Learn Ordinary
Differential Equations:
Free Course
with Videos
and Guided Notes
👇 Scroll down to access all the videos and guided notes for this course.
Welcome to our Ordinary Differential Equations Videos and Guided Notes page! This free resource is designed to help you learn and review the core concepts and solution methods taught in a standard college Differential Equations course. Whether you’re studying ordinary differential equations for the first time or preparing for an exam, our step-by-step video lessons and free downloadable guided notes PDFs will help you build confidence and mastery.
What’s Included in This Free Differential Equations Course?
Video Lessons
Our videos cover the essential topics in ordinary differential equations, following the structure of a typical undergraduate course. Each lesson includes clear explanations and worked-out examples so you can strengthen your understanding of concepts such as:
Classification of differential equations and basic terminology
First-order differential equations, including separable, linear, exact, homogeneous, and Bernoulli equations
Second-order linear differential equations, including reduction of order and equations with constant coefficients
Nonhomogeneous differential equations solved using the method of undetermined coefficients and variation of parameters
Modeling with differential equations, including spring–mass systems and electrical circuits
Series solutions of second-order linear equations, including power series methods and Bessel’s equation
The Laplace transform and its use in solving initial value problems
Systems of first-order linear differential equations
Numerical methods such as Euler methods, Runge–Kutta methods, and the finite difference method
Free Guided Notes for Ordinary Differential Equations
Each video comes with ordinary differential equations guided notes PDFs that you can download and complete as you watch. These notes help you:
Reinforce understanding by filling in key formulas and steps
Improve retention through active participation
Stay organized with a structured resource for quizzes, exams, and future reference
How to Learn Ordinary Differential Equations Effectively
Watch the videos for each section to follow along with step-by-step lessons.
Download the guided notes PDFs to complete while watching.
Work through examples in the notes to practice problem-solving.
Review your completed notes to prepare for exams or to strengthen your foundation for future courses.
Start Learning Ordinary Differential Equations Now!
With our free or=dinary differential equations course, video lessons, and guided notes, you’ll develop a strong understanding of the most commonly used solution techniques in a Differential Equations course. These resources are designed to help you succeed in differential equations and in the STEM courses that rely on it.
Get started today with clear lessons and guided notes PDFs that make ordinary differential equations easy to learn.
Videos and Notes
Chapter 1: Introduction
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Classification of Differential Equations| Type, Order, and Linearity Explained
In this video, we classify differential equations by type, order, and linearity—a foundational skill in any differential equations course.
Chapter 2: First-Order Differential Equations
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
1. Slope Fields
In this video, we introduce slope fields (also called direction fields) for first-order differential equations and show how they are used to visualize solution curves.
2. Autonomous Equations
In this video, we introduce autonomous first-order differential equations and show how to analyze their behavior using critical points, phase portraits, and slope fields.
3. Separable Equations
In this video, we introduce separable differential equations and show how to solve them using the method of separation of variables—one of the most important techniques in a first course on differential equations.
4. Linear Equations
In this video, we introduce first-order linear differential equations and show how to solve them using the integrating factor method—a core technique in any differential equations course.
5. Exact Equations
In this video, we introduce exact differential equations and show how to solve them using a systematic, step-by-step process.
6. Homogeneous Equations
In this video, we introduce homogeneous differential equations and show how to solve them using a systematic change of variables.
7. Bernoulli Equations
In this video, we introduce Bernoulli differential equations and show how to solve them by reducing the equation to a first-order linear differential equation using a substitution.
8. Application Examples
In this video, we apply first-order linear differential equations to several classic real-world modeling problems.
9. Euler’s Method
In this video, we introduce Euler’s Method, a numerical technique used to approximate solutions to first-order ordinary differential equations when an exact solution is difficult or impossible to find.
10. Logistic Growth Model
In this video, we study the logistic differential equation, a first-order separable differential equation used to model population growth with a carrying capacity.
Exam Review 1
In this video, we work through an exam review covering classification and first-order ordinary differential equations. The video is perfect for studying for midterms or a final exam.
Chapter 3: Second -Order Linear Differential Equations
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
1. Homogeneous Linear Equations with Constant Coefficients
In this video, we study homogeneous linear differential equations with constant coefficients, focusing primarily on second-order differential equations and extending the method to higher-order equations.
2. Reduction of Order
In this video, we study Reduction of Order, a method used to find a second, linearly independent solution to a second-order linear differential equation when one solution is already known.
3. Method of Undetermined Coefficients
In this video, we study the Method of Undetermined Coefficients, a standard technique used to solve second-order constant coefficient nonhomogeneous differential equations of the form: ay″ + by′ + cy = g(x) where g(x) is a polynomial, exponential, sine or cosine function, or a combination of these functions.
4. Variation of Parameters
In this video, we study the Method of Variation of Parameters, a powerful technique used to solve second-order nonhomogeneous differential equations of the form: ay″ + by′ + cy = g(x) for any function g(x).
5. Cauchy-Euler Equations
In this video, we study second-order homogeneous Cauchy–Euler differential equations, a special class of variable coefficient differential equations of the form: a x²y'' + b x y' + c y = 0.
New videos will be posted every Monday and Thursday! Stay tuned!