Just Another Calculus Question..

by FluteHolder Wed May 01, 2013 10:39 am

With so much interest in Calculus, thought I should post this question. Answer it without googling..

What are the practical/daily/day-to-day application of Calculus or its use in and around our home/work. For example where it is applied/used in any appliances/gadgets/equipments/design/economics/finance etc in and around home/work.

by Kris Wed May 01, 2013 11:09 am

FluteHolder wrote:With so much interest in Calculus, thought I should post this question. Answer it without googling..

What are the practical/daily/day-to-day application of Calculus or its use in and around our home/work. For example where it is applied/used in any appliances/gadgets/equipments/design/economics/finance etc in and around home/work.

>>> My son asked me this about trig yesterday. I told him that math in general will help him appreciate things more, which is about as vague as I could get. My personal opinion, sometimes you do things just because they are there. Kinda like what Edmund Hillary said about climbing Mt. Everest. I think he was the one who said this anyway.

by MaxEntropy_Man Wed May 01, 2013 11:23 am

you could get a more concrete answer had you asked for the things in life that don't involve calculus. the answer to the question you asked is too long.

also, while the utilitarian need for calculus and math in general is an ok question to ask, there is a deeper reason that some people are attracted to mathematics -- its intrinsic beauty. it appeals for the same reason one finds art and music appealing. there is no utilitarian reason required to study mathematics.

by MaxEntropy_Man Wed May 01, 2013 11:28 am

Kris wrote:
FluteHolder wrote:With so much interest in Calculus, thought I should post this question. Answer it without googling..

What are the practical/daily/day-to-day application of Calculus or its use in and around our home/work. For example where it is applied/used in any appliances/gadgets/equipments/design/economics/finance etc in and around home/work.

>>> My son asked me this about trig yesterday. I told him that math in general will help him appreciate things more, which is about as vague as I could get. My personal opinion, sometimes you do things just because they are there. Kinda like what Edmund Hillary said about climbing Mt. Everest. I think he was the one who said this anyway.

here are some utilitarian reasons to study trigonometric functions -- building construction, figuring out the relationship between the dimensions of everyday objects, and relationships between alternating currents and voltages in electrical engineering.

by FluteHolder Wed May 01, 2013 11:36 am

Kris wrote:
FluteHolder wrote:With so much interest in Calculus, thought I should post this question. Answer it without googling..

What are the practical/daily/day-to-day application of Calculus or its use in and around our home/work. For example where it is applied/used in any appliances/gadgets/equipments/design/economics/finance etc in and around home/work.

>>> My son asked me this about trig yesterday. I told him that math in general will help him appreciate things more, which is about as vague as I could get. My personal opinion, sometimes you do things just because they are there. Kinda like what Edmund Hillary said about climbing Mt. Everest. I think he was the one who said this anyway.

I stress this couplet from Chapter 40-Education from Kural to my daughter and also about Kural whenever get a chance:)

392. எண்ணென்ப ஏனை எழுத்தென்ப இவ்விரண்டும்
கண்ணென்ப வாழும் உயிர்க்கு.
eNNenba enai ezhuththenba ivviraNdum
kaNNenba vaazhum uyirkku.

வாழும் உயிர்களுக்கு கண்போல் அமைந்த கலைகள் இரண்டு. எண் எனப்படும் கணிதம் முதலான அறிவியல் ஒன்று, இலக்கணம்
இலக்கியம் முதலான அழகியல் மற்றையது
Two are the eyes of those who truly live--one is called numbers,and the other letters.

I was trying to see some real applications like basic math in finance/commerce used in daily life compared to use of Calculus. It would be great if schools introduce finance/economics/financial markets instead/apart/in-addition to Calculus.

by Marathadi-Saamiyaar Wed May 01, 2013 11:46 am

FluteHolder wrote:With so much interest in Calculus, thought I should post this question. Answer it without googling..

What are the practical/daily/day-to-day application of Calculus or its use in and around our home/work. For example where it is applied/used in any appliances/gadgets/equipments/design/economics/finance etc in and around home/work.

Here are some things that kids can relate to:

Shadow of kid, how moon shows up at different times on different days, predicting festivals, shooting basketball, throwing a ball at dad form different distances. The mind, eye/hand coordination (subconsciously) calculates trignometric pronciples. later we study those things that we have been using all along.

Car starting, speeding up, cruising, crashing the bike onto a wall, rocket launching etc... involve calculus.

by Jeremiah Mburuburu Wed May 01, 2013 12:22 pm

Kris wrote:
FluteHolder wrote:With so much interest in Calculus, thought I should post this question. Answer it without googling..

What are the practical/daily/day-to-day application of Calculus or its use in and around our home/work. For example where it is applied/used in any appliances/gadgets/equipments/design/economics/finance etc in and around home/work.

>>> My son asked me this about trig yesterday. I told him that math in general will help him appreciate things more, which is about as vague as I could get. My personal opinion, sometimes you do things just because they are there. Kinda like what Edmund Hillary said about climbing Mt. Everest. I think he was the one who said this anyway.

trig finds use in modeling numerous repetitive or cyclical phenomena. examples: the weather, parts of the economy, demand for products and inputs that are seasonal - skiing equipment, summer sports equipment, agricultural inputs like fertilizer and pesticides, gasoline, heating oil, tourism, school supplies and uniforms, construction materials, construction labour, perhaps even certain types of crime and illegal immigration.

much of electrical engineering depends on being able to model the alternating currents and voltages generated by modern power stations. our civilization's infrastructure and most appliances that have raised our standard of living depend on electrical equipment which are designed and manufactured by modeling and simulating cyclical electrical quantities using trig.

don't forget the modeling of numerous cyclical physiological phenomena that depend on the heart's rhythm, including blood pressure, especially under different pathological conditions, and those that depend on the 24-hour sleep cycle.

by FluteHolder Wed May 01, 2013 12:22 pm

MaxEntropy_Man wrote:you could get a more concrete answer had you asked for the things in life that don't involve calculus. the answer to the question you asked is too long.

also, while the utilitarian need for calculus and math in general is an ok question to ask, there is a deeper reason that some people are attracted to mathematics -- its intrinsic beauty. it appeals for the same reason one finds art and music appealing. there is no utilitarian reason required to study mathematics.

I was looking for some daily use/practical like basic math/arithmetic: Like we are planning a vegetable garden/drip irrigation and trying to calculate the no of sprayheads per lane per feet/length of poly pipe required. I asked my daughter to measure the length of the back yard to find out how much poly pipe required and cost per sprayhead and total cost etc etc. Also gph per sprayhead and total water consumption etc..

by MaxEntropy_Man Wed May 01, 2013 12:33 pm

FluteHolder wrote:
MaxEntropy_Man wrote:you could get a more concrete answer had you asked for the things in life that don't involve calculus. the answer to the question you asked is too long.

also, while the utilitarian need for calculus and math in general is an ok question to ask, there is a deeper reason that some people are attracted to mathematics -- its intrinsic beauty. it appeals for the same reason one finds art and music appealing. there is no utilitarian reason required to study mathematics.

I was looking for some daily use/practical like basic math/arithmetic: Like we are planning a vegetable garden/drip irrigation and trying to calculate the no of sprayheads per lane per feet/length of poly pipe required. I asked my daughter to measure the length of the back yard to find out how much poly pipe required and cost per sprayhead and total cost etc etc. Also gph per sprayhead and total water consumption etc..

i have to think about your specific problem, but here is one fairly practical application. whenever you have a constrained maximization (or minimization) problem, say with a fixed perimeter, you are trying to maximize area or vice versa, ike you would encounter in building a fence, you could use calculus (although i am quite certain for such really simple problems you could do without using calculus too).

edited to add: in your case if you had a fixed number of spray heads you could formulate a problem whereby you calculate the optmum spacing between spray heads to achieve maximum area of irrigation. alternately you could formulate the problem in terms of minimizing cost with a fixed area to be irrigated.

by Rishi Wed May 01, 2013 12:34 pm

Professor Steve Butler of UCLA says

We understand flat things very well. For example rectangles.

But we do not understand things which are not flat. For example curves.

We learn Calculus to understand things which are not flat.

In Calculus, we approximate things which are not flat by things which are flat.

by Idéfix Wed May 01, 2013 12:47 pm

You learn much of what you learn in high school not for its everyday utility, but as parts of a toolkit for life. There is little everyday utility for poetry, philosophy, history, chemistry, etc. But I would not support replacing them with stock valuation or accounting classes.

by Marathadi-Saamiyaar Wed May 01, 2013 1:07 pm

FluteHolder wrote:
MaxEntropy_Man wrote:you could get a more concrete answer had you asked for the things in life that don't involve calculus. the answer to the question you asked is too long.

also, while the utilitarian need for calculus and math in general is an ok question to ask, there is a deeper reason that some people are attracted to mathematics -- its intrinsic beauty. it appeals for the same reason one finds art and music appealing. there is no utilitarian reason required to study mathematics.

I was looking for some daily use/practical like basic math/arithmetic: Like we are planning a vegetable garden/drip irrigation and trying to calculate the no of sprayheads per lane per feet/length of poly pipe required. I asked my daughter to measure the length of the back yard to find out how much poly pipe required and cost per sprayhead and total cost etc etc. Also gph per sprayhead and total water consumption etc..

Your example is better than what many are giving. I guessed you were talking about a 9 or 10 yr old. One has to think from that age point of view. If she knew calculus and trigonometry, she will be able to design the sprinkler head itself, the pipe size, and thickness, etc. That is what they do before manufacturing. Since she does not know these fundamentals she will have to rely on trial and error.

by MaxEntropy_Man Wed May 01, 2013 2:21 pm

i strongly believe that the american tendency to find out a subject's utility before studying it is both a strength and a weakness. it lies at the root of their utter pragmatism but also their woefully inadequate grasp of high school level mathematics.

by Jeremiah Mburuburu Wed May 01, 2013 2:45 pm

Rishi wrote:Professor Steve Butler of UCLA says

We understand flat things very well. For example rectangles.

But we do not understand things which are not flat. For example curves.

We learn Calculus to understand things which are not flat.

In Calculus, we approximate things which are not flat by things which are flat.

i don't like what this professor says in this quote. perhaps he's referring to the notion that an instantaneous rate of change (at a point on a curve) is the slope of the (straight) tangent line (at that point on the curve). i still don't like it.

by Jeremiah Mburuburu Wed May 01, 2013 2:49 pm

MaxEntropy_Man wrote:you could get a more concrete answer had you asked for the things in life that don't involve calculus. the answer to the question you asked is too long.

also, while the utilitarian need for calculus and math in general is an ok question to ask, there is a deeper reason that some people are attracted to mathematics -- its intrinsic beauty. it appeals for the same reason one finds art and music appealing. there is no utilitarian reason required to study mathematics.

your response does not answer fluteholder's Q at all. he specifically asked about everyday uses of calculus.

by MaxEntropy_Man Wed May 01, 2013 3:04 pm

Jeremiah Mburuburu wrote:
MaxEntropy_Man wrote:you could get a more concrete answer had you asked for the things in life that don't involve calculus. the answer to the question you asked is too long.

also, while the utilitarian need for calculus and math in general is an ok question to ask, there is a deeper reason that some people are attracted to mathematics -- its intrinsic beauty. it appeals for the same reason one finds art and music appealing. there is no utilitarian reason required to study mathematics.
your response does not answer fluteholder's Q at all. he specifically asked about everyday uses of calculus.

after that response i did give him a couple of examples. here is a more specific response to fluteholder - whenever you have to calculate rates of change, say the rate of water flow from a drinking water tank of the type delivered by polar beverages, and you wish to calculate at what point the flow becomes too slow that you have to change it out. you might wish to consider using calculus to obtain the relationship between the water column height (and thus the pressure head) and the water flow rate at the opening at the bottom.

by Jeremiah Mburuburu Wed May 01, 2013 3:28 pm

MaxEntropy_Man wrote:
Jeremiah Mburuburu wrote:
MaxEntropy_Man wrote:you could get a more concrete answer had you asked for the things in life that don't involve calculus. the answer to the question you asked is too long.

also, while the utilitarian need for calculus and math in general is an ok question to ask, there is a deeper reason that some people are attracted to mathematics -- its intrinsic beauty. it appeals for the same reason one finds art and music appealing. there is no utilitarian reason required to study mathematics.
your response does not answer fluteholder's Q at all. he specifically asked about everyday uses of calculus.

after that response i did give him a couple of examples. here is a more specific response to fluteholder - whenever you have to calculate rates of change, say the rate of water flow from a drinking water tank of the type delivered by polar beverages, and you wish to calculate at what point the flow becomes too slow that you have to change it out. you might wish to consider using calculus to obtain the relationship between the water column height (and thus the pressure head) and the water flow rate at the opening at the bottom.

thanks.

by Marathadi-Saamiyaar Wed May 01, 2013 6:54 pm

MaxEntropy_Man wrote:
Jeremiah Mburuburu wrote:
MaxEntropy_Man wrote:you could get a more concrete answer had you asked for the things in life that don't involve calculus. the answer to the question you asked is too long.

also, while the utilitarian need for calculus and math in general is an ok question to ask, there is a deeper reason that some people are attracted to mathematics -- its intrinsic beauty. it appeals for the same reason one finds art and music appealing. there is no utilitarian reason required to study mathematics.
your response does not answer fluteholder's Q at all. he specifically asked about everyday uses of calculus.

after that response i did give him a couple of examples. here is a more specific response to fluteholder - whenever you have to calculate rates of change, say the rate of water flow from a drinking water tank of the type delivered by polar beverages, and you wish to calculate at what point the flow becomes too slow that you have to change it out. you might wish to consider using calculus to obtain the relationship between the water column height (and thus the pressure head) and the water flow rate at the opening at the bottom.

This is what happens when you always think at high level... You need to come down and think like a 8 or 10 year old leaving out all the "technical" approach and "terminologies".

Anyways...

by bw Wed May 01, 2013 7:02 pm

FluteHolder wrote:With so much interest in Calculus, thought I should post this question. Answer it without googling..

What are the practical/daily/day-to-day application of Calculus or its use in and around our home/work. For example where it is applied/used in any appliances/gadgets/equipments/design/economics/finance etc in and around home/work.

when you drive a car?

by pravalika nanda Wed May 01, 2013 7:19 pm

very nice. I learned a lot from flam and max today.

by Guest Wed May 01, 2013 7:46 pm

my coaching class was once told, 'sir there is no beauty in math'. Sir replied in bimaru accent, 'bhaiya aisa hai, there is math in everything that you think is beautiful'.

by FluteHolder Wed May 01, 2013 10:47 pm

My higher secondary math teacher used to say like this; 'Mathematics is the easiest subject if you understand it; And it is the toughest subject if you donot understand it'. He was okay in teaching but was explaining in more detail at 'tuition class at his home' for students who could pay.

My question was more in terms of explaining in simple terms. If you say Calculus is in driving a car, explain this in a simple way. Let me post in another post with some more detailed question..

by MaxEntropy_Man Wed May 01, 2013 10:59 pm

here is a specific example. suppose you have fencing material that is 200 ft in length and you are trying to calculate the maximum area that you can fence off for your vegetable garden. what should be the dimensions of a rectangular plot which maximizes the area? you can use calculus to do this.

here is how. assume the length is x and the breadth is therefore 100-x (remember total perimeter is 200). the area of the plot is now:

A(x) = x (100-x)

the idea is to find x to maximize A. to find the maximum, you can take the derivative of A w.r.t x and set it equal to zero, like so:

A'(x) = (100-x) -x = 100-2x

A'(x) = 100-2x = 0 which gives a solution of x = 50.

you can verify that this is the maximum by taking the second derivative and examining its sign, like so:

A''(x) = -2

since this is negative, the solution you found is a maximum.
you certainly did not need calculus to do this trivial problem, but similar but more complex problems will require calculus. cannot get more everyday or mundane than what i just wrote.

by Marathadi-Saamiyaar Wed May 01, 2013 11:48 pm

MaxEntropy_Man wrote:here is a specific example. suppose you have fencing material that is 200 ft in length and you are trying to calculate the maximum area that you can fence off for your vegetable garden. what should be the dimensions of a rectangular plot which maximizes the area? you can use calculus to do this.

here is how. assume the length is x and the breadth is therefore 100-x (remember total perimeter is 200). the area of the plot is now:

A(x) = x (100-x)

the idea is to find x to maximize A. to find the maximum, you can take the derivative of A w.r.t x and set it equal to zero, like so:

A'(x) = (100-x) -x = 100-2x

A'(x) = 100-2x = 0 which gives a solution of x = 50.

you can verify that this is the maximum by taking the second derivative and examining its sign, like so:

A''(x) = -2

since this is negative, the solution you found is a maximum.
you certainly did not need calculus to do this trivial problem, but similar but more complex problems will require calculus. cannot get more everyday or mundane than what i just wrote.

Max:

You are still missing the whole point. How can he (or anyone) explain this to a 10 yr old that mathematics is important without getting into details on differentiation, integration, trigonometry etc.... At that age, they have concept of geometry and trig/algebra/calc are years away.

by Captain Bhankas Thu May 02, 2013 2:06 am

MaxEntropy_Man wrote:here is a specific example. suppose you have fencing material that is 200 ft in length and you are trying to calculate the maximum area that you can fence off for your vegetable garden. what should be the dimensions of a rectangular plot which maximizes the area? you can use calculus to do this.

here is how. assume the length is x and the breadth is therefore 100-x (remember total perimeter is 200). the area of the plot is now:

A(x) = x (100-x)

the idea is to find x to maximize A. to find the maximum, you can take the derivative of A w.r.t x and set it equal to zero, like so:

A'(x) = (100-x) -x = 100-2x

A'(x) = 100-2x = 0 which gives a solution of x = 50.

you can verify that this is the maximum by taking the second derivative and examining its sign, like so:

A''(x) = -2

since this is negative, the solution you found is a maximum.
you certainly did not need calculus to do this trivial problem, but similar but more complex problems will require calculus. cannot get more everyday or mundane than what i just wrote.

that's a good example, but won't the kid argue that it is easier and perhaps quicker to arrive at that answer by using intuition? 50X50 is almost an intuitive answer to that question.

the only time i used math learned in college was when i had forgotten the formula for converting deg C to deg F. i had a few data points for both the temperatures in front of me in a tabular format and i used the newton-raphson method to arrive at the formula. i fancied i could use the same method to find answers to stock movements much later in life but stocks are not governed by any rules.

by Merlot Daruwala Thu May 02, 2013 2:49 am

Captain Bhankas wrote:the only time i used math learned in college was when i had forgotten the formula for converting deg C to deg F. i had a few data points for both the temperatures in front of me in a tabular format and i used the newton-raphson method to arrive at the formula. i fancied i could use the same method to find answers to stock movements much later in life but stocks are not governed by any rules.

I used calculus only once in my life, while still in college. By law, distillery owners have to maintain charts for each of their storage vats which translate the liquid level into volume in litres. I used to generate these calibration charts using simple computer programs I'd written in BASIC, and made some money on the side. My initial orders were all for cylindrical or conical vats, so it was just a simple formula. And then, I got a vat that was an inverted conical frustum. So it was integration to the rescue. Once I wrote a program for that, I got many more orders for such vats. But that was it. I now don't recall anything in calculus beyond the basics.

by Captain Bhankas Thu May 02, 2013 3:37 am

Merlot Daruwala wrote:I used calculus only once in my life, while still in college. By law, distillery owners have to maintain charts for each of their storage vats which translate the liquid level into volume in litres. I used to generate these calibration charts using simple computer programs I'd written in BASIC, and made some money on the side. My initial orders were all for cylindrical or conical vats, so it was just a simple formula. And then, I got a vat that was an inverted conical frustum. So it was integration to the rescue. Once I wrote a program for that, I got many more orders for such vats. But that was it. I now don't recall anything in calculus beyond the basics.

now that's what your knowledge should fetch you.

by MaxEntropy_Man Thu May 02, 2013 8:39 pm

Merlot Daruwala wrote:
Captain Bhankas wrote:the only time i used math learned in college was when i had forgotten the formula for converting deg C to deg F. i had a few data points for both the temperatures in front of me in a tabular format and i used the newton-raphson method to arrive at the formula. i fancied i could use the same method to find answers to stock movements much later in life but stocks are not governed by any rules.

I used calculus only once in my life, while still in college. By law, distillery owners have to maintain charts for each of their storage vats which translate the liquid level into volume in litres. I used to generate these calibration charts using simple computer programs I'd written in BASIC, and made some money on the side. My initial orders were all for cylindrical or conical vats, so it was just a simple formula. And then, I got a vat that was an inverted conical frustum. So it was integration to the rescue. Once I wrote a program for that, I got many more orders for such vats. But that was it. I now don't recall anything in calculus beyond the basics.

great application of integration, but you could have done it without integration. just complete the frustum, to form a full cone, stand it back on its base, and keep subtracting the empty volume (which is a cone) from the volume of the (whole) complete cone.

by MaxEntropy_Man Thu May 02, 2013 8:54 pm

MaxEntropy_Man wrote:
Merlot Daruwala wrote:
Captain Bhankas wrote:the only time i used math learned in college was when i had forgotten the formula for converting deg C to deg F. i had a few data points for both the temperatures in front of me in a tabular format and i used the newton-raphson method to arrive at the formula. i fancied i could use the same method to find answers to stock movements much later in life but stocks are not governed by any rules.

I used calculus only once in my life, while still in college. By law, distillery owners have to maintain charts for each of their storage vats which translate the liquid level into volume in litres. I used to generate these calibration charts using simple computer programs I'd written in BASIC, and made some money on the side. My initial orders were all for cylindrical or conical vats, so it was just a simple formula. And then, I got a vat that was an inverted conical frustum. So it was integration to the rescue. Once I wrote a program for that, I got many more orders for such vats. But that was it. I now don't recall anything in calculus beyond the basics.

great application of integration, but you could have done it without integration. just complete the frustum, to form a full cone, stand it back on its base, and keep subtracting the empty volume (which is a cone) from the volume of the (whole) complete cone.

actually never mind. i don't think there is an easy way to do it without integration. but you gave FH another great example.

by Merlot Daruwala Fri May 03, 2013 5:15 am

Captain Bhankas wrote:
Merlot Daruwala wrote:I used calculus only once in my life, while still in college. By law, distillery owners have to maintain charts for each of their storage vats which translate the liquid level into volume in litres. I used to generate these calibration charts using simple computer programs I'd written in BASIC, and made some money on the side. My initial orders were all for cylindrical or conical vats, so it was just a simple formula. And then, I got a vat that was an inverted conical frustum. So it was integration to the rescue. Once I wrote a program for that, I got many more orders for such vats. But that was it. I now don't recall anything in calculus beyond the basics.

now that's what your knowledge should fetch you.

I wish there was something - anything - that all that time spent futilely trying to understand Controls Engineering would fetch me. Till date I have absolutely no idea of the earthly uses of Root Locus Diagrams and other mumbojumbo, other than to get me sufficient marks to pass the darn paper.

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