Basic calculus, algebra and comfort with functions are recommended. Familiarity with vectors and matrices is helpful for the final recording. The classroom contains explanatory videos, with no instructor-marked problem set, full textbook or academic credit included.
About this course
Explore differential equations through an eight-video visual teaching sequence from 3Blue1Brown. This free course preserves the published lessons on differential equations, the heat equation, Fourier series, Euler’s formula, Laplace transforms and matrix exponentials. The aim is to connect the mathematical symbols with the changing systems they describe.
Course at a glance
| Provider / Teaching team | 3Blue1Brown |
|---|---|
| Platform | YouTube · 3Blue1Brown |
| Access | Free Video |
| Level | Intermediate |
| Language | English |
| Videos | 8 |
| Video duration | 3h 16m · allow extra time for practice |
| Format | Self-paced recorded training |
| Certificate | Not included with video viewing |
What you’ll learn
- Recognize how a differential equation relates a quantity to its change.
- Explore the heat equation as an introduction to partial differential equations.
- Connect Fourier-series and Laplace-transform explanations with dynamic systems.
- Understand the role of matrix exponentials in the final source lesson.
Skills you’ll gain
- Differential equations
- Dynamic systems
- Heat-equation intuition
- Fourier series
- Laplace transforms
- Visual reasoning
Course Overview
The sequence begins with a tourist’s guide to differential equations and the idea of describing change. The next recordings introduce partial differential equations and the heat equation, then use Fourier series to connect mathematical decomposition with a visual example. Euler’s formula provides a bridge into the two Laplace-transform lessons, while the final matrix-exponential recording extends the view to linear systems. All eight source videos are retained. This is a conceptual teaching tour, not a promise of every computational technique in a university differential-equations syllabus. Its strength is helping you recognize why a method is useful and how a symbolic description can connect with geometry, motion or the evolution of a system.
How to study the course
- Begin with the introductory guide and the two heat-equation recordings. Keep track of which quantity changes and what the equation says about that change.
- Work through Fourier series and the Euler-formula prelude. Recreate a small visual example so the transformation remains connected with something you can describe.
- Complete both Laplace-transform lessons and the matrix-exponential recording. Compare the problems each method is helping you understand instead of treating their names as interchangeable.
Use the searchable classroom lesson list to revisit a specific explanation. Pause after a useful demonstration, reproduce a small example and explain the result in your own words. Keep a short note of what worked, what changed and what you still need to understand before moving on.
Who is this for?
The course suits students beginning differential-equations study, technically curious learners and people who want a visual supplement to symbolic coursework. It can also help a returning learner rebuild intuition before practising formal solution methods elsewhere.
Before you start
Basic calculus, algebra and comfort with functions are recommended. Familiarity with vectors and matrices is helpful for the final recording. The classroom contains explanatory videos, with no instructor-marked problem set, full textbook or academic credit included.
Put the lessons into practice
Choose a simple changing system, such as a cooling object or a pendulum, and describe its variables and the type of change you want to understand. Sketch how a possible state evolves without attempting to claim a precise real-world prediction. Next, make a comparison sheet for Fourier series, Laplace transforms and matrix exponentials, noting the question each explanation addresses. Reproduce one small visual idea from the relevant lesson and write what the picture makes easier to understand. Keep any uncertain algebra separate from your conceptual explanation and revisit the source recording.
This optional activity is provided by WikiFree for independent practice. It is not a graded assignment from the instructor. Keep your working notes, check the result against the task you defined and return to the relevant lesson when an assumption or technique is unclear.
Certificate / Assessment
Watching the public videos and using WikiFree progress tracking does not award a certificate, exam voucher, academic credit or instructor assessment.
Use your practice output to review what you can now explain and repeat independently. Completion tracking records your study progress; it does not replace an assessed qualification or professional experience.
Related courses for your next step
- Explore a higher-level optionDifferential Equations: Free Course
Focus: First-order methods · Second-order equations
Professional - Compare another approachFree MIT Course: Differential Equations through Short Lessons
Focus: Gilbert and Cleve Introduction · Impulse Response and Step Response
Intermediate - Compare another approachDifferential Equations: AP Calculus BC: Free Course
Focus: Slope fields · Separable equations
Intermediate
Compare course focus, level and study time
| Course | Level | Focus | Study time |
|---|---|---|---|
| This course — Visual Differential Equations: Free Course | Intermediate | Differential equations · Dynamic systems · Heat-equation intuition | 3h 16m of video; practice time is additional |
| Differential Equations: Free Course | Professional | Differential equations · First-order methods · Second-order equations | 8h 20m of video; practice time is additional |
| Free MIT Course: Differential Equations through Short Lessons | Intermediate | Gilbert and Cleve Introduction · Impulse Response and Step Response · The Tumbling Box in 3-D | 16h 25m of video; practice time is additional |
| Differential Equations: AP Calculus BC: Free Course | Intermediate | Slope fields · Separable equations · Euler's method | 2h 59m of video; practice time is additional |
Frequently asked questions
Is this course free to watch?
Yes. The public video lessons can be viewed in the WikiFree classroom. Free viewing does not include paid software, service subscriptions, provider membership benefits or a credential.
How long does the course take?
The 8 source videos total approximately 3h 16m. Allow additional time for pausing, practice, reviewing an example and checking your own result.
What background do I need?
Basic calculus, algebra and comfort with functions are recommended. Familiarity with vectors and matrices is helpful for the final recording. The classroom contains explanatory videos, with no instructor-marked problem set, full textbook or academic credit included.
Does watching the course award a certificate?
No. Video viewing and WikiFree progress tracking do not award a certificate, credit or an exam voucher.
Can I study on a phone?
Yes. The classroom has a responsive player and searchable lesson list. A larger screen and suitable practice environment are helpful for following software demonstrations or technical examples.
Provider: 3Blue1Brown. Videos play from the 3Blue1Brown channel on YouTube.
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