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
Figure 1

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.