# Differential equation

There have been 1 completed talk and 3 topic suggestions tagged with **differential equation**.

## Related Tags

- stochastic equation
- ecology
- computational biology
- fractal
- applied mathematics
- computational mathematics
- integration
- biology

## Completed Talks

### Integrability of Riccati Equations

Delivered by Letian Chen on Friday January 27, 2017

In 1841, 3 years before Joseph Liouville discovered transcendental numbers, Joseph Liouville showed that the Riccati equation $y' = ay^2 + bx^m$ has a quadrature solution if and only if $m = 0, -2, -\frac{4n}{2n±1}$. Nowadays, we see Liouville's results as the foundation to qualitative analysis to differential equations, a fascinating subarea of DEs, which studies for example the existence and uniqueness of different kinds of equations. In my talk, I will (hopefully) prove the classical result of Liouville after a quick review of history and related linear theory.

## Talk Suggestions

### Differential Equations on Fractals

Possible reference materials for this topic include

Robert Strichartz : Differential Equations on Fractals - A tutorial

Quick links: Google search, arXiv.org search, propose to present a talk

analysis differential equation fractal

### Gillespie Algorithm

The Gillespie Algorithm for stochastic equations is used heavily in a number of fields of applied mathematics, in particular computational systems biology.

Possible reference materials for this topic include

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algorithm applied mathematics biology computational biology computational mathematics computer science differential equation probability stochastic equation

### The Stochastic Lotka-Volterra Equation

The famous Lotka-Volterra equations model the population of a predator and a prey, which are of course closely related. Stochastic variations on the Lotka-Volterra equations can be an illuminating introduction to the methods used to solve stochastic differential equations.

Possible reference materials for this topic include

Quick links: Google search, arXiv.org search, propose to present a talk

applied mathematics differential equation ecology stochastic equation