Hi, I'm Evan, a Postdoctoral Fellow at Colorado State University.
My mathematical skills and interests lie in:
Spectral theory and functional calculus
Markov chain Monte Carlo methods
My textbook: Ordinary Differential Equations Done Right
See above for my textbook: Ordinary Differential Equations Done Right. This book should serve as a second course in ODEs for a traditional undergraduate path, or as a first course for advanced undergraduates and early graduate students. Most notably, a full sequence of calculus and linear algebra are necessary prerequisites.
Topics covered include:
Complex numbers and functions
Linear algebra (including Jordan form, matrix functions, and the spectral mapping theorem)
Infinite-dimensional vector spaces, function spaces, and inner product spaces
The Fourier series, Fourier and Laplace transforms
The matrix exponential solution to systems of linear ODEs
Duhamel's principle for nonhomogeneous linear ODEs
Variation of parameters for nonhomogeneous linear ODEs
Nonlinear maps, and linearization
Closed-form solutions to nonlinear ODEs (exact equations and integrating factors)
Euler, Runge-Kutta, and Galerkin methods for approximating solutions
Chaos theory, and the Hartman-Grobman theorem for stability of equilibrium points
The Lie series, and an introduction to PDEs
Both proofs-based, and purely computational exercises are included, with the intent that the course could be administed with-or-without a formal proofs course as a prerequisite.
Furthermore, video lectures (each a guided read-through) corresponding to the entire book may be found on my YouTube channel (see below).
129 Weber Building, Colorado State University, Fort Collins, CO
Institutional email: evan [dot] camrud [at] colostate [dot] edu
Personal email: evancamrud [at] gmail [dot] com
Ars in omnibus est. "Art is in everything." I took Latin in high school, which makes me 5x more likely to accidentally summon demons as an adult. But in all seriousness, I like to find art in everything, and such a notion defines my approach to mathematics, as well as life.
I am currently a postdoctoral fellow at Colorado State University, in Fort Collins, Colorado. I study nonlinear stochastic differential equations, statistical sampling algorithms, and related problems in functional analysis.
I reside with my wife Kira Rahn and our adorable cat Jillie Bean.
When I am not researching or teaching, you will most often find me hiking, where I enjoy foraging for wild fruits. I also enjoy cooking/baking, drinking at the local breweries (should I be advertising that?), and playing tabletop games.