying physics makes me think about the world, and I have struggled with but enjoyed my other undergraduate physics and math classes.

This semester, however, I am taking multivariable calculus and differential equations in addition to my modern physics classes, and a terrible thing has happened; the further along I go with math and physics, the more I find I dislike it. Calc I was great, Calc II was hard, and now I get a pit in my stomach every single time I sit down to do my math homework. I hate it. I hate spending hours and hours working on extremely complicated math problems. I absolutely cannot stand solving differential equations and doing vector calculus and Laplace transforms and all of it. I am capable of solving the problems, but I find every minute of it to be laborious and painful and dull. My physics classes are definitely slightly more interesting, and I like the way they make me think about the world and about problem solving, but when it really comes down to it it is all of course just applied mathematics.

Okay so I just spent the entire last paragraph ranting, but to get to the point I am wondering if I should change my major to another field of study. I am looking at Chem/Biochem as a possible alternative but not sure if I would really enjoy either of these more. I just find the concepts of physics so interesting, but in practice I really dislike doing physics for any considerable amount of time. I feel kind of lost like I really don't know what I enjoy doing now.

Any and all advice would be appreciated.

I got stuck hard on diff eq until my genius roommate tutored me on the integrating factor method. I struggled with calc II as well. I think a lot of it was memorization over understanding. It's not that I suck at memorizing things, but I felt useless without understanding. It's funny, because I never really got much of calc II until I got into a career and I use it like second nature (numerical stuff, so all your Taylor expansions and what not). I'd say get some tutoring outside of the lectures to help you understand how the math works. If you still really hate it, well, then, at least where I went to college, there were a lot more cute women in biochem of that's your thing.

 

[CrysPhys]

As far as applying math to physics problems, I still find a lot of my physics homework to be about the same as most of my math homework.

Whenever a physics student carps about physics blurring into a tangle of equations, I ask this question: Have you done any lab work yet? Unlike math, physics is grounded in experiments. At my undergrad school, I was fortunate that physics lab was offered as an elective in the freshman and sophomore years (in addition to required junior lab and required senior thesis). I also had the opportunity to sign on for undergrad research with professors. Lab work made physics come alive for me. What about you? Any lab courses or lab experience so far?

 

[vela]

A terrible thing has happened; the further along I go with math and physics, the more I find I dislike it. Calc I was great, Calc II was hard, and now I get a pit in my stomach every single time I sit down to do my math homework. I hate it. I hate spending hours and hours working on extremely complicated math problems. I absolutely cannot stand solving differential equations and doing vector calculus and Laplace transforms and all of it. I am capable of solving the problems, but I find every minute of it to be laborious and painful and dull.

Perhaps your courses are uncharacteristically difficult, but assuming they're like the typical courses in the US, I'd say if you consider the problems in these lower-division classes extremely complicated and are spending hours and hours on them, physics is not the major for you. Math, ironically, might be. After the first two years, you're pretty much done with most calculations, focusing instead on proving things. On the other hand, if you don't find the math interesting in itself, that wouldn't be a good sign for majoring in math.

Are you just exaggerating out of frustration? Can you give us an example of one of these problems with a long, complicated solution?

 

[symbolipoint]

Everything ChrisPhys says in post #14 ! !

 

[paralleltransport]

"Calc I was great, Calc II was hard, and now I get a pit in my stomach every single time I sit down to do my math homework. I hate it. I hate spending hours and hours working on extremely complicated math problems. I absolutely cannot stand solving differential equations and doing vector calculus and Laplace transforms and all of it. I am capable of solving the problems, but I find every minute of it to be laborious and painful and dull. My physics classes are definitely slightly more interesting, and I like the way they make me think about the world and about problem solving, but when it really comes down to it it is all of course just applied mathematics."

The laymen perspective on doing physics is thinking about deep conceptual problems like black holes etc... That's true to some extent. However, you will find out that most of physics learning will involve exactly that:
spending hours upon hours doing challenging problems that pretty much like applied math. If you don't enjoy that, I don't think it will get easier.

I found out that the the more modern the physics I studied, the more the math got intricate (and fascinating!), which got me even more interested.

I found this article fairly representative of the experience: https://inference-review.com/letter/an-ode-to-ugly-physics

To give you some idea, the typical undergrad problem set in diffEQ took me 3-4 hours and had 5-6 problems. The typical problem in graduate QFT had 3 problems and took a combined team of several grad students 10-15 hours to solve. The problems just get harder (both conceptually and technically). Each problem would take 2-3 pages of latex math to write out.