# Lecturing Material

# Fall 2022

# Spring 2022

Lectures at Instituto de Matemàtica, Universidade Federal do
Rio de Janeiro, May 3–12, 2022

Lecture 1: Mappings of the torus

Lecture 2: From the torus to the disk

Lecture 3: Braids

Lecture 4:

All four lectures in one file:
[pdf]

# Spring 2021

# Fall 2020

# Spring 2020

# Fall 2019

# Summer 2019

## Minicourse on *The unified transform method*

Some
partial
notes
.

Lecture 1: Introduction; Steps 1 and 2

Lecture 2: Step 3; Vanishing terms

Lecture 3: A third-order example; Final thoughts

### References

Archive
of papers that use the Uniform Transform Method (maintained
until 2014).

# Spring 2019

# Fall 2018

# Summer 2018

## Minicourse on *Exit time problems for swimming microorganisms*

All lectures
in one
file.

Lecture 1: Drift and diffusion

Lecture 2: The mean exit time equation

Lecture 3: Examples of exit time calculations

Lecture 4: The swimming Brownian needle

Lecture 5: Introduction to stochastic calculus

Lecture 6: The Fokker–Planck equation

# Spring 2018

# Fall 2017

# Spring 2017

# Fall 2016

# Summer 2016

Lecture 1:
Stirring and mixing

Lecture 2:
Filament model and effective diffusivity
(Matlab example files:
[zip]
[tar.gz])

Lecture 3:
Stirring by swimming organisms, part 1

Lecture 4:
Stirring by swimming organisms, part 2

# Spring 2016

# Fall 2015

# Summer 2015

Lectures at the Summer Program
on Computational
Dynamics and Topology
at ICERM, Brown University,
Providence, RI, 14–16 July 2015

All three lectures in one file:
[pdf]

# Spring 2014

# Fall 2013

# Spring 2013

# Fall 2012

# Spring 2012

## Math 321: Applied Mathematical Analysis I

# Fall 2011

## Math 322:
Applied Mathematical Analysis II

# Spring 2011

# Fall 2010

# Summer 2010

## Woods Hole GFD Lectures: Swimming and Swirling in Turbulence

All lectures in one file: [pdf] [djvu]

Lecture 1:
Stirring and mixing
[pdf]
[djvu]
(Matlab example files:
[zip]
[tar.gz])

Lecture 2:
Stirring by swimming organisms
[pdf]
[djvu]
(Slides: [pdf]
[djvu])

Lecture 3:
Local stretching theories
[pdf]
[djvu]

Lecture 4:
Mixing in the presence of sources and sinks
[pdf]
[djvu]
(Slides: [pdf]
[djvu])
(Matlab example files:
[zip]
[tar.gz])

# Spring 2010

## IMA Tag Team Tutorials: Transport and Mixing in Incompressible Flows

All lectures in a single
file
[pdf]
[djvu]

Lecture 1:
Stirring and Mixing
[pdf]
[djvu]

Lecture 2:
Linear Flows
[pdf]
[djvu]

Lecture 3:
Effective Diffusivity
[pdf]
[djvu]
(Matlab example files: [zip]
[tar.gz])

Lecture 4:
Stochastic Models (part 1)
[pdf]
[djvu]

Lecture 5:
Stochastic Models (part 2)
[pdf]
[djvu]

Lecture 6:
Topological Mixing
[pdf]
[djvu]

# Spring 2009

# Fall 2008

## Math 415:
Applied Dynamical Systems, Chaos and Modeling

## Math 705:
Mathematical Fluid Dynamics

# Spring 2008

## Math 221: Calculus and Analytic Geometry

# Fall 2007

## Math 705: Mathematical Fluid Dynamics