Calculus? What is the point?

[Daisy]

I'm showing my profound math ignorance here. I only took Algebra 1 & 2 and geometry. I took the CLEP and tested out of all of my college general requirements in math.

 

What exactly is the point of calculus and trig? Are these maths useful in everyday life or are they really just for those going into fields that require this level of knowledge?

 

Can you tell me fields that require and USE this math other than engineering (I know that one. LOL)?

[kristinannie]

I am pretty sure that trig is necessary for the SAT. I was a Chem major and definitely needed my calculus!

[Daisy]

When did they change the SAT to include it? I'm dating myself by asking, probably. LOL.

 

And yes, I would imagine anyone in a science field would need those higher maths.

[Daisy]

I am pretty sure that trig is necessary for the SAT. I was a Chem major and definitely needed my calculus!

 

Can you explain to me what kinds of problems you'd need calculus for? Really, I'm just trying to explain to my daughter why this subject would be important and I don't know enough about it to tell her. I obviously never use it. LOL.

[Dmmetler]

Physics and Statistics come to mind immediately. In both cases, calculations can be done in parts using just algebra, but it's much, much harder and slower. And while physics may not be useful if you're outside STEMs fields, Statistics is necessary for many, many more fields-human sciences, medicine and business all come to mind off the top of my head.

Edited May 7, 2011 by dmmetler

[....]

I had to take calc to graduate with my degree in biological sciences. Honestly, I think it's better understood in college than in high school. Math seemed to click better in my early 20's than it did in my teens, for some reason.

[8filltheheart]

I had to take calc to graduate with my degree in biological sciences. Honestly, I think it's better understood in college than in high school. Math seemed to click better in my early 20's than it did in my teens, for some reason.

 

That is a generalization. There are students that are more than ready for cal in their early high school yrs. Many are ready as seniors.

 

For the OP, a lot of college majors are going to require cal. I'd have to go and look in our books, but I am pretty sure that the SAT only goes through alg 2 and the ACT includes trig.

[Just Robyn]

Can we add that a lot of majors don't require calc though? It just feels like this thread is going the way of, "You should definitely take calc. You'll regret it if you don't."

 

If a student doesn't believe they'll be going into a field that requires that level of math, I don't see why they shouldn't take an elective instead. They can always take it in college if they change their mind.

[jennynd]

physics/engineering related subject uses calculus extensively..

[8filltheheart]

Can we add that a lot of majors don't require calc though? It just feels like this thread is going the way of, "You should definitely take calc. You'll regret it if you don't."

 

If a student doesn't believe they'll be going into a field that requires that level of math, I don't see why they shouldn't take an elective instead. They can always take it in college if they change their mind.

 

:confused: I'm not sure how that addresses "what's the pt of calculus?"

 

"Real" physics is cal-based. But, it goes beyond engineering and physics, most bio majors are going to require 2 semesters of cal as well.

[boscopup]

 

If a student doesn't believe they'll be going into a field that requires that level of math, I don't see why they shouldn't take an elective instead. They can always take it in college if they change their mind.

 

For some majors, it might be useful early on, and some kids change their minds last minute. I was going to do music education, but at orientation, I changed to electrical engineering. I'm glad I already had calculus 1 and 2 under my belt!

 

(I'm not saying that you should make your child take calculus necessarily... Just giving an example of not pigeon holing our children based on choices made in high school)

[jennynd]

Can we add that a lot of majors don't require calc though? .

 

yes, i will agree, if u are going for liberal art. calculus is useless. In Taiwan, high school kids are not req to take calculus unless they are going for science/engineering/medical majors

[kpnick in nc]

Being required to take calculus and actually using it are two different things. I have degrees in biochemistry and genetics, and the only times I encountered calculus were in my three required calc courses and two required physics courses. None of the academics I worked with used calculus on a regular basis, that I know of. I'm saying that it's possible to go into a science field without being an expert in calculus.

 

The wikipedia entry on calculus (under Applications) does a decent job of listing various 'real world' uses of calculus (defined there as "the study of change"). In the same way that algebra makes work with operations/equations 'easier', calculus makes dealing with things that are changing (radioactive decay, flow of a liquid, etc) much easier.

[8filltheheart]

Being required to take calculus and actually using it are two different things.

 

Oh, I don't disagree with you at all. I would suggest that about 35% of the courses that are "required" for a degree fit into that category. :tongue_smilie: (I specifically remember a certain philosophy course that I **know** has had zero relevance to anything in my life ever!! :lol: )

 

However, that said, it does serve a purpose......you can't earn your degree w/o it. ;)

[Dana]

Rough explanation....

 

Everything before calculus deals with a static system. For instance, with algebra you can find the slope of a line. This shows how fast what you're measuring is changing.

 

But in reality, things don't change at a constant rate (or very rarely). The concept of a limit lets you figure how something is changing in a given instant rather than over a static period of time.

 

For instance: What was your average speed on a trip? (algebra)

How fast were you driving at a given point of time? (calculus)

 

In calc I, you generally cover the idea of a limit, differentiation (applications including related rates and maximum/minimum problems), antidifferentiation (the integral), and the definite integral (where applications include finding the area under any curve, so you aren't limited to just the basic area formulas; volume of any figure; length of any curve).

 

I believe trig used to be used (and may still be) in surveying. Laws of sines/cosines are good for finding all relationships between a triangle. This can be used in navigation. I think it also is used in forestry (calculating height of a tree for instance... had students do a project once on that).

 

Economics uses calculus for predictions. Marginal cost, marginal revenue, marginal profit: calculus describes what these are. A max/min problem would show what you should price something at to get maximum profit for instance. (Of course, the big question then in the real world becomes how accurate the mathematical model is!)

[kpnick in nc]

In science/tech fields other than physics and engineering (someone can correct me if I'm wrong on that), a working knowledge of calculus is an optional skill. In other science fields, calculus would be handy in various research specialties, but there are plenty of areas for which it wouldn't be needed. So I see it as an academic math - used by people who make mathematical models, etc.

 

As a side note, statistics is a math that I didn't take, but I wished I had many times!

[Pata]

I also have a biochemistry degree and I agree that I didn't use calculus in my biochem classes per se, but calculus did help to train my brain to think analytically, which I did use in my biochem classes. If you student is ready for it, go for it. Many universities would like to see calculus no matter what major they are applying for, so I think it's worth it if you have the time. It's critical to do if you student is hoping to major in the sciences, engineering, architecture or in math :).

[kpnick in nc]

However, that said, it does serve a purpose......you can't earn your degree w/o it. ;)

 

Very true!

[laundrycrisis]

.

 

Economics uses calculus for predictions. Marginal cost, marginal revenue, marginal profit: calculus describes what these are. A max/min problem would show what you should price something at to get maximum profit for instance. (Of course, the big question then in the real world becomes how accurate the mathematical model is!)

 

:iagree: Calculus is necessary for financial calculations in business. Cash flows, return on investment, payout time, market analysis, profit predictions, etc.

Edited May 8, 2011 by laundrycrisis

[Just Robyn]

:confused: I'm not sure how that addresses "what's the pt of calculus?"

 

"Real" physics is cal-based. But, it goes beyond engineering and physics, most bio majors are going to require 2 semesters of cal as well.

 

It addresses it by modifying the seemingly implied answer that calculus is generally useful and required to finish college, as I would consider that an exaggeration. Perhaps that was not the intended implication, but it felt to me like that's what the accumulation of answers was adding up to, so I attempted to balance it out, thus making it more accurate.

[kpnick in nc]

I also have a biochemistry degree and I agree that I didn't use calculus in my biochem classes per se, but calculus did help to train my brain to think analytically, which I did use in my biochem classes. If you student is ready for it, go for it. Many universities would like to see calculus no matter what major they are applying for, so I think it's worth it if you have the time. It's critical to do if you student is hoping to major in the sciences, engineering, architecture or in math :).

 

:iagree:Oh yes, it did help me think! It provides great training for the brain.

[Capt_Uhura]

:iagree: Calculus is necessary for financial calculations in business. Cash flows, return on investment, payout time, market analysis, profit predictions, etc.

 

If I knew that, I certainly forgot it! Thanks for the info! I remember enjoying calculus but I didn't take it until college.

[boscopup]

Being required to take calculus and actually using it are two different things.

 

:iagree:My dad is an electrical engineer, and has been one for 30 years now. A year or so ago, he finally used Laplace Transforms. He hadn't used those since college. He was thrilled to finally have a use in a project he was working on. :lol:

 

I never used calculus in my work either, nor any of my electrical engineering knowledge (which has ALL gone out the window). I developed software. I occasionally had to do some math due to the project I was working on, but it was not calculus. I just had to do sines and cosines mostly.

 

I wish I'd had more use for calculus. I LOVED it. Seriously loved it.

[Daisy]

Thanks! This has been helpful.

 

We are doing physical science next year so I checked a book out from the library about physics. It has mentioned calculus a few times when discussing speed, variables, etc. I've never had physics either so I'm trying not to sound like a total idiot when I teach my kids next year. I was a biology, zoology, ecology, chemistry kinda gal. LOL.

[EKS]

Here's the thing. You will use what you know. So if you don't know something, it is inconceivable to you that someone might use it. But if you do know something (really well, so that it is a part of you) you will use it. I know my father uses calculus and other advanced math in his daily life. I, on the other hand, only use elementary algebra and geometry in my daily life because that is what I truly understand.

[Heather in VA]

Can we add that a lot of majors don't require calc though? It just feels like this thread is going the way of, "You should definitely take calc. You'll regret it if you don't."

 

If a student doesn't believe they'll be going into a field that requires that level of math, I don't see why they shouldn't take an elective instead. They can always take it in college if they change their mind.

 

You know though, you could use this argument for a lot of things that are studied. I never understand why it's a valid argument to not study something in the math or science arena because you'll "never use it". We study lots of things to don't officially use in your day to day life but that doesn't mean studying them have no value.

 

Heather

[Daisy]

Here's the thing. You will use what you know. So if you don't know something, it is inconceivable to you that someone might use it. But if you do know something (really well, so that it is a part of you) you will use it. I know my father uses calculus and other advanced math in his daily life. I, on the other hand, only use elementary algebra and geometry in my daily life because that is what I truly understand.

 

Right. I agree. I just want to be able to explain to my daughter why she should be smarter than me. :lol:

 

I told her I would take it with her when the time comes if she wants. I'm game.

[silliness7]

I also have a biochemistry degree and I agree that I didn't use calculus in my biochem classes per se, but calculus did help to train my brain to think analytically, which I did use in my biochem classes. If you student is ready for it, go for it. Many universities would like to see calculus no matter what major they are applying for, so I think it's worth it if you have the time. It's critical to do if you student is hoping to major in the sciences, engineering, architecture or in math :).

 

I would like all of my children to take calculus. I did not. But I would like them too because I really, truly believe that learning math (and Latin too) helps train the brain. At least that's what I tell them when they start griping about both math and Latin. :D

[NittanyJen]

Thanks! This has been helpful.

 

We are doing physical science next year so I checked a book out from the library about physics. It has mentioned calculus a few times when discussing speed, variables, etc. I've never had physics either so I'm trying not to sound like a total idiot when I teach my kids next year. I was a biology, zoology, ecology, chemistry kinda gal. LOL.

 

 

Okay, there's an opening. I took a 300-level ecology course with a bunch of bio majors who hadn't yet finished their calc series, and it was TORTURE for me. WHY? Because we could have covered the ENTIRE population ecology (6 weeks) portion of the course in 2 lectures if the other students had been competent in calculus. Iinstead of the painstaking, painfully slow and kludgy methods that you have to use to get things done without calculus, we could have used some very, very simple and straightforward calculus found in pretty much every beginning level calc text, including ecology examples, and been done with it in 2 lectures! Those slow and klunky calculations can be done in a flash with calc.

 

Calculus describes how systems behave as they are changing-- be they physics systems, population changes, biological systems, graphs of functions, marketing behavior models, ocean waves, the movement of fluid through pipes, the sound waves generated by a drum, how an ocean wave forms, you name it.

 

I have many times seen research teams analyzing data in painful, long, and sometimes error-prone means (because there are too many unnecessary steps) when a simple calc-based calculation would have sufficed, and made life far easier. Also, in today's calculus classes, students are introduced to mathematical processing software to speed along these calculations and illustrate them. It is horrifying to watch people in other fields such as biology crank data in Excel that doesn't actually belong in a spreadsheet (I have worked as a bench scientist in this field and have witnessed that particular sin more times than I can say).

 

There are many who say they don't "need" calculus, but who could benefit greatly from it if they used it. Sometimes it's just fascinating (so, what DOES happen as you get closer and closer to dividing by zero?? How do things change as you accelerate??)

 

Not everyone needs it. I would not artificially hold a student back from taking it-- young adults frequently change majors after arriving at college. But it's very true that not everyone needs it (my physical therapist has probably never used calculus in the course of his career. I bet my pastor never has either. Neither has my physician. All are very smart people at the top of their careers). My husband, on the other hand, uses calculus daily-- and when he set out for college as an undergrad, he was not originally a math major, a field in which he is now a PhD.

 

Honestly the best place to answer this question is-- a scan of the college catalogs. Hit the websites of the colleges your child is most likely to apply to and see what they expect, and check the course of study requirements for the majors your DC is interested in and see how many of them require calculus. That should really answer your question!

 

Best of luck!

 

Jen

[Just Robyn]

You know though, you could use this argument for a lot of things that are studied. I never understand why it's a valid argument to not study something in the math or science arena because you'll "never use it". We study lots of things to don't officially use in your day to day life but that doesn't mean studying them have no value.

 

Heather

 

I certainly did not say that studying calculus has no value. There is a big difference between that and, "Let's not exaggerate the necessity of studying calculus to graduate college." I'm sure whatever elective a student might choose to take instead of calculus would have value as well. Which classes are more or less valuable, at that level especially (as contrasted with, say, basic addition or literacy), varies from person to person, and for each person, the value of a particular subject may vary from time to time throughout their life. For sure, I think more knowledge is always better in every subject, but deciding not to take calculus means you're deciding to take some other course and vice versa. No matter what, you're deciding to either skip or delay knowledge and/or skills in one area or another.

[Karen in CO]

I've used calculus and trigonometry in my work. I've worked on computer programming projects that used Fourier Transformations to turn satellite data into maps predicting where oil could be found on mountainous slopes in South America. I've also written programs to generate utility maps that use trig to determine not only where/how to draw each utility structure but also where to place and how to orient the text on the printed map. And of course targeting maps for smart bombs are generated by people using trig - don't ask me how I know that because I couldn't tell you.

 

My brother is a math teacher - apparently he uses trig when he does construction in the summers (and in my basement in the winters).

Edited May 8, 2011 by Karen in CO

[Carol in Cal.]

Some calculus is needed for every science or engineering major in college, as well as for math, statistics, and I think some business majors.

 

Also, it just makes calculations so easy.

 

You know how once you learn algebra, even just Algebra 1, you can make a lot of easy calculations that used to be long and iterative or just hard to wrap your head around, very easily? Calculus is exactly like that. It's a wrap up of everything you learn up to that point, which provides amazing shortcuts to things that were formerly extremely difficult.

 

I would want most kids to get through calculus, even if they didn't major in that stuff. The end of first year calculus is a decent place to stop studying math.

[In The Great White North]

My brother is a math teacher - apparently he uses trig when he does construction in the summers (and in my basement in the winters).

 

Trig comes in very handy in home renovation/construction type projects :001_smile:

 

Here's the thing. You will use what you know. So if you don't know something, it is inconceivable to you that someone might use it. But if you do know something (really well, so that it is a part of you) you will use it. I know my father uses calculus and other advanced math in his daily life. I, on the other hand, only use elementary algebra and geometry in my daily life because that is what I truly understand.

 

:iagree::iagree:

 

Okay, there's an opening. I took a 300-level ecology course with a bunch of bio majors who hadn't yet finished their calc series, and it was TORTURE for me. WHY? Because we could have covered the ENTIRE population ecology (6 weeks) portion of the course in 2 lectures if the other students had been competent in calculus. Iinstead of the painstaking, painfully slow and kludgy methods that you have to use to get things done without calculus, we could have used some very, very simple and straightforward calculus found in pretty much every beginning level calc text, including ecology examples, and been done with it in 2 lectures! Those slow and klunky calculations can be done in a flash with calc.

 

:iagree::iagree:

 

There was a thread a while ago (which I can't find) which talked about the retention levels of people who had had algebra years ago. Algebra proficiency deteriorated with time EXCEPT for those who had had caLculus! Their data covered people who had taken algebra 5 to 50 years ago. Those who had studied calculus, even 50 years ago, retained ALL of their algebra today. Those who had not studied calculus, had lost their algebra.

[Capt_Uhura]

You all have me excited to take Calculus again! What texts would you recommend? OH I'm sure AoPS must have something. I'm totally enthralled w/ the AoPS intro to alg1 text right now.

[Hedgehogs4]

Rough explanation....

 

Everything before calculus deals with a static system. For instance, with algebra you can find the slope of a line. This shows how fast what you're measuring is changing.

 

But in reality, things don't change at a constant rate (or very rarely). The concept of a limit lets you figure how something is changing in a given instant rather than over a static period of time.

 

For instance: What was your average speed on a trip? (algebra)

How fast were you driving at a given point of time? (calculus)

 

In calc I, you generally cover the idea of a limit, differentiation (applications including related rates and maximum/minimum problems), antidifferentiation (the integral), and the definite integral (where applications include finding the area under any curve, so you aren't limited to just the basic area formulas; volume of any figure; length of any curve).

 

I believe trig used to be used (and may still be) in surveying. Laws of sines/cosines are good for finding all relationships between a triangle. This can be used in navigation. I think it also is used in forestry (calculating height of a tree for instance... had students do a project once on that).

 

Economics uses calculus for predictions. Marginal cost, marginal revenue, marginal profit: calculus describes what these are. A max/min problem would show what you should price something at to get maximum profit for instance. (Of course, the big question then in the real world becomes how accurate the mathematical model is!)

 

very interesting and good description. I always wondered myself. I'm heavy on humanities, and want to give my kids a balance of the math and sciences.

[Crimson Wife]

Okay, there's an opening. I took a 300-level ecology course with a bunch of bio majors who hadn't yet finished their calc series, and it was TORTURE for me. WHY? Because we could have covered the ENTIRE population ecology (6 weeks) portion of the course in 2 lectures if the other students had been competent in calculus. Iinstead of the painstaking, painfully slow and kludgy methods that you have to use to get things done without calculus, we could have used some very, very simple and straightforward calculus found in pretty much every beginning level calc text, including ecology examples, and been done with it in 2 lectures! Those slow and klunky calculations can be done in a flash with calc.

 

I felt this way sitting in a professional development training session for my first job out of college. The teacher needed to teach us how to do some sort of cost analysis. She showed the handful of us who knew calculus how to do the calculation in about 5 minutes. Then she proceeded to spend over an hour showing the rest of the class how to do the work-around. Unfortunately, the teacher was not permitted to let me leave for this portion as I was "on the clock". So I just had to sit there bored and thinking that everyone else just should've learned calculus in high school and/or college!

 

I used calculus only occasionally in my old profession, but my DH uses it all the time as a stock analyst.

[stripe]

I've observed that those who have taken calculus are able to think about large numbers, and progressions towards infinity, and progressions towards a point, whereas those who have not, find this confusing.

 

For example the idea of a term dominating as x--> infinity. Like in 3x^3 + 4x + 15. This really doesn't make sense if you've only ever plugged in numbers < 100, or usually < 10, into an equation. Those without calculus experience tend to see all the terms as having an equal effect, or fixate on the constant.

[Veritaserum]

I took three semesters of calculus through the community college while I was in high school. I used it my first semester at a university in my physics class. Dh and I met because he needed help with his calculus. :tongue_smilie:

 

My calculus is very rusty at this point, but I'm glad I studied it. I think learning higher maths gave me a better understanding of algebra/geometry/etc. I plan on my kids getting through calculus before they graduate from high school. If they don't end up needing it, fine. But if they do end up needing it, they will be prepared. :)

[Penelope]

Some calculus is needed for every science or engineering major in college, as well as for math, statistics, and I think some business majors.

 

Also, it just makes calculations so easy.

 

You know how once you learn algebra, even just Algebra 1, you can make a lot of easy calculations that used to be long and iterative or just hard to wrap your head around, very easily? Calculus is exactly like that. It's a wrap up of everything you learn up to that point, which provides amazing shortcuts to things that were formerly extremely difficult.

 

I would want most kids to get through calculus, even if they didn't major in that stuff. The end of first year calculus is a decent place to stop studying math.

 

:iagree: You need it for physics, which back in the day was required for all science majors. I even knew some psych. majors that took it, though don't know if it was required, because they needed it for stats and research applications.

[serendipitous journey]

... that would be my answer. An unconventional and flawed, but superbly interesting, resource is the original Mathematics for the Million by Hogben. If it annoys you, though, as it does many (the history's iffy, and he's quite left-wing), it won't be much help. Another oft-annoying but quite good book is Barron's Trigonometry the Easy Way.

 

The world around us lives in calculus-space -- it is full of dynamic, or changing, systems -- and in trig-space -- you can figure out yourself how far away the sun is, and check estimates of the size of the moon, or build a sturdy fort and arm it with catapults that shoot over your moat (given a bit of yard, and perhaps some books on catapult-building). Given these equations you can develop an understanding of how fireflies synchronize their flashing and the flocking behavior of birds ... these are the marvelous, fun bits of math that enrich one's entire experience and (if you are of the faith to believe so) echo the voice of the Creator. If not, you may see these maths as the very picture of nature.

Edited May 8, 2011 by serendipitous journey

[Monica_in_Switzerland]

Understanding the physical sciences is enriched greatly with calc. Knowing that position, velocity, and acceleration are inherently related mathematically is much better than memorizing the formulas.

 

Knowing calc in order to thoroughly understand statistics is important for anyone going into any field that involves research- knowing the strengths (and limitations) of statistical analysis of data is very important.

 

Calculus is simply a very, very powerful tool, and I happen to think it's incredibly fun to learn.

 

Knowing that you can take a section of a function on a graph, spin it about the x-axis, then calculate the volune of what you've just created seems useless, but just understanding that simple math, done by hand even, can do such a thing is AMAZING! Calc was my favorite class in highs school. :-)