# Hi, I'm Evan, a Lecturer and Visiting Research Scholar at Middlebury College.

My mathematical skills and interests lie in:

Markov semigroups

Spectral theory and functional calculus

Random dynamics

Markov chain Monte Carlo methods

Hypocoercivity

Stochastic homogenization

# My textbooks:

## 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).

## Partial Differential Equations Done Right

This book should serve as a first course in PDEs for a traditional undergraduate path. Most notably, a full sequence of calculus, linear algebra, and ODEs are necessary prerequisites.

Topics covered include:

Construction of PDEs from physical principles

Domains and boundaries in arbitrary dimension

A review of ODEs solution methods

Outer products and tensor fields

The Taylor series for scalar fields

The Fourier series and transform for scalar fields

Flows, Hamiltonians, and the method of characteristics

Construction of the Laplace, heat, and wave equations

Separation of variables

Fourier methods for the solution to the Laplace, heat, and wave equations

Classification of elliptic, parabolic, hyperbolic PDEs

Integral transforms, the Dirac delta function, and Green's functions

Eigenvalues and eigenfunctions

The spectral theorem for Hermitian PDE operators

The Cauchy-Kovalevskaya theorem and power series methods

Finite difference and Galerkin methods

Video lectures (each a guided read-through) corresponding to the entire book may be found on my YouTube channel (see below).

## Contact Information

Department of Mathematics & Statistics, Middlebury College, Middlebury, VT

Institutional email: ecamrud [at] middlebury [dot] edu

Personal email: evancamrud [at] gmail [dot] com

## About Me

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 lecturer and visiting research scholar at Middlebury College. 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.