Visuals confuse me, but I'm good at math - help with mechanics resources?

[kepherax]

Hiya. I'm an undergrad taking my first major's physics course in mechanics (calc based, but not much calc involved thus far), and I am fairly lost. Straight A's in calc 1-3, currently in differential equations math wise and doing well, but having problems with the physics course because it is so diagram oriented and I lack physical intuition (prof is all visual also).

The only part of any calc I had an issue with were washers/shells and the triple integral set ups where one needed to use a visual to set up the equation, and I hated geometry - I seem to have a disconnect and cease to understand anything if I have to interpret this way.

Are there any resources that will just take you step by step (here is the equation sequence that led up to this point with the logical connections, these are the steps and where they were obtained from in the diagram, explain it to me like I'm 5 and don't assume I'm going to get any concept connection when looking at a picture).

I'm good at pattern recognition, once I get it I get it and can fly through the math, but everything so far has given me a headache as it is not explained in a way I grok. Are there any physics books or resources that might help? If it's *just* explained straight forwardly and logically versus as being tied to reality I tend to get it more - no issues with equations of motion, for instance, but I had to ignore the conceptual and get the mathematical first.

We are working on rotational motion now and I'm hoping there is a resource that focuses on the math versus "what's going on" (that part I tend to get second)?

 

[berkeman]

Welcome to the PF.

I think that it's great that you are very strong with math as a foundation in your studies. I think it is a lot harder for somebody with good visualization skills to try to make up the math, rather than you in your position, where you are strong in math, and wanting to learn visualization skills.

Do you play chess? If not, I'd recommend picking it up and playing games against friends or against a computer at a basic level. At least for me, chess works my visualization and mental simulation brain pathways a lot, so it may help you exercise the spatial parts of your brain some. My favorite book to learn good chess tactics is shown below.

Also, have you done any crafts, woodworking, wood shop, metal shop or automotive classes or projects? The more hands-on projects that you do, the better you will be able to think spatially, IMO.

 

[symbolipoint]

By chance did you skip your high school Geometry course, or also or both skipped the same Geometry course in college? If you did skip, even if you skipped it in only one of the institutions, STUDY GEOMETRY! Some of the intuition as well as some of the more rational parts are needed in Trigonometry. All of Physics and MOST of Mathematics requires drawing, diagramming, and sketching skills, including some of three-D sketching on your two-D paper surface. YOU WILL NEVER BE RID OF THE NEED TO MAKE DRAWINGS AND DIAGRAMS for Physics, Mathematics, any physical sciences.

 

[DEvens]

Like many things, practice is important. And you need to keep in mind the difference between skill (which can be developed) and talent (which is innate). Understanding graphs and pictures is a skill. You can learn it. Unless you have some major neurological thing, which you don't mention.

So find some intro books that do the kind of thing you have trouble with and practice it. Find old exams or old problem sets in classes that use these features, and go through them in detail. Get comfortable with it.

See if you can find a class in drafting. Going through the isometric drawing class was a thing. We had to learn to draw a 3-D thing according to drafting rules. And we had to be able to move between the 3-D relief drawing and the cross-section slice diagrams.

 

[Mark44]

The only part of any calc I had an issue with were washers/shells and the triple integral set ups where one needed to use a visual to set up the equation, and I hated geometry - I seem to have a disconnect and cease to understand anything if I have to interpret this way.

This doesn't make a lot of sense to me -- it's sort of like saying I want to be able to play the violin, but I hate using my left hand. The metaphor isn't too far off, I don't think. My understanding is that the two halves of your brain process different kinds of information, with one side processing visual images, and the other more adapted to manipulating symbols. If you use only the one side, ignoring images, you're not using all of your brain.

The reason that we draw some figures in, say, setting up an integral that represents a volume of rotation is that the volume element is either a disk, a geometric object with a known volume, or a shell, also a geometric object that we can unroll to a rectangular slab. The geometric objects motivate and are the reason for the formulas for volume. If you are merely memorizing formulas with no understanding of how they are derived, that's a real disadvantage.

If it's *just* explained straight forwardly and logically versus as being tied to reality I tend to get it more

You're putting the cart before the horse. It's the reality (which you seem to want to ignore) that drives the logical explanation.

YOU WILL NEVER BE RID OF THE NEED TO MAKE DRAWINGS AND DIAGRAMS for Physics, Mathematics, any physical sciences.

This...

 

[Mark44]

... and I hated geometry...

I infer from this that you had geometry in high school...
It was my least favorite math class in high school, but I didn't hate it. The parts of this class that have been most useful were the formulas for area and volume of basic geometric shapes, in addition to the ability to use logic in writing simple proofs.

or also or both skipped the same Geometry course in college?

I think we talked about this before. Of all the colleges I've attended (> 10) or taught at (5), there was no course in Geometry. All of these had courses called Analytic Geometry or a phrase equivalent to this. The difference between Geometry and Analytic Geometry is the addition of algebra and functions and coordinate systems to the latter.

 

[symbolipoint]

I think we talked about this before. Of all the colleges I've attended (> 10) or taught at (5), there was no course in Geometry. All of these had courses called Analytic Geometry or a phrase equivalent to this. The difference between Geometry and Analytic Geometry is the addition of algebra and functions and coordinate systems to the latter.

Maybe we did talk about that before. What I am aware is this:
One of the college preparatory courses in high school is Geometry, the one with the topics of points, lines, planes, angles, planar and spatial figures, including triangles, and proofs; and learning to use straight-edge, compass, and protractor. The same course is also taught in community colleges and is considered to be a remedial course at such institutions. The universities typically do not offer this "Geometry" course.

 

[Mark44]

In reference to high school geometry courses:

The same course is also taught in community colleges and is considered to be a remedial course at such institutions.

Perhaps some community colleges teach this course, but none of the ones I've taught at taught a course equivalent to high school geometry. They did, however, have courses that dealt with analytic geometry, which I described in my previous post.

 

[symbolipoint]

In reference to high school geometry courses: Perhaps some community colleges teach this course, but none of the ones I've taught at taught a course equivalent to high school geometry. They did, however, have courses that dealt with analytic geometry, which I described in my previous post.

If the community college systems are cutting away Geometry, this is a serious educational administration or supply trend problem. Geometry (not the Analytical Geom kind) NEEDS to be present at the c.c. in order to support a course path leading to Trigonometry, College Algebra, Pre-Calculus, and Calculus 1. In case students after high school become deficient in qualifying for the beginning college level Mathematics courses, such students need to go into one or two or so remedial courses. Just because students had four years of college prep math in high school does not mean that they still keep all their conditioning when starting college. Some such students DO need to start as low as "Elementary" Algebra or "Introductory" Algebra, and work upward.

 

[Tom.G]

I'm good at pattern recognition, once I get it I get it and can fly through the math, but everything so far has given me a headache as it is not explained in a way I grok.

That "good at pattern recognition" comment triggered a recollection of people with a particular brain functionality having that characteristic. It has gotten some bad connotations over the years, it is currently call "Autism Spectrum Disorder"... and it really is a Spectrum of both capabilities and of degree. A few large companies actually look for such employees to spot underlying relationships that are missed by most people.

It could be worthwhile to find a clinical psychologist, or even an enlightened educator, that can give you tips/approaches to either take advantage of, or work around such uniqueness.

Cheers and Best Wishes,
Tom

p.s. If you pursue this, please let us know how it goes.

 

[CrysPhys]

I'm an undergrad taking my first major's physics course in mechanics (calc based, but not much calc involved thus far), and I am fairly lost.
...
If it's *just* explained straight forwardly and logically versus as being tied to reality I tend to get it more - no issues with equations of motion, for instance, but I had to ignore the conceptual and get the mathematical first.
...

<<Emphasis added.>> Are you in fact majoring in physics? If so, your principal focus should be on reality; math is a tool for analyzing it. If your principal focus is not on reality, but on math per se, you should major in math, not physics.