Interactive mathematics

Learn by trying it.

These tools are built into the reference itself. Calculate, experiment and then jump straight into the mathematics behind the result.

Algebra

Solve and explore equations.

Solve equations of the form ax + b = 0 and understand the special cases.

Find real or complex roots and inspect the discriminant of ax² + bx + c = 0.

Solve two simultaneous linear equations and connect the result to matrix form and geometry.

Calculus

Differentiate a cubic polynomial, evaluate the slope at x₀ and generate the tangent line.

Inspect critical points of cubic functions and connect first and second derivatives to graph shape.

Compute a definite polynomial integral and compare it with a midpoint-rectangle approximation.

Watch geometric, p-series and alternating harmonic partial sums approach — or fail to approach — a limit.

Multivariable & vector calculus

Evaluate a quadratic surface gradient, its magnitude and the direction of steepest ascent.

Explore divergence and curl for a linear two-dimensional vector field.

More than calculators

Change inputs and build intuition from immediate feedback.

Each tool lives beside definitions, derivations and worked examples.

Use the tool to verify hand calculations without replacing the reasoning.

Follow the surrounding learning path instead of ending at a numerical answer.