Calculus animations made with AI

Limits, derivatives, integrals and series are easiest to understand when you can watch a secant line become a tangent or see Riemann rectangles converge. These narrated calculus animations were generated from one-sentence prompts and verified so that every label and formula stays readable.

Prompts to start from

• Show how the derivative of sin(x) is cos(x) using the unit circle
• Animate Riemann sums converging to the integral of x² from 0 to 2
• Visualize the chain rule as nested rates of change

Calculus animations from the gallery

Where e comes from: compounding more and more often

This animation tracks one dollar growing under 100% annual interest as the number of compounding periods incre…

Gradient descent: walk downhill on the loss

A ball rolls along the parabola L(w) = (w-3)^2 + 1, starting at w = -1 and updating via w <- w - eta dL/dw wit…

The harmonic series diverges

Bars representing 1/n shrink toward zero, illustrating why it seems the sum should settle down. The animation …

The squeeze theorem: why sin x / x tends to 1

This animation visualizes why sin x / x approaches 1 as x approaches 0, even though the function itself is und…

Optimization: the biggest rectangle for a fixed perimeter

An animation shows a rectangle with fixed perimeter 20 changing shape as its width varies, tracing the area fu…

Newton's method: follow the tangent to the root

Starting from x0 = 2.5 on f(x) = x^2 - 2, this animation draws each tangent line and follows it down to the x-…

1/2 + 1/4 + 1/8 + ... = 1: filling a square

A unit square is progressively filled by repeatedly halving the remaining area, generating the series 1/2 + 1/…

Taylor polynomials of sin x

This animation overlays the sine curve with its Taylor polynomials of degree 1, 3, 5, 7, 9, and 11, drawn one …

The fundamental theorem of calculus: area has a derivative

A curve f is shown alongside a second graph tracking A(x), the running area under f from 0 to x. As x sweeps r…

The derivative as the limit of secant slopes

An animation tracks secant lines through the fixed point (2, f(2)) on f(x) = x^2/4 + 1/2 as the second point s…

Riemann sums become the integral

This animation approximates the area under y = x^2 from 0 to 2 using rectangles, starting with four and doubli…

Solving Second-Order Linear ODEs

This animation walks through solving a linear second-order differential equation with constant coefficients by…

Questions

What is in the Vismo Library?

Hand-reviewed, verified math and science animations organised by topic: calculus, algebra, geometry, trigonometry, linear algebra, probability, number theory, physics, chemistry and computer science. Every item passed the frame-by-frame layout check and a human review. Anyone can watch; paid members download the video and the Manim source file.

Can I use Library animations in my lessons and videos?

Yes. Paid plans include unlimited MP4 downloads for classroom use, plus Adapt: change the pace, colours, numbers or narration of any Library animation and create a version for your classroom or course. Adaptations show an estimate before you start and charge actual usage. Creators are credited on the Library page; no attribution is required inside your lesson.

How long does it take to generate an animation?

Generation time depends on the model, scene complexity, video length and narration. Vismo shows progress while it writes the scene, prepares speech and renders the video. Complex lessons can take several minutes.