Classification of second order partial differential equations into elliptic, parabolic and hyperbolic by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16One major application of this classification is that different boundary conditions are suitable for different types of partial differential equations as explained at: which boundary conditions lead to existence and uniqueness of a second order PDE.
Isothermal means "at fixed temperature".
This is to contrast with the more well established polymerase chain reaction, which requires heating and cooling the sample several times.
Like PCR, but does not require thermal cycling. Thus the "isothermal" in the name: iso means same, so "same temperature".
Not needing the thermo cycling means that the equipment needed is much smaller and cheaper it seems.
Caused by slipped strand mispairing.
oriC = Origin of Chromosomal replication.
Most of these are going to be Whole-genome sequencing of some model organism:en.wikipedia.org/wiki/Whole_genome_sequencing#History lists them all. Basically th big "firsts" all happened in the 1990s and early 2000s.
- 1975 by Sanger et al.: 5 kbp of the single-stranded bacteriophage ΦX174 using Sanger's radiolabelling method
- 1981 by Sanger et al.: 17 kbp of human mitochondrial DNA via Sanger method, known as the Cambridge Reference Sequence
- 2003: Human Genome Project (3 Gbp)
Experiments that involve sequencing bulk DNA found in a sample to determine what species are present, as opposed to sequencing just a single specific specimen. Examples of samples that are often used:
- river water to determine which bacteria are present, notably to determine if the water is free of dangerous bacteria. A concrete example is shown at: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it".
- sea water biodiversity: ocean-microbiome.embl.de/companion.html
- food, including searching for desirable microorganisms such as in cheese or bread yeast
- poo, e.g. to study how the human microbiome influences health. There are companies actively working on this, e.g.: www.microbiotica.com/
One related application which most people would not consider metagenomics, is that of finding circulating tumor DNA in blood to detect tumors.
The by far dominating DNA sequencing company of the late 2000's and 2010's due to having the smallest cost per base pair.
To understand how Illumina's technology works basically, watch this video: Video 1. "Illumina Sequencing by Synthesis by Illumina (2016)".
Illumina Sequencing by Synthesis by Illumina (2016)
Source. The key innovation of this method is the Bridge amplification step, which produces a large amount of identical DNA strands.
This step is genius because sequencing is basically a signal-to-noise problem, as you are trying to observe individual tiny nucleotides mixed with billions of other tiny nucleotides.
With bridge amplification, we group some of the nucleotides together, and multiply the signal millions of times for that part of the DNA.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact