I always felt a little cheated when I took my Economics and Mathematics degree – because the differential equation work was fairly light touch. Well actually very light touch – to the point I can’t really recall a significant amount of what was covered. The module itself was worth 30 credits: for those au fait with the UK university system, 1/36th of the total degree.
For anyone interested in the world around us, it’s hard not to be lured in by differential equations. They are descriptions of the world in a language that the entire mathematical world can understand. One thing that certainly adds a huge amount of appeal is their history. The equations were invented by Isaac Newton (and Liebniz), which is in itself a pretty impressive fact. It also brings about a debate I have had on many long train rides (with myself) was Mathematics invented or discovered? Attending Trinity College in the mid to late 1600s, the father of calculus realised that these equations could relate functions of real physical things to their rate of change, creating the differential equation. Methodus fluxionum et Serierum Infinitarum lists the following differential equations (very helpfully able to be cut and paste from Wikipedia). [Note: to the average reader stumbling upon a Physics blog in their free time this likely basic knowledge; but do bear with it, I would like to express my appreciation from the start.]
To me this is just the coolest. All those things you saw in A-level text books and got so familiar with… you forget there was a time these things had never been written down. They didn’t always exist, and here they are at their origin. Anyway enough – I am sure most people have already made their own minds up on differential equations.
I had started my journey on the aforementioned lecture notes from Prof Binney which served me well for complex numbers; but I will hold my hands up and say that they were a little dense for my starting point. Perhaps I would of been fine sat in the lectures, but with nothing but the notes it was a little too much. In search of a more thorough resource, I stumbled across a wonderful find (which I now realise I unwittingly used in my study of complex numbers. MIT (yes the Massachusetts Institute of Technology) have issued an entire course. I just cannot praise this enough – it goes through all the basics and takes you through each topic in small, bitesize chunks. As a part timer this is wonderful.
You can think of your life as a jar full of marbles. The marbles are the full time job. You have a choice; you content yourself with the fullness of your jar, or you fill the gaps. Add sand until your jar is full. And then when you are done, fill the space with liquid…. your jar is starting to look a little fuller. This course provides the sand and the water. Lots and lots of nuggets of information you can fit around a busy schedule. What makes this course special is the problems – reems upon reems of problems. There are small check your understanding style problems, right up to an exam at the end of each section. With a little discipline I found this course was very very close to being back at univerisity (but considerably cheaper).
Overall, I have been a little spoilt this post – and every post won’t be this luxury. This course is perfect for anyone looking to gain some skill with DEs to a university level, and comes highly recommended from me.