532nm

# Example 1: Old HP application notes

Quote: "In a real sense, Hewlett-Packard sold MEASUREMENTS as well as products. According to one marketing professional, when you go to a hardware store to buy a 5mm drill bit, what you really want is a 5mm hole. So, likewise, as HP developed their massive line of innovative measurement instruments, the customers often had to be educated in the newer processes of the new measurement techniques, permitted by the newest product."

I'm too young to have experienced the heyday of HP as a test & measurement company, but they produced spectacularly good material. Many of their application notes introducing the fundamentals of a field such as spectrum analysis, signal analysis, modal testing etc. remain excellent introductions even today, despite being decades old and thus predating my birth. I've thoroughly enjoyed the following ones (amongst others):

[1] AN243 The Fundamentals of Signal Analysis

[2] AN243-3 The Fundamentals of Modal Testing

[3] AN150 Spectrum Analysis Basics (updated version)

# Example 2: LTC application notes, especially by Jim Williams

A big chunk of my electronics knowledge comes from data sheets and application notes. The application notes by Jim Williams (RIP) stand out to me. Jim obviously was very gifted, but always sides with the (probably much less skilled) reader, making complicated material accessible. He always retains a holistic picture, and also addresses many practical aspects one can easily stumble upon. He does it all with a minimum of math, a maximum of intuition, and a great sense of humour.

While there are many dozens of application notes by him, I particularly like the following one:

[4] AN47: High Speed Amplifier Techniques

Links:

You're close! This can indeed be done properly and is then called the Euler-Maclaurin formula. For this, you define the "shift to the left by n operator" e^(nD) where D is the differentiation operator d/dx.

You then always take the current value of f(x), multiply it by the small shift n to get the first rectangle. Then you shift to the left by n, i.e. to e^(nD)*f(x) = f(x+n), multiply that by the small shift n to get the next rectangle etc.

The book "street-fighting mathematics" [1][pdf] has a very hands-on and playful derivation of this in chapter 6.3.

Gunter Stein's inaugural Bode prize lecture from 1989 titled "Respect the Unstable" [0]. In this talk, he uses a minimum of mathematics to clearly demonstrate the fundamental (and inevitable!) trade-offs in control systems design. He effortlessly makes the link between his (in)ability to balance inverted rods of various lengths on his palm (with shorter rods being harder to balance) to why the X-29 aircraft was almost impossible to control and why Chernobyl blew up.

The fundamental message is extremely important and the derivation is so crystal clear that it is simply marvelous to watch him present it. I like it so much that I re-watch it about once a year.

This is probably the most useful book I have read during my studies in physics and I highly recommend it to everybody with some technical interest because it focuses on teaching general and useful tools (using science and engineering examples (mainly physics)).

During the first years of my studies I did reasonably well, but it always felt like I was just manipulating symbols on paper, and the results didn't mean much to me -- it was all just theory (and if the results would have come out some other way I probably would have believed that too). This book taught me how to be reckless and throw away unnecessary complexity in order to make said theory simple enough to apply it easily to real-world problems, which suddenly made my theory knowledge much, much more useful (previously it was mainly good for passing exams). Now, during my PhD I still use the methods from the book almost daily!

Compared to the earlier book draft [1] that has been floating on the web for many years, the final book is much improved, mainly because it focuses on general tools rather than specific physics topics. However, if you want to have a quick demonstration of how powerful the methods from the book are, I'd recommend to read chapter 9.3 about waves in [1], which unfortunately only partially made it into the final book. Within a few pages you quickly derive all the properties of waves in different regimes and draw practical conclusions such as the speed limit for boats, the speed of tsunamis, why bugs walking on water don't generate waves, etc!