Interesting calculus problems for beginner

Question

Recently I started learning calculus and I think I have grasped the basics. However when calculating examples I tend to drift away and not put much effort in it.

When I was learning programming in Smalltalk I had the very same problem until I found something that I was interested in to work on.

So the question is:

Are there any interesting calculus problems from real world that a beginner can try, that will keep said beginner occupied for a long time while simultaneously granting him experience in a subject?

As I said something applied would be very much appreciated.

Thank you for your time.

Answer 1

There are MANY interesting calculus applications and you'll meet some of them in exercises (maybe in an exam), if you're planning to take other calculus courses, then you better wait until then. Anyway, any recommendation depends on your level too, on what you've learned and you know until know.

Answer 2

I believe calculus is interesting when you observe the fundamental concepts of a derivative and an integral. Most introductory courses (ie high school) would only teach "techniques" rather than "concepts".

In order to familiarise yourself conceptually, my recommendation is that you research the following keywords:

Basic Calculus 1. Derivative from First Principles (Differentiation) 2. Riemann Sum (Integration)

Analysis 1. Limit 2. Continuity & Differentiability

Once you've begin studying, you'll recognise that calculus can be quite unintuitive and therefore, it is also essential, as a beginner, to learn the "techniques". The "techniques" and applications will shed light to the true motivation of calculus, which is to solve real-world problems.