# Mechanics without calculus how useful?

Gold Member
So we currently study mechanics without the use of calculus (currently only statics...soon we start kinematics). Does calculus make things easier? What's its effect on solving exercises?... I wonder. Could we solve more complicated problems with calculus that we can't now?

## Answers and Replies

Jack21222
You can only solve mechanics problems from scratch using calculus. In algebra-based classes, the professor just does some of the calculus for you before just handing you the results to use.

Instead of just being handed the kinematic equations, calculus allows you to understand where they came from, and even extend it to nonuniform acceleration.

Reshma
So we currently study mechanics without the use of calculus (currently only statics...soon we start kinematics). Does calculus make things easier? What's its effect on solving exercises?... I wonder. Could we solve more complicated problems with calculus that we can't now?
Depends on the level of the course as well. I don't remember using much calculus in high school mechanics courses. But calculus was an integral part of almost all undergraduate physics courses.

Gold Member
So what you're saying is that I can't truly understand what I'm doing without calculus?

Reshma
So what you're saying is that I can't truly understand what I'm doing without calculus?
More or less, after all Newton developed calculus to explain the laws of motions. And if you intend to study more physics then calculus is almost indispensable.

Staff Emeritus
Gold Member
So what you're saying is that I can't truly understand what I'm doing without calculus?

There are many things you will take away from non-calculus physics. For example, you say you're studying statics now...well, you're learning how to draw a force diagram. That's very useful in calc-based physics.

I wouldn't think of high-school level physics it as wasted time, if that's what you're wondering.

Chunkysalsa
In my physics I class we barely used any calculus. However everything was taught in calculus terms and it made it easier to understand for me. Most of the formulas used calculus but simplified to basic algebra, which is what they teach you. The calculus will also allow you to solve problems where things are not constant or uniform. I hardly ever got problems like that though.

Maximizing functions is another useful thing you can do with calculus that showed up in a good amount of problems in my physics classes.

Now in my physics II class, I use alot more calculus even if they all solve very easily, it would be impossible to memorize all the different equations for all the different little situations.

mccoy1
So what you're saying is that I can't truly understand what I'm doing without calculus?

You can actually understand stuff without the maths behind them. Maths make it easy to see where the folks are coming from..

Gold Member
I wouldn't think of high-school level physics it as wasted time, if that's what you're wondering.

When I took HS algebra-based physics, my teacher told the class that you couldn't solve x(t)=at2/2+v0xt+x0 for time because "there's a t in two places and one of them is squared." She also thought the density of water was 1 kg/m^3 and that work only occurred if a force was applied in the x direction...it was miserable.

2VtQCxn
Calculus is the language of change, and physics describes how nature changes, so physics sans calculus won't give you much insight into nature except for situations with no change.

Homework Helper
You can learn how to plug numbers into a some formulas to answer your homework and test questions.

Or you can learn physics.

One of these requires calculus, the other does not.

Gold Member
I see what you guys are saying, and I greatly appreciate all the replies. I would even appreciate more opinions on the subject. Thanks for the insight. Next semester we have calculus on our list, so we definitely gonna get familiar with it. :)

viscousflow
Back at home they only offered physics without calculus. When I transfered to a large university I had to retake all my physics courses since I needed physics with calculus.

I learned infinitely more in physics with calculus. Equations also give you insight into the physics. Just seeing A=BC 100 times over doesn't say much. In my opinion physics is best learnt in the language it was derived in. What you're getting are the left overs not the main course.

qspeechc
There are actually quite a few things you can do in mechanics with no calculus at all: statics (hydrostatics too), uniform motion, Newton's laws, the basics of energy, momentum etc., so no, I would not say mechanics without calculus is useless. And if you know calculus but not the proofs of calculus, then it is not much better than not knowing calculus, isn't it? The only thing that matters is the idea of "limiting" or approximating something in many small steps, and then saying that in the limit everything works out. Archimedes knew this long before calculus was invented. This is the idea behind many calculus proofs anyway, and exactly why calculus is so important to physics. In fact, if you know calculus but not its proofs, then it seems it is sometimes used as a magic tool where results pop out, with not much intuition for WHY things should be so, and it is usually the idea of limiting that is obscured. Calculus allows you to do a lot more, but it doesn't necesarily add insight.

I know I'm blabbing and not saying anything precise, sorry...

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Gold Member
Back at home they only offered physics without calculus. When I transfered to a large university I had to retake all my physics courses since I needed physics with calculus.

I learned infinitely more in physics with calculus. Equations also give you insight into the physics. Just seeing A=BC 100 times over doesn't say much. In my opinion physics is best learnt in the language it was derived in. What you're getting are the left overs not the main course.

Excellent insight! I can't wait to start calculus then :)