This repository contains the notes I prepared as a teaching fellow for Eli Fenichel's Applied Math for Environmental Scientists Course at the Yale School of the Environment in the Fall of 2025.
The repository has two primary folders, class notes and section notes. Class notes are taken during Eli's in-class lectures. Section notes are prepared by myself before Monday evening sections. I do not expect you to read the section notes before the section. However, they can be helpful to have in front of you during section.
Note: You can ignore the .tex files. The PDFs are what are viewable and what you want! The .tex files are just how I make the pdfs.
My office hours are Tuesdays from 5:00 - 6:30 p.m. in Sage 41C. The first half will typically be my prepared material, which will prepare you for the problem sets. The second half will be open office hours where I can answer any questions.
Email: andie.creel@yale.edu
- class notes: sets, properties, functions and vocab
- section notes: sets, solving system of equations, quadratic equations, domain/range
- zoom recording of section
- class notes: level sets, solving system of equations, quadratic formula, trig, expectation operator, Jensen's inequality, units
- Monday class notes: convex/concave, sequence and series
- Andie's Section Notes: Intuition for problems 1, 2, 5, 6 on pset 1
- Zoom Recording of Section
- day one slides: thinking like a computer
- R Tutorial: write and run scripts, basic data types, ways to make collections of data, variable assignment, Functions, Loops, If Else statements
- R in-class exercises
- R in-class excercises answers
- Old Section notes: quasi-convex/concave, log rules
- Zoom recording of section
- wednesday class notes: defn of derivative, notation, chain rule, product rule, derivative of log, percent change, log rules and e
- Monday class notes: treating derivative like a fraction, finding max and min, eqn for mean derivation, mean value theorem, taylor series
- Section notes: Language of limits, setting up ordinary least squares (OLS) derivation
- audio from section
- Wednesday class notes: total derivatives, implicit function theorem (envelope theorem), Taylor series, logistic grown
- Monday class notes: integrals, Riemann sums, additively separable, derivative rules, integral rules, u-substitution
- Andie's section notes: help with pset2
- Wednesday class notes: Importance of discount factor (exponential decay), thin and fat tails, integration by parts, integrating logs, double integrals
- Monday class notes: probability density function (pdf) and integrals, mean, median, uniform distribution example
- Section recording: how to solve OLS (goes through algebra)
- Old Section recording: double integral, integration by parts example, finding mean using pdf
- Wednesday class note: probability density functions (integrals of them, which is cumulative distribution function), normal distributions, uniform distributions, finding the median using a pdf, finding the mean using a pdf
- Monday Midterm Review: exponential function, percent change with derivative of log of function, importance of graphs, find max and min, find inflection points, taylor series, integration by parts
- Old Zoom of midterm review
- Monday class notes: matrix addition and subtraction, multiplication, identity matrix, rank, transpose of a matrix
- Wednesday class notes: squaring matrices, idempotent matrix, Kronecker product, trace, linear regression (OLS), Life cycle assessment
- Old Section recording: review of u-substitutions (week 6, Monday class notes) and discussion of weighting matrices and how they apply to linear regression (week nine, Monday class notes)
- Old Section Notes: Setting up a population growth model
- Monday Class Notes: inverting matrices
- Section recording: how to write matrix multiplication function in R
- Wendesday Class Notes: Cramer's rule, jacobian and Hessians (convexity and concavity, quasi)
- Old Section Zoom Recording: Solving a system of 3 equations using Cramer's rule, element to element comparison of matrices
- Monday class notes: Differential equation, recursion eqn, difference eqn, differential eqn, using differential equation to find stock level in time period T, steady states
- Wednesday class notes: Review stable and unstable equilibrium (steady states), equilibrium in a lotka voltera model (use of implicit function theorem to determine dynamics around an equilibrium), different types of equilibrium in phase planes, modeling tipping points
- Monday class notes: Eigen values and a bit on eigen vectors
- Old section notes: Pset 5, Q1 and Q2
- Old recording of section
- Wednesday class notes: summary of eigenvalues and eigenvectors, solve for eigenvector, variance and covariance matrices, principle component analysis, graph analysis
- Monday class notes: constrained optimization, lagrangian, FOCs
- Final Review: calling "bs" on units, aged staged population model, life cycle analyses (input-output table), means and OLS w/ calculus and linear algebra, test strategy
- Zoom recording of final review 2023: age-stage population models, means and OLS, pset 5 Q3 and first part of Q6