Notes on Calabi–Yau ordinary differential equations

Notes on a Family of Inhomogeneous Linear Ordinary Differential Equations

In the note, the authors find several simple and explicit forms for a family of inhomogeneous linear ordinary differential equations studied in “D. Lim, Differential equations for Daehee polynomials and their applications, J. Nonlinear Sci. Appl. 10 (2017), no. 4, 1303–1315; Available online at http://dx.doi.org/10.22436/jnsa.010.04.02”. 1. Motivation and main results In [3, Theorem 1], it was ...

Lectures Notes on: Math 6410: Ordinary Differential Equations

2 Linear Equations 14 2.1 Matrix Exponentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Normal Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Non-Autonomous Linear Equations . . . . . . . . . . . . . . . . . . . . . 19 2.4 Inhomogeneous Linear Equations . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Stability and Boundedness . . . . . . ....

8 Notes on Calabi - Yau Ordinary Differential Equations ∗

We investigate the structures of Calabi-Yau differential equations and the relations to the arithmetic of the pencils of Calabi-Yau varieties behind the equations. This provides explanations of some observations and computations in the recent paper [12].

Lecture Notes (spring 2012) 119b: Ordinary Differential Equations

Ordinary Differential Equations Notes for Mat 550 Spring 2013

DEFINITION 1.1. Let D ⊂ R be a domain, i.e., an open connected set. (i) A time-dependent vector field on D is a pair consisting of a domain V ⊂ D × R together with a continuous map F : V → R. (ii) The time-dependent vector field F is said to be autonomous (or one simply omits the adjective time-dependent) if V = D × R and for each x ∈ D, F (x, ·) is constant. That is to say, a vector field on D...