I would put a lot more stock into algebra, especially solving word problems, to increase your logical thinking skills. That, or geometry. Calculus is actually a lot of memorization, once you get beyond the theory and into the application.
I’ve actually found algebra rather helpful in real life.
One perhaps nonobvious example of this is that you can use algebra to break down complex arithmetic problems into more easily manageable chunks. Quick, what is 57 + 108? You could write it down and do longhand addition, or you could realize that 57 = 50 + 7 and that 108 = 100 + 8. You then know that 57 + 108 = (50 + 7) + (100 + 8). Remove the parentheses (since addition is commutative and associative anyway, they are irrelevant), and reorder the expression to 100 + 50 + 7 + 8. Now, you probably know what 100 + 50 is without needing to work it out on paper or even think very hard. You may have 7 + 8 memorized, but if not, it’s easy enough. Now you have 150 + 15. You can do the rest in your head without needing to “carry” any place values.
If you forgot what 7 + 8 is, you might still remember that 8 + 8 is 16. 8 = 7 + 1, therefore 7 + 1 + 8 = 8 + 8, , subtract 1 from both sides (more algebra), therefore 7 + 8 = 8 + 8 - 1, i.e. 16 - 1, i.e. 15
With these techniques, you can turn arithmetic from a “sweat” exercise to a creative problem solving one.
I pretty much do that automatically. It used to annoy my boss, as she had to rely on a calculator for anything over two digits. I could even ballpark large numbers, which just infuriated her.
I write software for a living and have degrees related to that. I’ve taken a lot of math classes. The only thing I’ve ever used calculus for is passing calculus courses.
My calculus class in college taught me that a 45% can be an A, as long as most everyone else did substantially worse than that (they did, so it was). Other than that, I didn’t really take anything practical out of it. Of course, I only took one semester of Calc. Maybe those who took DiffEQs learned something I never got to.
Calculus is the bane of Pepper Mill’s existence. She took pre-Calc for her Business Math course, and almost fell into despair. Her instructor gave her a passing grade, but made her promise not to ever take it again.
MilliCal is more math-able than Pepper Mill, but she hates Calculus, as well, and keeps asking “What am I going to need this for? When will I ever have to use this?” She’s going into a non-technical field, so the answer is probably “never”.
I was surprised to find that two of our friends (married to each other), despite being in science/engineering, never have to use calculus, either.
I find al this bewildering. I use calculus all the time, and love it. I can talk about its advantages and insights all day. But if you don’t like math, or if, like Pepper, you have serious problems with higher math, there’s no point in it.
I think the main advantage of calc for people who aren’t specifically using it for STEM-type stuff is not really in having the ability to figure out the exact derivative of an exact equation you’re looking at, but learning a new model for how things relate to one another. Just learning the basis of calculus, even if you never figure out those terrible trig formulae, gives you new insight into how the amount or rate of change in one thing affects the change in others. It gives you a new way to conceptualize things like why the obnoxious wibble noise in your car gets worse when the temperature goes down AND your revs go up.
Other than that, it’s thoroughly useless. I often wished in college that they’d divide the calc classes like they did the algebra classes, into “calculus for people who enjoy calculus and intend to go into a field where it will be used” and “calculus for people who could do with learning about relationships between functions, but will otherwise resent the entire exercise and never use this again”.
They do—that is, at many colleges and universities, there are at least two different “versions” of calculus, one of which is a class that works (or can work) much the way you describe, often called “Business Calculus” or “Calculus for Social Scientists” or something like that.
When my father was building a koi pond, I happened to be taking college calculus. I was able to use calculus to come up with a much better approximation of the volume and surface area for his oddly-shaped pond. Most of the calculators provided online assume you have either a rectangle or a circle.
I did a little science fiction writing where I could have used calculus but was too lazy to. However, I think that it helped to understand at least the concepts of the underlying calculus even while I was using algebraic shortcuts.
Like a few others here, I do find myself using calculus in a daily life, not so much in actually solving problems, but simply in understanding relationships and concepts. I actually had some level of intuitive understanding of calculus for a long time, and I’d often derive my own formulae and all, and when I finally took calculus in high school, fortunately at the same time with physics, covering the similar concepts, there was a bunch of stuff that just… made sense.
The best example I have, is similar to one used up thread, relating time, position, speed, and acceleration. I can’t quote any kinematics equations about them off the top of my head anymore, but it’s precisely these sorts of relationships that I think some people don’t have a truly intuitive understanding of. For instance, I remember spending a whole segment learning “distance equals rate times time”; that always seemed so ridiculously obvious as to be a waste of a segment, but yet a lot of people struggled with the concept.
Once I got onto the idea of tangents to the curve and areas on the the curve and how they directly related to real world, everyday occurences, there was suddenly this beautiful connection between something I had some intuitive understanding of but couldn’t explain, to a real hard concept that I could then expand to explain and understand other similar concepts. The weird thing about calculus, at least for me, is that it’s both not intuitive at all, in that our brains don’t inherently think in terms of the intermediate steps between algebra and calculus like limits, but once you get there, it feels very intuitive and opens up a whole new perspective.
Personally, though, I think the idea of comparing it to a third arm is way to drastic. It’s not necessary, and most or all of the everyday stuff done with calculus can be approximated in ways that don’t requite understanding it. Really, what’s missing without it, in my mind, is just a basic beauty and elegance. I think a better analogy would be like a painter discovering a new color. Beautiful art can be created without it; but having access to more of the spectrum in creating the art just removes the limit and lets him be that much more expressive.
Having a knowledge of Calculus (even from years ago) doesn’t provide a third arm, as much as a third eye that provides an intuition to more complicated issues of problem solving.
For example, you understand why you’re supposed to transfer leftovers from a big pot into a smaller container before you put it into the fridge. And when you make your first mortgage payment, you’re not suprised when almost all of it is applied to the interest and not the principal. Or when you’re playing poker, why it’s important to consider the size of the remaining chip-stacks in front of your opponents before you make a bet.
And although it’s rare that I have to apply calculus in a business decision, just understanding it gives me insight as to when the apparent “easy solution” to a problem may not be sufficient.
I think if even 20% of our Political leaders had even a modest understanding of Calculus then the whole selling of derivatives mess that almost ended Capitalism never would have been allowed.