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Comment by aliljet | Hacker News Reader

Funny seeing this here, but a decade ago, this professor's differential equations explanations saved me from endlessly meandering through tough engineering lectures and dense math textbooks. I'm frankly curious to know if undergraduates and high school students still use this...

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I just graduated university this year and used the site in high school and a little bit in university (just freshman year calculus). I don't remember how I found the site, either I was Googling math stuff, or a friend was and sent me a link. Many friends in high school and university used the site, it's definitely still popular. A high school teacher may have recommended it as well. It's a great site.

High school student here who self-studied multivariable calculus and differential equations. I absolutely LOVE Paul's Online Math Notes.

why are differential equations so difficult? it would seem even smart people struggle with understanding them. Is the problem is how they are taught or is the concept inherently hard/ It should not be that hard given that we're taking 'rates of change' broadly speaking, yet it is.

The concept of a differential equation is not hard. Solving differential equations can range from trivial to non-trivial.

Both. They are taught, generally speaking, by giving a series of techniques to solve problems without the underlying mathematics (i.e why those techniques work on those problems). Calculus generally takes some time to grok, which typically doesn't have unless your really into it. Think how many people fail to grasp exponential growth (the simplest ODE).

Good scientists are often terrible teachers.

That and people default to being scared of mathematics rather than seeing difficulty as proof of it being rewarding to learn.

Even among the engineering-oriented lower division math courses, material in differential equations courses is both antiquated and presented like a laundry list. This essay is more than 20 years old now, but the complaints are basically as relevant today.[1]

[1] https://web.williams.edu/Mathematics/lg5/Rota.pdf

Learning hard things is difficult for anyone, even smart people

Can confirm that they do. At least at the schools I’ve been at, “Paul’s Online Math Notes” is an instantly recognizable name for most STEM students.

In high school right now; my calc teacher links to this all the time when the textbook's explanation/examples are unsatisfactory

I graduated in '17 and used his site a ton once I got to classes beyond what Khan academy offered. It's an excellent resource!

In the last year of my Aerospace Engineering degree. This site got me through calculus and I still use it any time a differential equation shows up in my studies since they still scare me.

I used this when I took differential equations while working on my math major (graduated in 2016). It's simply invaluable for the anxious, confused student.

In my senior year of undergrad now, every maths student I know shares "Paul's Notes" to people struggling.

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