I enjoy your writing, but calculus often makes everything easier. Extensive algebra is far more difficult then that. I cannot be the only one who hated his professor's remark "an the rest is SIMPLE algebra."
Calculus is pretty much standard for university bound high school students these days. Outside of those studying humanities, it is a prereq for pretty much anything (physics, economics, finance, engineering, computer science,...). If anything, I used calculus, stats and probability all the time in my twenties, but what I never did is complete all the calculations. We have computers for that. I have an old TI-92 calculator I bought 25 years ago to be able to deal with non-simple math in random places.
I think calculus is pretty essential for clear thinking. It was the first truly elegant thing I learned in school. It is everywhere. I think we should be teaching it to more people. The US would be a better place if more people had a basic command of calculus, and statistics. I have spent most of my life trying to explain facts to important people, and the world would be a much better place if the individuals running companies and public sector agencies could understand the most basic tools used in operations, finance and technology.
If you will excuse me, I need to get off this horse. I need a stool for how high I am sitting.
> Calculus is pretty much standard for university bound high school students these days.
If you're bound to study EE or CS, perhaps?
But you're right, I should've put it a bit differently: I don't have beef with calculus, which is really just the study of change. That's essentially what we're doing here from first principles, and it's even more prominent in other articles (e.g., the "core concepts" one).
What I have beef with are articles for general audiences that explain concepts by defaulting to *specific prior knowledge of calculus concepts*, especially stuff like Laplace transforms, Taylor series, etc. If you still remember that, you're in a minority, I think? If someone's looking for "what's capacitance", I think there's a 95%+ chance they are not looking for a Laplace representation.
The other snag here is that calculus is often explained by giving rules without truly explaining their fundamental origins. That's OK if the calculus is not the point and you just need a tool that gives you the correct result... but then leads to unsatisfying outcomes if when using that to explain physical phenomena. The internet is full of people who assert stuff like "<x> in physics is the way it is because of <some property of the Fourier series>", and that just *sounds* smart.
I enjoy your writing, but calculus often makes everything easier. Extensive algebra is far more difficult then that. I cannot be the only one who hated his professor's remark "an the rest is SIMPLE algebra."
Calculus is pretty much standard for university bound high school students these days. Outside of those studying humanities, it is a prereq for pretty much anything (physics, economics, finance, engineering, computer science,...). If anything, I used calculus, stats and probability all the time in my twenties, but what I never did is complete all the calculations. We have computers for that. I have an old TI-92 calculator I bought 25 years ago to be able to deal with non-simple math in random places.
I think calculus is pretty essential for clear thinking. It was the first truly elegant thing I learned in school. It is everywhere. I think we should be teaching it to more people. The US would be a better place if more people had a basic command of calculus, and statistics. I have spent most of my life trying to explain facts to important people, and the world would be a much better place if the individuals running companies and public sector agencies could understand the most basic tools used in operations, finance and technology.
If you will excuse me, I need to get off this horse. I need a stool for how high I am sitting.
> Calculus is pretty much standard for university bound high school students these days.
If you're bound to study EE or CS, perhaps?
But you're right, I should've put it a bit differently: I don't have beef with calculus, which is really just the study of change. That's essentially what we're doing here from first principles, and it's even more prominent in other articles (e.g., the "core concepts" one).
What I have beef with are articles for general audiences that explain concepts by defaulting to *specific prior knowledge of calculus concepts*, especially stuff like Laplace transforms, Taylor series, etc. If you still remember that, you're in a minority, I think? If someone's looking for "what's capacitance", I think there's a 95%+ chance they are not looking for a Laplace representation.
The other snag here is that calculus is often explained by giving rules without truly explaining their fundamental origins. That's OK if the calculus is not the point and you just need a tool that gives you the correct result... but then leads to unsatisfying outcomes if when using that to explain physical phenomena. The internet is full of people who assert stuff like "<x> in physics is the way it is because of <some property of the Fourier series>", and that just *sounds* smart.
I see your point. I agree with everything. You are probably right. Thanks for the reply.
Beautiful analysis. Could you write a post for when V/I are out of sync? Please keep posting!