Free Multivariable Calculus Course: 35+ Video Lectures from Academa

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A complete multivariable calculus course, free, with 35+ video lectures. You can start learning in 30 seconds with no signup.

TLDR:

35+ video lectures covering a full university semester of multivariable calculus, from vectors through Stokes’ theorem.
Lectures are 20–40 minutes each, with clear blackboard-style explanations and a built-in video player with chat.
No signup, no ads, no paywall. Open the site and start watching.
Runs on the Academa.ai platform with video quality options and a sidebar for navigating topics.

Prerequisites: Single-variable calculus (derivatives, integrals, the fundamental theorem). Familiarity with basic linear algebra helps but is not required.

Step 1: Open the course

Go to calculus.academa.ai. That’s it. No account, no email, no “start your free trial.” The lecture list loads immediately with five sections: Vectors and the Geometry of Space, Vector Functions, Partial Derivatives, Multiple Integrals, and Vector Calculus.

Step 2: Pick your starting point

The course is designed to be taken in order, but each lecture stands on its own if you need to review a specific topic. Vectors start with the basics (magnitude, direction, addition) and build up through dot products, cross products, and lines and planes in 3D space; this is about six lectures total. If you already know this material, jump straight to Partial Derivatives or Multiple Integrals.

Step 3: Watch and follow along

Each lecture is a recorded blackboard session with a live instructor. The video player includes a chat panel on the right for questions. Lectures range from 9 minutes (Tangent Plane, Normal Vector to Surface) to 41 minutes (Double Integration), with most around 25–30 minutes.

The sweet spot is the Multiple Integrals section: eight lectures covering double and triple integration in Cartesian, polar, cylindrical, and spherical coordinates, plus a general change of variables. This is where multivariable calculus really separates from single-variable.

Step 4: Work through Vector Calculus

The final section covers vector fields, line integrals, Green’s theorem, curl and divergence, parametric surfaces, surface integrals, and Stokes’ theorem. This is the payoff, the material that makes sense of Maxwell’s equations and fluid dynamics. Stokes’ theorem in particular is worth the whole course.

Pro tip: Watch Lecture 33 (Big Picture of Integration, Stokes’ Theorem) even if you skip everything else. It connects all the integration theorems into a single framework and is the best explanation of the generalized Stokes theorem I have seen in a free course.

If it breaks

There is nothing to break. It is a web page with videos. If a video does not load, try a different browser. The site uses Bunny.net for video delivery, which generally works everywhere.