Calc based physics with no calc experience/how to learn?

[Tagl00king]

Hello! I'm going to take calculus based physics and calculus 1 in the fall. At my school they're corequisites. But I'd like to do well in both of them.
It really worries me that I'm taking calculus based physics when I haven't ever taken any calculus before. Should I take cal based physics while taking cal 1? Even if you can take them concurrently?

I really want to graduate on time, so I was thinking of trying to learn the gist of calculus 1 on my own. Do you think that would help?
I also would like to learn the basics of physics? Do you have any cheaper book recommendations? I can't afford a textbook...

 

[Cake]

Go to MIT's open course website and watch their single variable calculus course over the summer. They have problem sets you can do to go along with the course. Working through the basics of derivatives and integrals and learning how to minimize or maximize a function is really all you'll need for calculus based mechanics, and they teach it well on the website. For additional problems sets, check out Schaum's Outline for Calculus. It's 12 dollars and it's basically a small textbook. You can find it on amazon.com

 

[symbolipoint]

A student should learn some Calculus (understand derivatives, and at least know how integrals work) and basic Trigonometry as requirements of studying Physics 1.

 

[axmls]

If they're coreqs, it should be set up to where you don't have much difficulty.

That said, intro calculus-based physics doesn't actually have much calculus. The only calculus you'll see in the beginning, for instance, is in the derivation of kinematicd equations. After that, you typically just memorize them.

 

[micromass]

As axmls said, f they are corequisites, then you should be ok. Nevertheless, it would be a very good idea to start learning a bit of calculus over the summer so you're more comfortable. I recommend the excellent book by Keisler: https://www.math.wisc.edu/~keisler/calc.html It's completely free as well (but that was not the main reason for suggesting it).

 

[QuantumCurt]

You should be fine. Physics uses very little calculus at first, and if the classes are corequisites then it will be understood that not all of the students will get the calculus. The calculus contained in a first semester of physics is pretty minimal really. You'll be doing far more algebra than calculus.

That being said, reading ahead is never really a bad thing.

 

[Tagl00king]

Thank you so much for all of your help everyone!

 

[mathwonk]

here are my free notes introducing derivatives in the special easiest, but very useful, case of polynomials:

http://alpha.math.uga.edu/~roy/polynomial_tangents_without_limits.pdf

 

[MidgetDwarf]

Just took calculus based mechanics. There was really no calculus involved. Mostly algebra and trigonometry. It may differ if you take an honors versions, say Berkeley. Calculus was used for only a few problems, however it was trivial derivation/ integration problems. Mostly using the rules of integration/differentiation.

Some derivations required calculus. Of the hardest derivation we did in class, was the inertia formulas. Many students had problem with these, because they were taking calculus at the same time, or were taking calculus and just memorized there way through these math courses. Momentum, energy work theorem can be derived with algebra.

The most important skill is understanding the physical concepts. Is this your first physics course? Or have you taken an algebra based physics course?. In my case. I had already Calculus 2 under my belt when I took an algebra based prep course for calculus based physics. It was my first science class. I ended up with a B (mostly do to nonsense instructor/good class however). Maybe take algebra based mechanics first?

The prep course really helped me out and I breezed through Cal. Mechanics.

You can always use a calculus based textbook ie Giancoli Physics for Scientists and Engineers. It reads clearly better than the other algebra based physics book.

 

[ZapperZ]

I used to teach such a class, and I will tell you that it also depends on the instructor.

When I taught it, while it used "minimal" amount of calculus ,there were still cases where knowing calculus will help you get a clearer idea on how things came about, it would have helped you quickly solve a problem, and it would made other things a lot easier.

I remember telling the students that all the kinematical equations that they have seen can all be derived from just one starting equation, that being F=ma, and knowing that a=dv/dt. Then via straightforward time-integration, derive ALL of the kinematical equations. I emphasized that there really is no need to remember all those different equations, just ONE, and so the students always knew where to start when tackling such problems (knowing how and where to start is the #1 most common issue most students have). In fact, one of their first quizzes that I gave was to derive all those kinematical equations from that one starting point.

Secondly, when dealing with position-dependent or velocity-dependent forces (such as Hooke-law force), solving for the equation of motion requires one to know the calculus chain rule. Depending on how deep one delve into this at this level, one will need to know calculus. This was something I went over with the students, and not knowing calculus will cause you to scratch your head.

Finally, the concept of Force-time graphs, and velocity-time graphs having physical meanings for their area-under-the-curves requires knowledge of calculus. Again, if you had me as an instructor, you would have had to do time-integration of these curves to answer some of my exam questions.

My suggestion would be to directly ask the instructor in cases such as this. Tell the instructor that you haven't had calculus, and that you are taking in concurrently. Ask him/her if this will be a problem. This will eliminate any question on whether you can or cannot survive in such a class. Otherwise, you will get some generic responses from us here that may or may not pertain to your situation, because we will all be guessing.

Zz.

 

[MidgetDwarf]

I used to teach such a class, and I will tell you that it also depends on the instructor.

When I taught it, while it used "minimal" amount of calculus ,there were still cases where knowing calculus will help you get a clearer idea on how things came about, it would have helped you quickly solve a problem, and it would made other things a lot easier.

I remember telling the students that all the kinematical equations that they have seen can all be derived from just one starting equation, that being F=ma, and knowing that a=dv/dt. Then via straightforward time-integration, derive ALL of the kinematical equations. I emphasized that there really is no need to remember all those different equations, just ONE, and so the students always knew where to start when tackling such problems (knowing how and where to start is the #1 most common issue most students have). In fact, one of their first quizzes that I gave was to derive all those kinematical equations from that one starting point.

Secondly, when dealing with position-dependent or velocity-dependent forces (such as Hooke-law force), solving for the equation of motion requires one to know the calculus chain rule. Depending on how deep one delve into this at this level, one will need to know calculus. This was something I went over with the students, and not knowing calculus will cause you to scratch your head.

Finally, the concept of Force-time graphs, and velocity-time graphs having physical meanings for their area-under-the-curves requires knowledge of calculus. Again, if you had me as an instructor, you would have had to do time-integration of these curves to answer some of my exam questions.

My suggestion would be to directly ask the instructor in cases such as this. Tell the instructor that you haven't had calculus, and that you are taking in concurrently. Ask him/her if this will be a problem. This will eliminate any question on whether you can or cannot survive in such a class. Otherwise, you will get some generic responses from us here that may or may not pertain to your situation, because we will all be guessing.

Zz.

Although I can see your reasoning, I have to disagree. Yes the velocity graphs etc would make sense having taken calculus. However, most of the examples you have given can be learned in a few hours. Ie basic derivations. Unless the class is being taught using KK, no calculus apart from basic diff/int is needed.

Deriving the kinematic equations is trivial.

 

[QuantumCurt]

I think @ZapperZ summed it up best. It's really going to depend largely on the instructor. A first semester physics course could potentially be done without using any calculus, but this would mean that you'd basically be given a list of equations without necessarily having any intuition of where those equations came from or how they relate to one another. This isn't a good thing. One cannot do serious physics without calculus, but given that calculus I is a corequisite, it's likely that calculus won't be used heavily; at least not at first. It will likely start utilizing calculus more as the semester moves on. On the bright side though, a calculus I course will often cover a derivation of the basic kinematics equations, although from a more mathematical perspective rather than a physical perspective.

 

[ZapperZ]

Although I can see your reasoning, I have to disagree. Yes the velocity graphs etc would make sense having taken calculus. However, most of the examples you have given can be learned in a few hours. Ie basic derivations. Unless the class is being taught using KK, no calculus apart from basic diff/int is needed.

Deriving the kinematic equations is trivial.

Not for someone who had NEVER had calculus before! How do you expect someone to do "basic diff/int" when that student had never done any of that kind before? What may seem obviously easy to you is not so when one has never done it before! I've seen it. What ended up happening is that the student "memorize" the derivation! And then, when I modify slightly the question, the student will inevitably tank because it is not what he/she had memorized!

Secondly, and this has been echoed by Mary Boas in her "mathematical methods in the physical sciences" text, one of the difficulties students often associate with physics is that they can't do the math! Learning physics is already daunting. To force them to also learn the math at the same time makes it a difficult subject! I've lost track how many times I had to backtrack in teaching physics because the student couldn't do the math!

So no. Based on my own personal experience, students who took my class (that had a calc class as a prerequisite) who had never had calculus didn't do well in it. Oh, some of them passed, but none of them got A's. If getting a mediocre grade is OK, then I'd say go for it.

Zz.

 

[QuantumCurt]

Although I can see your reasoning, I have to disagree. Yes the velocity graphs etc would make sense having taken calculus. However, most of the examples you have given can be learned in a few hours. Ie basic derivations. Unless the class is being taught using KK, no calculus apart from basic diff/int is needed.

Deriving the kinematic equations is trivial.

I don't agree with this. Although I think one can certainly do well in a calculus based physics class while taking calculus I concurrently, it does put them at a distinct disadvantage. When I took calculus I we weren't even introduced to integration until the last 4 weeks of the semester. Having a knowledge of integration prior to seeing it in physics is of great benefit. You may think that deriving these equations is trivial, and indeed it is. If one knows calculus. If one is in the process of learning the calculus, it does not seem so trivial because they are not able to fluently read the mathematical language that is used to derive it. I can look at and understand an integral and what it means both mathematically and physically. It took time to develop this intuition though. I think in many respects I didn't get the physical intuition for it until physics, but understanding the mathematical structure allowed me to focus solely on developing that physical intuition when approaching a calculus based problem in physics.

 

[MidgetDwarf]

Not for someone who had NEVER had calculus before! How do you expect someone to do "basic diff/int" when that student had never done any of that kind before? What may seem obviously easy to you is not so when one has never done it before! I've seen it. What ended up happening is that the student "memorize" the derivation! And then, when I modify slightly the question, the student will inevitably tank because it is not what he/she had memorized!

Secondly, and this has been echoed by Mary Boas in her "mathematical methods in the physical sciences" text, one of the difficulties students often associate with physics is that they can't do the math! Learning physics is already daunting. To force them to also learn the math at the same time makes it a difficult subject! I've lost track how many times I had to backtrack in teaching physics because the student couldn't do the math!

So no. Based on my own personal experience, students who took my class (that has a calc class as a prerequisite) who had never had calculus didn't do well in it. Oh, some of them passed, but none of them got A's. If getting a mediocre grade is OK, then I'd say go for it.

Zz.

It has a lot more to do with student preparation, and how seriously they took their previous classess. Ie in cal 2 when I took it, many people had problems with u substitution, what a limit was, and weak algebra/trig. There is a difference between memorization and actually learning. Some students are more motivated than others.

I don't know you personally, but are you an excellent lecture? From first hand experience, I know you contribute a lot of knowledge to this forum. I really loved the If you want to be a Physicist thread. However, being g knowledgeable in a subject area does not automatically qualify you as a good teacher. Note I am not saying u are bad or good. Did the students approach you during office hours or talked to other students?

The same situation happened in my course, I did a 2 hour study session (sometimes volunteer around school for community hours), and I showed everyone how integration and derivatives works. I also showed people how vectors worked also another time. The ones that went and asked questions understood. The others that did not care, did not so well. Maybe the failure rate of your students could be attributed to being students first time in college, and these students still had a no care high school mentality.

In my experience, the greatest offenders are pre me students. They always complained about course load, and why are we being shown this if we are not going to be tested. Hey there was even a Jewish kid in my class who did all his work looking at solutions manual every 5 min.