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What is required to read this article?

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  • Thread starter MidgetDwarf
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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
Simon Bridge
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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
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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
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
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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
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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
 

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