Differential Equations Tutorial Will Return....Soon

[Chris L T521]

Hi all,

Back on MHF, my Differential Equations Tutorial was beneficial to many members and I was proud of my contribution to the site. However, with the fall of MHF, I have not been able to retrieve my old posts. So my plan is to start a completely new one on this site -- from scratch. I will be incorporating the following sources into my tutorial: DiPrima, Edwards and Penney, THE ORIGINAL Hirsch and Smale, and Arnold (for the theory parts). My goal is to have the tutorial started by the middle of next week, and a pdf version will be attached to each post. I hope to address things I never focused on in the first tutorial, including but not limited to power series methods, numerical methods (Euler's method, Runge Kutta, etc.) and a bit on bifurcations and dynamical systems.

Please stay tuned for updates!

 

[Chris L T521]

Update #1: I have started writing the LaTeX document (book) that will have the contents of my future posts. I'm about 20% of the way through of what I want to write about for my first tutorial post(s). My plan is to make a thread for each chapter in my book, and subsequent posts will be on the sections of each chapter. This way, it will be easier to edit mistakes instead of reading through pages of the same thread to find said mistakes.

At the end of each chapter in the pdf version, there will be a bunch of exercises for you to try; they will usually incorporate what was covered in that chapter and I'll try to make some of the application questions interesting! (Tongueout)

 

[Chris L T521]

Update #2: I've been busy with coursework lately, but have finally found the time to continue working on material I'll be using in my first post. I should have the first chapter of my tutorial finished sometime this weekend. I'm excited by how things are turning out, and I can't wait to share it with you all! (Bigsmile)

 

[Chris L T521]

Update #3: I realize we're about half way through July and I haven't started the tutorial yet. Well, that's in large part due to me being busy with coursework and prelims since February. I'm currently at the UC-Berkeley campus (for my MSRI workshop on mathematical general relativity) until July 20th, so I won't be able to make any new posts until after the workshop is finished. I'll post what I currently have so far in the meantime, but expect posts on new topics to appear after August 1st (I'm also helping my sister move from Hawaii to San José, so that's why I can't promise anything before August 1st).

 

[blue_raver22]

As a fellow scientist, I am excited to see that you are planning to continue your Differential Equations Tutorial. It is clear that your previous contributions were highly valued and I have no doubt that this new tutorial will be just as beneficial to the community.

I am especially impressed by the sources you have chosen to incorporate into your tutorial, as they are all reputable and well-respected in the field of mathematics. Your plan to cover topics that were not included in your previous tutorial, such as power series methods and numerical methods, shows a dedication to providing comprehensive and informative content.

I look forward to following your updates and learning from your tutorial. Thank you for your commitment to sharing your knowledge and expertise with others.