What is required to read this article?

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In summary, the research paper in question requires a strong understanding of advanced topics such as differential equations, complex variables, normed spaces, and topology. It would also be helpful to have a background in linear control theory. It is recommended to take courses in these subjects at the college or graduate level in order to fully understand the paper. Additionally, interdisciplinary knowledge may be necessary for a comprehensive understanding.
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Out of curiosity, I was wondering what is required to read and understand this research paper. The person who wrote it was one of my favorite professors. Very demanding, but helpful at the same time. I was an awe watching him lecture. As a result, I chose to major in mathematics. It is more for sentimental and educational milestone purposes.

http://ejde.math.txstate.edu/Volumes/2005/84/alwash.pdf
 
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  • #2
Presumably you want to be able to understand it ... but to what depth?

I think it would take at least 2nd year college level math to understand the first paragraph from "We consider..." through, "...an open set." But that would be understood at 2nd year college level.
 
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  • #3
MidgetDwarf said:
Out of curiosity, I was wondering what is required to read and understand this research paper. The person who wrote it was one of my favorite professors. Very demanding, but helpful at the same time. I was an awe watching him lecture. As a result, I chose to major in mathematics. It is more for sentimental and educational milestone purposes.

http://ejde.math.txstate.edu/Volumes/2005/84/alwash.pdf

Here's a list of things I see in the paper:
- Of course ODE. But Ross' ODE book likely won't cut it, you'll need something more advanced such as Teschl http://www.mat.univie.ac.at/~gerald/ftp/book-ode/
- Complex analysis language is used freely in the paper, including Rouche's theorem. A book like Freitag-Busam should cover enough: http://www.springer.com/us/book/9783540939825
- Normed spaces would be analysis. Carothers covers this well. https://www.amazon.com/dp/0521497566/?tag=pfamazon01-20
- He uses language from topology, but I'm sure you can actually get away with not knowing topology for this.
 
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  • #4
micromass said:
Here's a list of things I see in the paper:
- Of course ODE. But Ross' ODE book likely won't cut it, you'll need something more advanced such as Teschl http://www.mat.univie.ac.at/~gerald/ftp/book-ode/
- Complex analysis language is used freely in the paper, including Rouche's theorem. A book like Freitag-Busam should cover enough: http://www.springer.com/us/book/9783540939825
- Normed spaces would be analysis. Carothers covers this well. https://www.amazon.com/dp/0521497566/?tag=pfamazon01-20
- He uses language from topology, but I'm sure you can actually get away with not knowing topology for this.

Great, thanks Micromass. Looks like if I work hard enough, I can get an understanding of these topics in 1 year, maybe 2 years. Thank you for taking your time responding with a well structured list of topics and resources.
 
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  • #5
I think you would need an introductory course in differential equations at approximately the sophomore/ junior level, an advanced course in differential equations at about the jr/sr level. Complex variablles would also ne helpful and perhaps necessary. I also had a graduate course in advanced control systems (Electrical or Aerospace Engineering) that treated this material best. To prepare for this advanced course, you should have linear control theory at the sr or graduate level. You seem just the math may not give you the sufficient background. You may need to be interdisciplinary to treat this material best
 

1. What is the purpose of reading this article?

The purpose of reading this article is to gain knowledge and a better understanding of the subject matter discussed.

2. Do I need any prior knowledge or qualifications to read this article?

No, you do not need any prior knowledge or qualifications to read this article. However, having a basic understanding of the topic may make it easier to comprehend the information presented.

3. How long does it take to read this article?

The time it takes to read this article will vary depending on the length and complexity of the content. On average, it may take around 10-15 minutes to read thoroughly.

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