How is Calculus useful in life?
What is the purpose of calculus besides solving physics equations. I mean in real life, there could only be approximations, since the real life couldn't be an equation. I have finished multivariable calculus 15 years ago, however, I still do not understand the purpose. My teachers in my college taught me that it is very useful in physics, chemistry and economics. I know a handful of engineers who all say they rarely use calculus in real life. So, back to my question, what is the purpose?
The great importance of calculus is quickly noticed by taking a look at the number of fields that use calculus to solve important problems. Calculus is used to solve from biology problems to economy problems.
Problems monitoring the dynamical changes of biological samples, all kind of optimization problems or economical problems involving the interest rate need calculus to be solved.
Besides the significant aspect that this part of mathematics helps in development of an analytical mathematical thinking, calculus proves its effectiveness by solving real, practical problems.
I think maybe we need to take a wider view on subjects such as calculus rather than focusing upon their direct application. Surely, all learning is beneficial in terms of what it teaches us about expanding our horizons and our brains. Therefore, even though we may not use calculus for anything in our lives, I think we need to fight against the temptation of considering that any learning is wasted.
I remember taking calculus in college. I can honestly say that I studied every minute of the day. It was a challenge and my brain definitely received a work out. I believe any subject that makes you think is good for you. The more you use your brain, your intellectual reasoning, the better prepared you are in life. I teach my students that learning something new is as if you are building the brain as you would build the body in a workout. It is important to focus on the learning and not be put off by not seeing the need for the subject. While you are learning, your brain is being strengthened.
Requires calculus. A perfectly competitive firm faces a market price of $10 for is output X. It owns two plants, A and B, whose total costs are
I agree that only small part of the entire population of the world uses calculus to create something useful, but I can also say that all of us are enjoying the luxury of every useful thing made available for us because of calculus. This is a fact that only few people realize. One good example is the internet...without the satellites this may not be possible. To launch a satellite requires complex yet precisel calculations using tools such as calculus. Hence, it is indirectly useful to all of us.
The question whether to teach calculus in school, I think it should be for everyone. Just to give each one the opportunity to find out what calculus is and how it can be useful to us. Those who see and pursue to discover its value, they become part of the small group I mentioned earlier.
Some interesting topics in calculus I can still recall are Slopes & MAXIMA-MINIMA. In road design & construction, oftentimes I am asked to locate the lowest point & and slope at any point on the vertical curve that are design as parabola (y=Ax²+Bx+C). Here I can easily apply slope & maxima-minima to generate result quickly instead of using the conventional method that requires some sketching and lenghty computation.
Calculus is useful in day to day life in predicting the rates of change of various quantities. If you keep track of grocery price for a few days, you can predict the prices for a reasonable time further considering the rate of change. In stock prices you can predict the future price of a stock after finding its rate of change. Since real life situations do not fit mathematical equations you can use them only as approximations.
If you have habit of saving money regularly, you are using Integration function to predict how musch your savings will be worth after accounting for the interest rates. It is true that we do not use complex equations but what we use in rate of change and accumulation calculations is really an important part of calculus.
For me, I had a number of calculus classes in college and could follow instructions on how to solve problems. I was never taught a tangible application for calculus and for the life of me, have seen no benefit in taking it. Sure, it was difficult and exercised the brain, my perspective on life was not effected by calc.
Perhaps I'm being too sentimental here, but I do believe that everyone should (and can!) learn some calculus. For me, calculus was when mathematics became beautiful. All my math before came together to form a whole.
I can't tell you that calculus will save your life or you'll integrate functions on a daily basis (why would you want to?), but I think the purpose of calculus goes beyond it's "practical" uses. It's an end in of itself.
If you want some more "down-to-earth" reasons to study calculus, then here's my best shot.
- Discipline: Calculus is hard. It demands your attention if you want to succeed. You have to take notes, memorize trig identities, common derivatives and friends, and be able to recognize what to do when faced with a problem. If you didn't know how to study before learning calculus, you probably did afterwards.
- Mental Exercise: As litteacher8 noted, calculus is like cardio for your mind. If you usually study history or literature, studying mathematics can be the change of pace your brain needs; after all, the brain thrives of diversity! Also learning a new skill is a great way of keeping your mind in shape.
- Self-Assessment: Challenging yourself is one of the best ways to get to know yourself. Taking math up to calculus is a great way to know whether or not you'll be happy handling the hard stuff. From a college courses viewpoint, calculus opens up avenues of study that wouldn't be available otherwise. It gives you choices.
Hope this helps!