Engineering Math: Differential Equations and Dynamical Systems

This series presents a comprehensive introduction and overview to Differential Equations & Dynamical Systems. Dynamical systems are differential equations that describe any system that changes in time. Applications include fluid dynamics, elasticity and vibrations, weather and climate systems, epidemiology, biomechanics, space mission design, and control theory.

I assume that students have taken some calculus (but might not remember it) and are interested in modeling the real world.

Engineering Math: Vector Calculus and Partial Differential Equations

Vector calculus is the language we use to describe physics, conservation laws, and partial differential equations. This playlist begins with basic vector calculus (divergence, gradient, curl) and quickly develops many of the most fundamental partial differential equations in physics.

Engineering Math: Crash Course in Complex Analysis

This series provides a high level overview of complex analysis needed to understand differential equations. This is meant to be about a two week course.

I assume that students have taken some calculus (but might not remember it) and are interested in modeling the real world.

Fourier Analysis

Fourier analysis is a cornerstone of all modern signal processing (e.g., image and audio compression) and scientific computing. This playlist starts from scratch and develops the Fourier Series, Fourier Transform, and how to implement them on a computer. We also discuss wavelets and image compression in general. This follows Chapter 2 from "Data-Driven Science and Engineering".