If you had the traditional engineering education, you’ve made your peace with calculus. If you haven’t, you may have learned it on your own, but for many people, calculus has a reputation for being super difficult. While some of the details can be very tricky, the core concepts are actually simple and [Mathologer] has a very simple explanation along with some good graphics that can help you get started on calculus mastery if you’ve been putting it off. Using a car on the highway as the prototypical example, he covers quite a bit of ground in the 30 minute video that you can see below.
Of course, this isn’t a unique idea that calculus is actually simple. The video credits the great book “Calculus Made Easy” that we’ve talked about before. That 100-year-old (and then some) book has a similar approach to the topic.
Continue reading “Calculus Made Easy In The Car” →
We always like to call out a commercial success stemming from projects that got their start on Hackaday.io, and so we’re proud to announce the release of MAKE: Calculus by Joan Horvath and Rich Cameron, a book that takes a decidedly different approach to teaching calculus than traditional courses. Geared to makers and hackers, who generally tend to have a visual style of learning, the book makes heavy use of 3D-printed models to illustrate the relationships between functions. The project started five years ago as a 2017 Hackaday Prize entry, and resulted in a talk at the 2019 Supercon. Their book is now available for preorder, and might be a great way to reacquaint themselves with calc, or perhaps even to learn it for the first time. Continue reading “Hackaday Links: July 10, 2022” →
Most people who deal with electronics have heard of the Fourier transform. That mathematical process makes it possible for computers to analyze sound, video, and it also offers critical math insights for tasks ranging from pattern matching to frequency synthesis. The Laplace transform is less familiar, even though it is a generalization of the Fourier transform. [Steve Bruntun] has a good explanation of the math behind the Laplace transform in a recent video that you can see below.
There are many applications for the Laplace transform, including transforming types of differential equations. This comes up often in electronics where you have time-varying components like inductors and capacitors. Instead of having to solve a differential equation, you can perform a Laplace, solve using common algebra, and then do a reverse transform to get the right answer. This is similar to how logarithms can take a harder problem — multiplication — and change it into a simpler addition problem, but on a much larger scale.
Continue reading “Talking Head Teaches Laplace Transform” →
There’s a line from the original Star Trek where Khan says, “Improve a mechanical device and you may double productivity, but improve man and you gain a thousandfold.” Joan Horvath and Rich Cameron have the same idea about improving education, particularly autodidacticism or self-learning. They share what they’ve learned about acquiring an intuitive understanding of difficult math at the Hackaday Superconference and you can watch the newly published video below.
The start of this was the pair’s collaboration on a book about 3D printing science projects. Joan has a traditional education from MIT and Rich is a self-taught guy. This gave them a unique perspective from both sides of the street. They started looking at calculus — a subject that scares a lot of people but is really integral (no pun intended) to a lot of serious science and engineering.
You probably know that Newton and Leibniz struck on the fundamentals of calculus about the same time. The original papers, however, were decidedly different. Newton’s approach was more physical and less mathematical. Leibniz used formal logic and algebra. Although both share credit, the Leibniz notation won out and is what we use today.
Continue reading “Understanding Math Rather Than Merely Learning It” →
If you went to engineering school, you probably remember going to a lot of calculus classes. You may or may not remember a lot of calculus. If you didn’t go to engineering school, you will find that there’s an upper limit to how much electronics theory you can learn before you have to learn calculus. Now imagine Khan Academy, run by an auctioneer and done without computers. Well, you don’t have to imagine it. Thinkwell has two videos that purport to teach you calculus in twenty minutes (YouTube, embedded below).
We are going to be honest. If you need a refresher, these videos might be useful. If you have no idea how to do calculus, maybe these are going to whiz by a little fast. However, either way, the videos have some humor value both from the FedEx commercial-style delivery to the non-computerized graphics (not to mention the glass-breaking sound effects). Of course, the video is about ten years old, but that’s part of its charm.
Continue reading “Calculus In 20 Minutes” →
Mathematics, as it is taught in schools, sometimes falls short in its mission to educate the pupils. This is the view of [Joan Horvath] and [Rich Cameron], particularly with respect to the teaching of calculus, which they feel has become a purely algebraic discipline that leaves many students in the cold when it comes to understanding the concepts behind it.
Their Hacker Calculus project aims to address this, by returning to [Isaac Newton]’s 1687 seminal work on the matter, Philosophiae Naturalis Principia Mathematica. They were struck by how much the Principia was a work of geometry rather than algebra, and they are seeking to return to [Newton]’s principles in a bid to make the subject more accessible to students left behind when it comes to derivatives and integrals. They intend to refine the geometric approach to create a series of practical items to explain the concepts, both through 3D printed items and through electronics.
We can see that this is an approach that has considerable merit, given that most Hackaday readers will have at some time or other sat through a maths lesson and come away wondering what on earth the teacher was talking about and having been baffled by further attempts to explain it through impenetrable maths-speak. If you were the kid who “got” calculus when the relationship between speed and acceleration – another thing we have [Newton] to thank for describing – was explained in your physics lessons, then you will probably understand.
The pair have some Hackaday Prize history, you may remember them from such previous entries as their 3D prints for the visually impaired project from last year.
The first time I was in school for electrical engineering (long story), I had a professor who had never worked in the industry. I was in her class and the topic of the day was measuring AC waveforms. We got to see some sine waves centered on zero volts and were taught that the peak voltage was the magnitude of the voltage above zero. The peak to peak was the voltage from–surprise–the top peak to the bottom peak, which was double the peak voltage. Then there was root-mean-square (RMS) voltage. For those nice sine waves, you took the peak voltage and divided by the square root of two, 1.414 or so.
You know that kid in the front of the class? They were in your class, too. Always raising their hand with some question. That kid raised his hand and asked the simple question: why do we care about RMS voltage? I was stunned when I heard the professor answer, “I think it is because it is so easy to divide by the square root of two.”
Continue reading “Root Mean Square” →