Resources to make people understand the concepts of limits and continuity.

Question

How to explain fundamental concepts of limits and continuity to a non-mathematical background student?

I am a PhD student in Mathematics working in Differential Geometry. As a part of my teaching assignment I need to explain the concepts of Limits and Continuity to some undergraduates majoring in Physics.

I don't know how to explain these concepts easily to them.Will anyone at all listen to me?

Should I make a slide presentation to them? Is it possible to explain mathematical concepts uing powerpoint/latex?

Are there any sites or online resources which can help me to make them understand Mathematics in an easier way?

Please help .

Answer 1

As a high school student who plans to go on to study physics, I feel somewhat qualified to understand the point of view of your students.

For me, understanding continuity is all about understanding motion. I feel like showing how all motion is continuous would help physics undergrads come to a better understanding. They should catch on pretty quick to see what it means, as the motion of an object can't be undefined. This could be demonstrated with a powerpoint presentation pretty easily, maybe just show a small clip of a ball being thrown through the air and relate it to continuity of a function in the plane.

Limits might be a little more tricky, but if they have any aspirations on studying physics they must learn calculus, and for calculus, they must grasp limits. I looked around and found an interesting video that may be helpful

https://www.youtube.com/watch?v=kfF40MiS7zA

There is a whole series of calculus videos on this guys channel, so those might all be helpful. The way I understand limits intuitively is picturing a point on a function slowly moving towards the desired input, and a counter displaying what the output value is approaching (Something like a slider in desmos). That may just confuse them more, but with physicists, its all about intuition.