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Differentiation and integration considered by all scientists throughout the ages as one of the best sciences that guided the mind of man over all times The fields of the use of calculus are very wide. It enters into many fields and are not limited to specific people or to those who use it only. But to almost all human beings. Here are some examples of its ...


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Ibrahim: I would not think of it as either/or. Really, you should be able to understand and use the concepts in various ways. Algebraic symbol manipulation, "word problems" (to include not just physics, but chem, econ, business, bio, etc.), as well as graphical views. Perhaps even other conceptions (e.g. 500+ years ago, algebra was less ...


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You have asked two very different questions. I'll leave the differential equations for someone else. There is one particular application of integration which is my favorite last problem to do in Calc I. (We got behind this semester, and I was very sad not to have time for this. It feels like a perfect grand finale to me.) You probably learned the formula for ...


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Answer: I feel like a lot of these suggestions are quite complicated. Not complicated for us, but complicated for new-to-the-topic students. If you must (but see below) go with a life example, I think doing something like Zeno's paradox of motion might be helpful. first half of the trip, half of the second half of the trip, etc. (1/2^x) Too-long-for-...


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It occurred to me in thinking about the ménage problem that one could reformulate it as a story about students and advisors attending an awards dinner, with the requirement that advisors and students sit alternately, with no student sitting next to their own advisor. One must stipulate that no student has multiple advisors attending the dinner and that no ...


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Agents and missions are a good choice for maximum pairing problems for bipartite graphs. Edge linking agent to a mission means that agent can carry out the mission, so there are no edges linking mission to mission or agent to agent. Agent can't do another agent, or we have an entirely different problem :)


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As an amateur photographer, my first thought was the lens position for focus on an object. It should be easy to intuitively explain that the closer the object the further the image because the lens only bends the rays so much. As the object gets very far away, the location of the image moves toward a limit, which is the focal length of the lens. Like the ...


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A nice easy limit that can be seen in everyday life. Suppose your student looks along a perfectly level road, with perfect visibility. They look down at an angle that allows them to see the road 10m ahead of them. Then 20m ahead. Then 30m ahead. And so on, for any amount of distance ahead. You can easily show, draw, find an equation, even tabulate, and ...


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I have actually just finished teaching a first semester of calculus, and when I started it I was concerned about examples to start with. And as far as I can see, first two semesters of differential and integral calculus are about approximations: finite difference is an approximation of derivative (and vice versa!), Riemann sum is an approximation of Riemann ...


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Maybe these are too easy but... If you drop a bouncy ball, eventually you will stop hearing it bounce! Well, we can model the ball by accounting for the predominant mode of energy loss via collision with the floor but ignoring air resistance and assuming constant gravitational acceleration. Then on each bounce with impact speed $v$, its rebound speed is $v·r$...


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