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To: grundle

Honestly, calculus in high school is probably overkill for most students. A good mathematical foundation for college prep classes with rigorous courses in geometry, algebra, and trigonometry would probably suffice for most. Some study of probability and statistics would likely be more beneficial for most students than a calculus course. For those students interested in majoring in engineering, science, mathematics, or other disciplines requiring calculus, having an elective calculus course is fine.

There’s nothing magical about calculus that makes you automatically smart when you take it. It’s just a very useful branch of mathematics for many fields of study, but one that is not necessarily essential for the average citizen. It actually is not even really much more difficult to master than any other branch of math. The real issue is that it is most often taught with an eye to mathematical rigor rather than in a way that allows a more intuitive understanding. Anyone who has ever read a calculus text knows what I mean.

A good example is the basic concept of a limit. This is a concept that is readily understood intuitively. It is also a concept that is very confusing when expressed in mathematically rigorous fashion. Basically a limit is just a value a formula “gets clos to” when the input “gets close to” a specified value. It’s that “gets close to” part that’s tough to define rigorously. An example would help: consider the formula y= (x^2-1)/(x-1). For any value of x, we can calculate y using this formula, any value that is except for x=1. That value gives zero divided by zero, which we all learned is undefined. However we can look at values of x very close to 1 and see what happens. For x=0.99, we get y=1.99. For x=0.999 we get y=1.999, for x=1.0001 we get y=2.0001, and so on. Intuitively we see that as x gets close to 1, y gets close to 2, and indeed the limit as x approaches 1 for this function is indeed 2.

Basically at its heart, all calculus is is the study of limits. The derivative is just the limit of the slope formula (change in y)/(change in x) as we allow the change in x to approach zero. Integration is a limit process where we divide an area into rectangular regions whose area we know and add those areas. We find that we get a better approximation to the area by using narrower rectangles, so we take the limit as the width approaches zero. Infinite sums are just limits of finite sums as we allow the number of terms to increase. Basically once you grasp the idea of limits, calculus really is not that much harder than algebra or trigonometry.


106 posted on 03/13/2023 6:00:27 PM PDT by stremba
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To: stremba

A good “BS Meter” requires a solid Math background.


109 posted on 03/13/2023 6:11:46 PM PDT by dfwgator (Endut! Hoch Hech!)
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