The Relationship Between Differential Equations and Volterra Integral Equations

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Today I discuss the relationship between initial value problems in differential equations and Volterra Integral Equations.

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Timestamps:
0:00 Intro
0:27 Example I
1:14 Converting the ODE into an Integral Equation I
2:01 Analysis of Example I
4:42 Solving Example I
6:39 Short Disclaimer on Homogeneity of ODEs
7:01 Example II
7:41 Converting the ODE into an Integral Equation II
8:55 Solving Example II
10:01 Analysis of Example II
10:45 A Short Discussion on Unbounded Kernels
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Thanks, this was cool. I've seen all of the parts of this, but not put together. I have questions.

I'm familiar with the term singular in linear algebra, but not in this context. It sounds like singular in this context is an improperintegral that diverges?
In the second example, it looks like you took the double integral and turned it into a convolution integral? I've run into them in probability, but I don;t know a lot about them.
I'll have to watch your video on the ADM, but it looks like a taylor series?

Thanks?

walter