Eric Cytrynbaum

Use XPPAUT to create a bifurcation diagram with periodic solutions for a substrate-depletion model

Intro to working with functions in a spreadsheet

Slope fields as a qualitative tool to understand solutions to differential equations

Sampling from the uniform and normal distributions in MATLAB

Solving linear ODEs using a phase-line inspired method

Sketching Graphs - Minimum, Maximum, or Inflection point

Finding the derivative of an inverse function

The vector nature of Fourier series and how to use a dot product to calculate them

Optimization - a geometric example

Using Laplace transforms and convolution to solve an ODE

Calculating the global maximum for a two-variable function

Logarithmic differentiation

The general product rule

Finding the derivative of arcsin(x)

Implicit differentiation - infinite slopes on relations

Verifying solutions to differential equations and using ansatzes

More derivatives using logarithms - the general power rule and (x^x)'

Phase lines as a qualitative tool for analyzing differential equations

Derivative notation

Sketching Graphs - Critical points that are neither minima, maxima, nor inflection points.

Some modelling applications that lead to linear (and one non-linear) differential equations

Taylor polynomial - an application to calculating a series

Exponential functions and their derivatives

An applied optimization problem

Calculating a Fourier series for a periodic step function

Convolution, transfer functions, impulse response and a model for memory

Implicit differentiation

Taylor polynomial calculation shortcuts - example 2

Sketching Graphs - Rational Power Functions

Taylor polynomial calculation shortcuts - theory and an example

Use XPPAUT to create a bifurcation diagram with periodic solutions for a substrate-depletion model