Free, Open-Source ODE Textbook I'm adapting for this playlist: ~tbazett/diffyqs The ODE Course Playlist: In this video I'm giving an introduction to ODEs or Ordinary Differential Equations. Our goal is to model a world where properties are changing, and we note from Calculus that rates of change were encoded by the derivative of a function. But where did those functions come from? Often, the answer is differential equations. We're going to see two major examples of differential equations in this video, exponential growth and free falling under gravity. In both we will talk about infinite families of solutions, and the role of initial conditions. ♡♡♡SUPPORT THE CHANNEL♡♡♡ ►Support on PATREON: ►MATH BOOKS I LOVE (affiliate link): ►CURIOSITY BOX: use CODE drtrefor for 25% off awesome STEM merch boxes 0:00 Intro 1:59 Exponential Growth 6:10 Body in Motion 10:23 Motivating Questions COURSE PLAYLISTS: ►DISCRETE MATH: ►LINEAR ALGEBRA: ►CALCULUS I: ►CALCULUS II: ►MULTIVARIABLE CALCULUS (Calc III): ►VECTOR CALCULUS (Calc IV): ►DIFFERENTIAL EQUATIONS: ►LAPLACE TRANSFORM: ►GAME THEORY: OTHER PLAYLISTS: ►Cool Math Series: ►Learning Math Series: ►LaTeX: SOCIALS: ►X/Twitter: ►TikTok: @drtrefor ►Instagram (photography based):