# Ordinary differential equations

Thou, silent form, dost tease us out of thought / As doth eternity

March 28, 2019 — March 28, 2019

calculus

functional analysis

Hilbert space

statistics

Nothing here except a note about my favourite pragmatic intro to ODE analysis:

Homer Reid’s 18.305, *Advanced Analytic Methods in Science and Engineering*.

More to come, maybe. I might mention, say, the extensions to fractional DEs or stochastic DEs or partial differential equations or…

## 1 References

Alder. 2004.

*An Introduction to Complex Analysis for Engineers*.
Arnold, and Silverman. 1978.

*Ordinary Differential Equations*.
Ascher. 2008.

*Numerical methods for evolutionary differential equations*. Computational science and engineering 5.
Åström, Murray, and EBL. 2008.

*Feedback systems: an introduction for scientists and engineers*.
Borthwick. 2016.

*Introduction to Partial Differential Equations*. Universitext.
Borzì, and Schulz. 2012.

*Computational Optimization of Systems Governed by Partial Differential Equations*. Computational Science and Engineering Series.
Chen, Rubanova, Bettencourt, et al. 2018. “Neural Ordinary Differential Equations.” In

*Advances in Neural Information Processing Systems 31*.
Dandekar, Chung, Dixit, et al. 2021. “Bayesian Neural Ordinary Differential Equations.”

*arXiv:2012.07244 [Cs]*.
Hairer, E., Lubich, and Wanner. 2010.

*Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations*. Springer Series in Computational Mathematics 31.
Hairer, E., Nørsett, and Wanner. 2009.

*Solving Ordinary Differential Equations I: Nonstiff Problems*. Springer Series in Computational Mathematics 8.
Hairer, Ernst, Wanner, and Hairer. 2010.

*Solving ordinary differential equations 2: Stiff and differential-algebraic problems*. E. Hairer ; 2.
Logg, Mardal, Wells, et al. 2012.

*Automated Solution of Differential Equations by the Finite Element Method*.
Lyons, Caruana, and Lévy. 2007.

*Differential Equations Driven by Rough Paths*. Lecture Notes in Mathematics.
Reid. 2015.

*Advanced Analytic 18.305 Methods in Science and Engineering*.