I understand the physics but struggle with the math on tests

[BearShark]

Hey,
I guess anyone in physics have seen it a lot but I have trouble looking for tips and strategies for solving my problem so I thought I'll try here.

Problem: I currently take Waves and Optics. I already passed Mechanics, Electricity and Magnetism, Analytical Mechanics, Thermodynamics and PDEs. I feel like I understand the martial and sometimes develop solid intuition, and I solve the weekly exercises on my own or after help from the TA. However I struggle with long algebra.

I have a solid background in math, I got a B+ in my calculus class, so I do understand the math, I just get confused when a lot of algebra is involved so if there is a problem that requires thinking about physics, doing some math then thinking again, I might get stuck with the math so I will not be able to solve the problem from there.

What I'm doing so far:

1. If I can't do the math, I write what I would do if I could solve the equations, and if I have an idea how would the solution look like I write that. I managed to pass exams where I could solve only half of the math like that, but I don't get full score so I get C's when I use this approach.
2. I try to draw a diagram of the geometry of the problem which helps but not applicable to all problems.
3. I try to be as organized as possible but if the math is long enough, it does not always help.
4. Needless to say I also practice a lot before the exam. However, this hurts the effectiveness of my studying because I often have to solve the problem a couple of times because each time I find an algebra mistake.
5. I do "sanity checks" whenever possible, but knowing there is a mistake often means I have to find it and then repeat the derivation which takes a lot of exam time.

The university has a learning disability counselor, and she has good tips, but she is not in physics and I feel like this is a problem physicists are more familiar with so I'm asking here. I want to start getting Bs and As instead of Cs soon because I want to go to grad school, and I feel like this is what is holding me back.

Thanks!

 

[PeroK]

You seem to be already at a high level if you've studied PDEs. Can you give an example of the level of maths you can manage and an example of what is beyond your current capability?

 

[BearShark]

You seem to be already at a high level if you've studied PDEs. Can you give an example of the level of maths you can manage and an example of what is beyond your current capability?

Thank you for your response. I do ok when I need to solve classes of problems I am already familiar with.

For example I can usually do Fourier transforms ok because I am familiar with the theorems like the shift and convolution theorem, which allows me to skip a lot of algebra.

I am also familiar with most of the simple solutions of PDEs like the wave equation, so solving the wave equation for simple boundary conditions in a variety of symmetries is not that much of a problem, unless for example there is a situation where the Bessel function appears when there is no apparent drum symmetry so I have to get to the Bessel equation by simplifying the equation. If does not happen often but sometimes it does.

I struggle for example with multiplying a lot of matrices. It happens in Waves and Optics with ABCD and Jones matrices. Often an exam problem asks to chain a couple of matrices and I end up making mistakes in this process. I always check my answer by multiplying the base vectors and seeing if I get an expected result but it is not always possible and if I see I got it wrong it often means repeating pages of derivations.

I also struggle with finding transmittance and reflectence coefficients in scattering problems. I can set the equations and boundary conditions fine, but often get lost in the tedious algebra that follows, and a lot of times we are required to use the expressions we found in the next parts of the questions, which often results in unsolvable math if the expression is not right.

Summery: Basically if there is physical intuition \ meaning I can use to either guide me through the math of significantly simplify it I do ok, but if there is tedious "means to an end" math like matrix multiplication or solving a linear system with a lot of expressions and variables I tend to get lost.

 

[PeroK]

You may get a better answer but I don't think there is an obvious way to do lots of difficult algebra without mistakes. I wish I could do it. I usually try to break a calculation down into manageable chunks. But on any sufficiently complex problem I'll usually make at least one error somewhere.

 

[BearShark]

You may get a better answer but I don't think there is an obvious way to do lots of difficult algebra without mistakes. I wish I could do it. I usually try to break a calculation down into manageable chunks. But on any sufficiently complex problem I'll usually make at least one error somewhere.

Thanks. I do realize everyone makes mistakes, but no matter how much I practice I don't seem to manage to do as well as my classmates seem to do in this area. This is frustrating for me because it puts me at a disadvantage.

 

[DrClaude]

You mentioned the "learning disability counselor." Do you have a learning disability (dyslexia in particular)?

 

[BearShark]

You mentioned the "learning disability counselor." Do you have a learning disability (dyslexia in particular)?

I have have Dysgraphia, like dyslexia with writing, and I get an extended time accommodation in exams. It does help because it gives me more time to go over errors. I would still like to make less errors because I'd rather use the time to think about the problems rather than do algebra most of the time.

 

[Stephen Tashi]

I think it helps to approach calculations as you approach a job like replacing a window or repairing a floor. Before you do a step in such physical jobs, its best to visualize how things are going to turn out. The can't be done exactly, but if you don't imagine how things will turn out and instead begin to execute steps, there are often surprises.

For example before you multiply two matrices together, you can visualize the general process - which rows time which columns are going to produce a lot of terms? Will any of the terms be "like terms"? How many different "species" of terms will there be?

 

[Student100]

When you're doing something like a Jones matrix are you writing everything out or subbing dummy variables in during the calculations? Some of them are hideous and it's easier for me to just rename all those trig functions/stuff A, B, C... etc. and then do the math subbing back at the end.

It makes it easier for me rather than rewriting messy expressions over and over again while actually doing the simple algebra stuff, you might want to try something like that.