# Have you ever used calculus to solve a real life problem?

Asked by

cockswain (

15271)
October 25th, 2010

I know of its many potential applications, but I also know the vast majority of those that have had it never have actually used to to solve a real life problem. I also know there are people that have. If you have used it, what was the problem and how did you solve it?

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## 26 Answers

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Just for getting through mathmatics and graduating.

Yes, frequently—in avionics.

There is a wonderful book that was just published that talks about exactly this. Here is a Point of Inquiry podcast interview with the author.

Here is a Skepticality podcast (you’ll see it on the feed) with the same author.

I’m 52 years old and I’ve made it this far without calculus. I hope to make it about 30 more years without needing to know it.

Since you are asking about calculus, I assume that means that you have had practical application of algebra. If so, that puts you ahead of most people. I have a degree in math and am a computer programmer and I can count on one hand the number of times I have used algebra for anything remotely practical. I have definitely not had any practical use for calculus.

@chyna But you don’t make it without calculus. Every time you drive, your brain is using calculus to do stuff like figure out whether or not you can pass that guy in time to make the lane change for the exit.

@Rarebear I thought that was called “driving like a maniac”.

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Yes, but it was so long ago that I have forgotten what I used it for! LOL!

@LostInParadise I use algebra and geometry all of the time. I find your answer surprising. I think people use it without realizing they are using it. Calculus I have not used since school, but maybe if I could remember how to do it, I might find an apllication for it in my life.

If it is differential I’m sure most people at one point in life had to rely on that. If it is integral then that is a big NO!

I’m embarrassed to admit it… yes…wind turbine blade design.

While I’m not deriving formulas in my head all the time, the concept of differentiation, integration, and vectors makes me think differently about real world scenarios.

For example, when I approach a stop light, I notice my foot moving down on the brake pedal at a constant rate. I know that the rate of change of acceleration is the third derivative of displacement, so I can estimate that the distance from the stop light cubed is proportional to the time until I stop.

Very nerdy, but I’m sure it will help me in the future with applications of Calculus.

Like @Vortico said, its not so much the problems you’ll use, you just start looking at things differently.

OHHH YES I always find myself using derivatives in the grocery store. Very helpful. Glad I put myself through that torture.

Not calculus, but pre-calculus. I used trigonometric functions to calculate the length of the bookshelves I was making. That project made me use my left brain to support the habit of my right brain!

@worriedguy Can you get more specific? Nothing to be ashamed of there at all. I want to get into the renewable energy field as an engineer myself. Probably solar though. Anyways, what problem did you solve?

@renee How did you use trig to install shelving? I can’t picture why that would be necessary, but you must have had a reason.

@ratboy How did you apply it?

@Rarebear I’ll check out the podcast when I’ve got more time. Thanks for the link.

@Vortico @uberbatman I agree, mathematics changes my view of reality. Occasionally I contemplate how the derivative of e^x = e^x and it sort of blows my mind.

Consider this problem:

You got a photovoltaic system on your roof facing west. What increase in energy harvest (number of photons) can you expect when you turn your house so your roof faces south.

Is it a factor? Say, 2.35 for example? Is it a function? If yes, depending on how many variables? Angle of the roof? Longitude? How would the function look like?

@mattbrowne I’m not sure if you’re asking for an answer or just proposing a theoretical calculus problem. I don’t quite see that as a calculus problem since there isn’t really a rate of change, unless you were monitoring production over time.

Just taking an educated guess, I’d say the angle of the solar panels matters relative to latitude and nothing to do with longitude. If you live in the northern hemisphere, you’d want the panel system to face south. You’d want a steeper angle at higher latitudes. I’d guess it is only an interesting function if you are rotating the house through all degrees, or else it is just the graph of the function of two constants (two horizontal lines with a discontinuity where the house was rotated). The variables are latitude, shading, panel angle, panel direction, general weather patterns, efficiency/age of panels, and number of panels. At least those are the only ones that have occurred to me so far, I’m near certain there should be many more.

@cockswain – Both, actually. Because it’s a real life problem when people consider installing a photovoltaics system on their roofs. Or before new buildings are being erected. What is the optimum angle of the roof for example?

I’m a bit puzzled about your latitude comment. I think it doesn’t matter whether your house is in New York, NY or in Madrid, Spain. Same latitude. But longitude does matter. It will be different in Stockholm, Sweden compared to Phoenix, AZ. The latter will get more solar energy.

Sure, that could be a calculus problem. Basically you’re suggesting one would test electrical output as the panel is passed through a range of angles, and the maxima of that parabola would be the optimal angle. Seems more algebraic to me though.

We are thinking the same thing on the latitude/longitude thing. If I live in NY or Madrid, yes same latitude, different longitude. Therefore the angle of the panels will be the same for best efficiency. Los Angeles and Anchorage are on approximately the same longitude but different latitudes. Therefore the panel angle will be different. This is what I mean by longitude doesn’t matter. You are saying movement along a line of longitude matters, which I’m calling a change in latitude.

Yes, but instead of a test, use a piece of paper and a pen. Trigonometry will be important, and differential calculus I think. What parts would be algebraic?

What I’d call algebraic would be the would be the way I’d personally have designed an experiment. Say we’re just looking at panel angle at one latitude. I would set up a light source to represent that latitude so I’m unaffected by weather and wouldn’t have to wait all day. I would start with the panel at, say 5 degrees, collect data on output, tilt another couple degrees, get another data point, etc.. Until I’ve moved the panel to the point it is no longer generating output. Then I’d plot the data, which I’d expect would be a parabola concave downwards. The maxima would be my optimal angle. That’s stuff I learned in algebra.

However, if what you are suggesting would be to collect the data and then by hand use quadratic linear regression techniques by hand to find a suitable function to fit the data, I think that would be calculus, but I can’t say which aspect. Maybe differential, yes.

As an aside, there is a “new” solar technology for terrestrial applications, the Sun Cube. They’ve used them in space since the 70s or so, but are now selling them to businesses and homes. They are something like 40% efficient (panels are around 18%), and they actually move throughout the day to track the sun and fold down at night. They also lay down when it is too windy.

I think some integral calculus is needed as well. We got some function f(t) depending on time between sunup and sundown and need to determine the accumulation of energy (count the photons so to speak).

Algebra I use regularly in calculating the unknown quantity in a conversion. Conversions involve ratios, and though most people might not view them as algebra problems, they are. Example: 1 kilometer = 0.621 mile. A highway in Canada has a speed limit of 85 km/h. What is the speed limit in miles/h. 1/.621 = 85/x, x=0.621×85, x = 52.8.

Trigonometry, I use less often. A couple of months ago I was building a sawhorse to be used as a rolling stand for my table saw. Two inch casters were to be mounted on the edge of a 2×4. I knew the height I needed for the wood to slide easily onto the saw table. The question was, what angle would I need to cut on each of the four 2×4 legs for it to lie flat against the top with the casters? Where on the 2×4 would I make the angled cut at the top, and where the complementary angle cut on the bottom, so that the legs would sit flat on the floor and the top angles would be flush with the top rest.

I’ve rarely used calculus in my daily life. Most problems involving calculus (like weather prediction) involve numerical methods on supercomputers. Some understanding of calculus is helpful in recognizing why the accuracy of the predictions degrade when you are further away from the time of interest. When I was involved, professionally, with navigation programs for n-stage rockets, they too were solved numerically. The engineering problem involved selecting numerical techniques that would quickly converge on solutions, thus using the minimal amount of computer time. On a day to day basis, my judgement would be that very few people will use it in their private lives. That being said, If you are interested in how things work, anything that changes over time, over distance, over temperature, over electrical current, etc., involves calculus at some level and knowing how it might and what are its limitations opens a powerful window on understanding.

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