Interactive visual explainers for CSIR NET Maths

Play with the theorems

Interactive explainers that let you move the mathematics: drag ε and watch δ answer, walk the topologist's sine curve, trap a subsequence by bisection, watch Newton's method fall into a cycle. 15 are free to play right here — the rest come with Trap Analysis.

Video explainers

Narrated walk-throughs of the trickiest ideas, made for this site — no ads, no recommendations pulling you elsewhere. Free to watch whether or not the interactive below is unlocked.

A set with no measure: the Vitali construction
Lebesgue Measure and Integration › Measurable sets and functions
Baire category, and the argument it powers
Metric Spaces › Completeness and Baire category

Unit 3Ordinary Differential Equations › Linear ODE, Wronskian, variation of parameters, systems#

The Wronskian: all or nothing, by Abel's identityinteractivefree

Step 1 / 4Abel's identity

For $y'' + p(x)y' + q(x)y = 0$ with $p,q$ continuous on an interval $I$ , the Wronskian of two solutions satisfies $W' = -pW$ , so

$W(x) = W(x_0)\exp\left(-\int_{x_0}^x p\right).$

The exponential never vanishes.

Unit 3Partial Differential Equations › Classification and canonical forms#

Classifying a second-order PDE, and the type that changesinteractivefree

Step 1 / 4The discriminant

For $Au_{xx} + Bu_{xy} + Cu_{yy} + \cdots = 0$ , compute $B^2-4AC$ :

$<0$ elliptic (Laplace)
$=0$ parabolic (heat)
$>0$ hyperbolic (wave)

Unlock every visual

Every interactive explainer comes with Trap Analysis — along with the worked solutions, the per-option trap diagnosis and the counterexample objects. The papers, the book and the video map are free without it.

See pricing