Back in the early 2000’s I had an evaluation copy of Wolfram Mathematica, which, don’t get me wrong, was great, but too clunky for me. I’m a hobbyist – love math, but easily confused. Also, the full featured product was like thousands of dollars, so – no way.

Fast forward a few years and I got an iPad and came across Wolfram Alpha and an app!! I think it was $2.99 – that’s my range đŸ™‚

Well it has been just great, highly recommended. But I really didn’t go much past the obvious formulas, even though the integration was spectacular, with the ‘show me how you did that’ feature.

Recently I started reviewing my calculus. My son’s old books were just sitting around. Paying hundreds of dollars for his books, I figure I might as well get some use out of them, right?

So I am at the point in his calculus book where they are showing how volumes are computed. It’s fairly straightforward so far. This problem I am going to detail here gives you two functions (just based on x and y) and asks you to rotate the enclosed area around an axis and determine the volume that the structure holds. See the charts, it will be clearer.

I’ll include the problem here and some images, along with the solution in the book.

So my first thought was to calculate the area in the R region and then just revolve it around the x axis. I was able to get the area (1/6) – but revolving it doesn’t really work. (Multiply by 2*pi*R) I think the problem there is that the radius changes, but I have to think about it some more. Wolfram Alpha was easily able to tell me that 1/6 was the right answer for the area.

The point here is not the solution, but it is the fantastic ability for the Wolfram Alpha program to understand input. So let’s get on to that.

Just for the heck of it (and based on the instructions from Wolfram to just enter what you think will work), I entered the following, and the freaking app knew exactly what I meant:

As you can see it showed the method of integration needed. We are talking about a washer type shape – a larger circle of rotation with a smaller section cut out. (based on circular area formula pi*r^2)

If I had this back in the day, I probably would have graduated a grade point higher than I did! Stupid Slide Rule.

Not only does the app give you that solution, but a plethora of other information AND a graph:

Totally radical, dude.

Here’s another example. Two pages from the book and two images from Wolfram Alpha on my iPad.

Here’s a cool new song, written by @doesdwars from the Netherlands (on Bandlab) who does most of the instruments and the mix. @kiwichrys from New Zealand (naturally) wrote the lyrics and did the vocals beautifully. @koenfu #sax and Frans #trombone.  I played the bass guitar and one of the electric guitars for a couple of licks in the middle.

The glade is dangerous and fraught with peril, but we have our warrior with us darling, so let’s dance into the night and pray to the gods for safe passage through the monsters. 

This is a new song by @chrysalynn on Bandlab. She’s a great vocalist and plays acoustic guitar as well. On this version, @thelonewulfproject plays acoustic and lead guitar as well, and I added bass and drums.

I found this fascinating, but I don’t know everything in detail. Here’s what I just did.

I downloaded a music track of a guitar playing from Bandlab. When I imported into my DAW, I noticed that the waveform was not centered. It appeared to be above the mid-line, leading me to think there was a DC component. It was present through the whole track.

I exported it from the DAW and then reimported it as an additional track. It was centered. It looks like the DAW export might have done some processing.

The differences brought me back to my EE days. The top image with the ‘DC’ component shows a step function. The image in the bottom has eliminated that DC component. Looking at the point where the step was, it looks like a little pulse remains, with some ringing afterwards.

I noticed in my DAW, I did have some other processing going on. By process of elimination, I found out that the ‘console emulator’ was what had cleaned up the signal. Here is a link to more information about the console emulator. https://www.cakewalk.com/Documentation?product=SONAR%20X2&language=3&help=ProChannel.8.html

With only the console emulator in the processing path, here is what the difference looks like on the stereo signal.

It looks like another component added some additional processing in the first image because there appears to be more of the ‘ringing’ activity after the pulse.

I guess the takeaway is that the console emulator, which I usually have on each track, contains some sort of brick wall high pass activity, and will remove the DC component for you.

Another great collaboration from Bandlab. @cocobark on vocals, @LoneWulfProject on Acoustic guitars. I added the other parts and did the mix/master.

From the first McCartney album – 1970 a great time to be alive. This one is sung beautifully by @chrysalynn on Bandlab.

I thank the Lord there’s people out there like you. A Good Friday release of this Elton John cover. Some great performances from

@thelonewulfproject vocals, @azzronika vocals and @mojoespage guitar – These guys are some of Bandlab’s best, it was a privilege to work with them.  I added bass, piano and mandolin. Wav Version [@thelonewulfproject vocals, @azzronika vocals and @mojoespage guitar – These guys are some of Bandlab’s best, it was a privilege to work with them.  I added bass, piano and mandolin. Download]

Here’s a cover of the great old Cat Stevens tune Wild World. @eungang and @eipi from Bandlab helped out with guitar and vocals.

An a capella vocal passage was uploaded to Bandlab by @therealmadamez – it was in bad shape so I used Izotope RX7 to restore it. Then I added Indian drums, bass and a strummed crescendo guitar.

Here’s a new song by Bill Farr (@eungang) – Bill is a Boston transplant now living in South Korea. I played piano on this one. Everything else is Bill!

An old Kenny Rogers song. Always loved it. Vocals and Rhythm acoustic guitar by @thelonewulf on Bandlab – check him out! I did bass, drums, picking guitar, keys and backup harmonies on this one.

Here’s my version of Imagine. I’ve played this on piano since it came out. At home on my old piano, at my girlfriend’s house, in my best friend’s basement, and many other places I don’t remember. Finally – here it is…done!!! @eipi did the vocals.