Differential Equations: Free Course

About this course

Learn methods for relating a function to its rates of change in this free Differential Equations course from Khan Academy. The complete forty-five-video edition covers first-order equations, second-order equations and Laplace-transform methods. Definitions, worked procedures and initial-value examples give a prepared calculus learner a way to connect the form of an equation with a suitable approach and then check whether a proposed solution satisfies the problem.

Course at a glance

What you’ll learn

• Recognize the structure and meaning of a differential equation.
• Follow the first-order methods demonstrated in the recordings.
• Explore second-order solution procedures and examples with forcing.
• Study Laplace transforms, shifting relationships and convolution examples.
• Check a proposed solution against its equation and initial conditions.

Skills you’ll gain

• Differential equations
• First-order methods
• Second-order equations
• Laplace transforms
• Initial-value problems
• Solution verification

Course Overview

The recorded curriculum has three principal teaching areas: first-order equations, second-order equations and Laplace transforms. Early explanations introduce the equation and its solution concept, while later demonstrations develop procedures appropriate to different forms. Transform recordings connect algebraic manipulation with a differential-equation problem and retain the multistep examples at the end of the source. All forty-five videos remain available. This is a mathematical methods course, so the learner should keep track of assumptions and verify a result by returning to the defining equation rather than judging it only by its appearance.

How to study the course

• Videos 1–11: this part of the source list includes “What is a differential equation” through “First order homogenous equations”. Write definitions and assumptions explicitly. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 12–22: this part of the source list includes “First order homogeneous equations 2” through “Undetermined coefficients 1”. Track the mathematical objects used in each operation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 23–33: this part of the source list includes “Undetermined coefficients 2” through “Laplace transform solves an equation 2”. Compare a simple example with a less obvious one. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 34–45: this part of the source list includes “"Shifting" transform by multiplying function by exponential” through “Using the convolution theorem to solve an initial value prob”. Verify the solution using its defining conditions. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits prepared college-level learners and returning students studying the specific advanced topic. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

The earlier algebra or calculus used in the recordings is assumed. Keep working notes and review definitions before following a proof or a multistep calculation.

Put the lessons into practice

Choose one first-order and one second-order example from the methods taught in the recordings. Write the equation and any initial conditions, solve the problem step by step and explain why the approach fits its form. Substitute the proposed solution back into the equation and check the conditions. When you reach the transform material, repeat the process with a suitable Laplace example. Keep the original equation, transformation steps and final verification together. Compare a changed coefficient or forcing term and identify which parts of the reasoning need to change.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.