Ordinary Differential Equations Courses and Certifications

Professor Leonard

Applications of Slope Fields - Differential Equations

Apply slope fields to real-life situations to model solutions and examine long-term trends in differential equations.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Professor Leonard

Introduction to Population Models and Logistic Equation

Explore how differential equations model population change through the logistic equation, including mathematical analyses of population explosion and extinction.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Professor Leonard

Integrating Factor for Exact Differential Equations

Learn how to use an integrating factor to solve exact differential equations.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Professor Leonard

Solving Exact Differential Equations

Practice solving exact differential equations by testing exactness, using mixed partials, and working through examples.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Professor Leonard

Reducible Second Order Differential Equations, Missing X

Learn to reduce second-order differential equations missing the independent variable through substitution, integration, and solving for the resulting first-order equation.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Professor Leonard

Reducible Second Order Differential Equations, Missing Y

Learn to solve reducible second-order differential equations by substituting when the y variable is missing.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Professor Leonard

Introduction to Slope Fields

Explore how slope fields visualize solutions to differential equations through a constructive example and optional computer graphing.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Michael Penn

Can You Define Trig Functions via a Differential Equation

A look at defining trigonometric functions through a differential equation.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

Michael Penn

A PHInominal Differential Equation

A playful 22-minute presentation of an interesting differential equation.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Steve Brunton

Second-Order ODE: Spring-Mass-Damper

Solve a damped harmonic oscillator by deriving its second-order ODE, using the characteristic equation and initial conditions, and plotting solutions in Python and MATLAB.

• YouTube
• 33 minutes
• Self-Paced
• Free Video

Steve Brunton

The Simplest Ordinary Differential Equation and Its Exponential Solution

Derive and solve the simplest first-order linear ODE, revealing how exponential functions model bunny growth, compound interest, radioactive decay, and thermal runaway.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Tom Rocks Maths

Oxford Calculus - Separation of Variables Integration Technique Explained with Examples

A worked introduction to separating variables in first-order differential equations, with solutions checked by differentiation.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Multivariable Differential Calculus and Ordinary Differential Equations

Rigorous multivariable calculus connects the implicit function theorem and differential equations with gradient descent and backpropagation.

• Swayam
• Available until Oct 9, 2026
• Free Online Course

NPTEL-NOC IITM

ODE-BVP: Shooting Method - Lecture 1

Learn to solve boundary value problems for ODEs using the shooting method, a powerful numerical technique for finding solutions.

• YouTube
• 16 minutes
• Self-Paced
• Free Video

Michael Penn

Solving a Tricky ODE with Reduction of Order - Step by Step

Master the reduction of order technique to solve challenging second-order differential equations through detailed step-by-step analysis in this live mathematics lecture.

• YouTube
• 16 minutes
• Self-Paced
• Free Video