Integrated calculus and physics(OhElizabeth)

[regentrude]

BTW, if we want to rabbit trail, I'd be interested to start thinking about integrated calc and physics and whether there are ways to make this accessible. I wasn't joking when I said it's my goal. They offered that at my high school, and they also offered it separately. (BC Calc and AP Physics) I'm not sure there are textbooks that do this, and the two teachers they used (tag team) were SO ill-liked that many people refused to take it and the rest dropped out mid-year. I always felt it was something we got jipped on, when I listened to people describing the beauty of what could be done in a straightforward way in physics if you knew calculus. (We sat in AP physics dropping packages from airplanes with algebra, ad nauseum, SO boring.) So I KNOW there has to be something better out there, a more holistic, integrated, big-picture, connected way of viewing it. And of course big picture, applied, that has special kids written all over it. There's of course the necessary tedium for basic calc instruction and practice, so I'm not sure how you actually pull that off in a functional way (merging the math and physics instruction). So then you end up with calc one year, physics the next. I've just been trying to figure out if it's possible to combine them in a practical way.

 

I think you could use any standard calculus based physics text and study calculus concurrently with physics.

For the mechanics part, you would only need the calc 1 content, up to basic integrations.

there are large parts of the physics course which would require no calculus, at during these periods the calculus instruction could cover some topics that have not so much relation to physics.

I have not taught this way myself, but here is how I would approach it:

 

I would begin to prep the student with the intro chapters (function review) somewhat before starting physics, or while reviewing units, SI system, unit conversion, dimensional analysis - the material every physics text covers in chapter 1.

The first physics topic is kinematics and requires the concept of the derivative, but at the same time gives a brilliant illustration for applications. So, teaching the calculus concept of derivatives and introducing derivatives of basic functions can be done very well concurrently with kinematics.

The typical second big topic, forces, requires no calculus for solving problems. (One exception are velocity dependent forces, but their treatment would require differential equations and techniques only introduced at the end of a calculus 2 course - so these could not be covered more thoroughly than a basic overview and the terminal velocity.

Energetics requires the concept of integration in order to introduce potential energies. So, while working on force problems in physics, the student should get through applications of derivatives and up to intro of the integral.

For the rest of mechanics, I'd work through integration and begin integration techniques.

To treat oscillations and waves, it would be nice to have differential equations, but intro calculus based physics texts do not require this of the students. the student is, at that point, proficient in derivatives and can verify the validity of the solutions without solving the diff eq.

Thermodynamics requires a bit of integration; specifically, the student needs to know the integral of the 1/T function to get be the natural logarithms. Important for the isothermal process.

 

Integration techniques will become important in electricity and magnetism treatment, typically the second semester of a college course. the student does not have to have completed calc 2, but should be familiar with setting up integral problems. The actual integrals will not be difficult to compute, but it requires some conceptual practice. As this occurs immediately after starting e&m, it would be good to have covered that chapter in math beforehand, so that e&m serves as additional practice and examples, but is not the first exposure.

[kiana]

Here's a link for the first part of a two-book series that was to integrated calc2/mechanics and calc3/e+m for an integrated course taught at some universities. The prerequisite would be calc 1 and a high school physics course (conceptual should be fine). I believe the book is longer in print, but it might be interesting if you can find one at a university library. I borrowed it through ILL and read it myself, but it was a while ago.

 

http://www.amazon.com/Integrated-Physics-Calculus-Volume-1/dp/0201473968

 

Some of the lower reviews say that the calculus material (especially the stuff that doesn't apply to physics) is on the weak side, but that the applications are great. As I already knew calculus before reading the book, I am not really able to evaluate that. Therefore, were I to use this, I would probably supplement with any standard calculus textbook in an older edition. (Stewart is what I would use because I already own it, but there are many other acceptable ones.)

[regentrude]

kiana, that sounds interesting. Does he change the order of topics from the typical physics sequence that begins with kinematics and forces? If not, how does he integrate calc 2 with kinematics and forces where one really can not use a lot of calc 2 material? (In fact, I have seen very few applications for the more complex integration techniques until it gets into actual theoretical physics for majors in their 2nd or 3rd year.) Does he invent particularly hard problems so he can work these in?

Thanks!

[Kathy in Richmond]

Calculus and physics were taught in an integrated fashion to freshmen at Carnegie Mellon back in the '70s. The experiment didn't last long, unfortunately. I think it's a great idea!

 

For anyone trying to combine calculus and physics at home, I'd recommend looking at the Calculus Primer posted by David Green on the Pretty Good Physics site for AP physics teachers. It's written to give the student just enough calculus background to get started in calc-based physics. You don't need to be a member to download his files.

[PeterPan]

Ok, I'm back! I spent some time looking at my dh's physics and calculus texts from college, and I'm now certain I'm NOT looking for something on that level, lol. :) Kiana, thanks for the textbook share. I didn't realize this was an idea that had not taken off. Regentrude, thank you for that list! I wrote down your info in columns so I could study it and see how things line up. Such is the case when delving into new territory.

 

So I guess I'll keep thinking. I now know it's likely to be two separate texts and that I don't want them to be intended for engineers. So maybe even a text aimed at humanities majors, something with more application would do. It's not like we need it immediately. I've just been trying to formulate our 4 year plan, and I was pretty fuzzy about those last two years. I had thought we could do physics and calculus our junior year, statistics and kicked up earth science topics our senior year. Seems like a nice way to finish things out with a humanities student. If I get exposure and lots of application, I think we'll be content. Just need to find the right way to go about that.

 

Kathy, you're right I had totally overlooked the AP classes as a way to look for ideas. I was searching the boards for statistics info this evening and found your post about the Profrock Press book. I ordered that and found a few neat books and rabbit trails to pursue (Simon Singh's The Code Book , The 39 Steps, etc.) that I think will be fun for us. We can either do them this winter if we need a change of pace or for a May Term project. See that's the thing, she can do a lot if I get it to her in a way that catches her and layer the experiences, rather than whomping her. For her history is a great door in, so I'm excited about that ability to connect math and history a bit. I don't think she'd be interested in Singh's Fermat's Enigma because that's overtly mathy and over her head. But the other book should work. And thanks for that link. I'll go check it out.

 

Well thanks for bursting my bubble ladies, lol. So now I have NO concrete plans for 2 years of science and math, and the idea I DID have doesn't even exist for all practical purposes. Awesome. :lol:

 

So if you happen to know of separate texts that are known for having lots of interesting application, books not directed toward freshman engineers, I'm all ears. All I wanted was really interesting physics and calculus. Can't turn her into an engineer to get it. :)

[PeterPan]

Ok, I'll back up and ask a question I'm realizing I should have been asking. What ARE the reasonable applications of calculus for a humanities person? I've just always assumed I would have her do it. I thought it would open doors to things she would enjoy doing. So if we make this effort and she's NOT headed toward engineering, where is this going?

[kiana]

kiana, that sounds interesting. Does he change the order of topics from the typical physics sequence that begins with kinematics and forces? If not, how does he integrate calc 2 with kinematics and forces where one really can not use a lot of calc 2 material? (In fact, I have seen very few applications for the more complex integration techniques until it gets into actual theoretical physics for majors in their 2nd or 3rd year.) Does he invent particularly hard problems so he can work these in?

Thanks!

 

 

I am not sure, because I am not familiar with the typical sequence of topics from physics books. They do appear to have resequenced the calculus course as well. They definitely do kinematics first, but they appear to have done a very early exposure to 3-d calculus and vectors and postponed some of the typical calc 2 stuff into calc 3. I think this would work as long as the university was also able to run a non-integrated sequence for transfer students.

 

Here's the website for the book, where you can find the table of contents (this is for both books, I don't remember where the actual split was). http://www.pearsonhighered.com/educator/academic/product/0,1144,0201473968,00.html

[NittanyJen]

You can do Ecology calculations without calculus in a long, demented, tortured sort of way. Or you can learn the mathematical part of beginning ecology in about a week (maybe two depending on how deep you consider the early level to be) if you use first semester calculus. It's a kind of fun application, actually, for a humanities type person to learn, and shows them how it can be applied and useful!

 

Jen

[kiana]

Ok, I'll back up and ask a question I'm realizing I should have been asking. What ARE the reasonable applications of calculus for a humanities person? I've just always assumed I would have her do it. I thought it would open doors to things she would enjoy doing. So if we make this effort and she's NOT headed toward engineering, where is this going?

 

Well, a basic knowledge of calculus is often prerequisite to taking a serious stat course, which might be required if she went for psychology or sociology. A stat course without a calculus prereq spends a lot of time saying "because I said so, that's why" because the underpinnings involve calculus. Calculus is also used more than you'd think in economics, especially if one goes for an advanced degree.

 

But if her interest is history or english or drama, well, eh, I can't really think of an application of calculus to those off the top of my head. I would see nothing wrong, though, with doing a "calculus for business and social sciences" course instead of an AP course. I think this'd be a lot more applicable. However, I doubt she'd get college credits for it, so if your goal is to have her get college credit for it, this wouldn't work unless she took it as dual enrollment. If, on the other hand, you want an understanding and appreciation for all the things that calculus is used for within other majors, that might work for you. Textbooks for this are commonly found used and cheaply so on amazon.

 

Another idea might be a course in finite mathematics with applications. This is usually a university-level course with a prerequisite of college algebra, however, again, she probably wouldn't be able to get college credit for it. The applications usually focus on business, social science, and life science, and textbooks are available cheaply on amazon. As a matter of fact, Lial does both an applied calculus and a finite mathematics text, as well as a combined text.

 

Another idea might be a mathematics for liberal arts course. I really like Jacobs' Mathematics: A Human Endeavor for liberal arts courses, but there are again many options. These types of courses tend to focus more on logic, mathematical reasoning/thinking, and appreciation than on strictly technical skills, but even if her technical skills are strong this might be an enjoyable course.

 

And finally, completely off the beaten track, she might enjoy a course based on a book called "math through the ages:a gentle history for teachers and others", recently published by the MAA. It's a book on the history of math which includes a fair amount of actual math, designed for future math educators but also very accessible to high-school students.

[PeterPan]

I'm back. I found some interesting books mentioned in other threads (Calculus Diaries, Pizza Calculus) that I think might help us explore this. I'm thinking though that I might also look more out of the box for those last two years. Maybe this wasn't a realistic idea. Just don't know. Anyways, thanks for chatting. It's good to get whomped a little.

[PeterPan]

You can do Ecology calculations without calculus in a long, demented, tortured sort of way. Or you can learn the mathematical part of beginning ecology in about a week (maybe two depending on how deep you consider the early level to be) if you use first semester calculus. It's a kind of fun application, actually, for a humanities type person to learn, and shows them how it can be applied and useful!

 

Jen

 

Ok, slow this down and say it in plain english. You're saying ecology (like studying bug populations or weed growth or something?) uses MATH? Totally did not know that, though it makes sense when you say it. :) So then if you explore that, it's sort of a way to dabble into calculus, get some concepts, go into application... What is the normal way humans explore this? Are there courses that are typically paired?

[PeterPan]

Kiana, that's it!!!!!!! That Lial's book (Calc with Applications) would be FABULOUS for her. Well as fabulous as a book can get, considering I'd have to teach it. But no matter. You're right, that's exactly where she needs to be. I want her to have that experience with calculus, and I didn't even know this was this whole other genre of calculus texts. I'm so glad you shared that! Oh, here's a link to samples, just in case anyone else is curious. http://www.pearsonhighered.com/lgrseries/calc/detail/sample-chapter/echapter/#/38/

 

So that doesn't solve my high school science sequence, but it does resolve the math. We can continue our TT/BJU pairing through pre-calc, do the Lial Calc with Applications, then a statistics class, and she's done. That's perfect for her. So do you have any marvelous suggestions for science? Things I haven't thought of or didn't know existed? :)

 

I'll go look for that history of math book. :)