Matrix A
Matrix B (for systems)
Preset examples
Extended Matrix Calculator
Concepts: determinant = area scaling · eigenvalues from λ² − tr·λ + det = 0 · rank reveals singularity · LU speeds up solving · Gram-Schmidt produces orthonormal basis · Power Method finds dominant eigenpair.
Derivation (KaTeX)
GeoGebra Script
f(x) = a·x³ + b·x² + c·x + d
a
b
c
d
Tangent at x₀ =
Preset examples
Concepts: f′(x)=0 locates critical points; f″(x)>0 ⇒ local minimum, f″(x)<0 ⇒ local maximum. Tangent slope at x₀ is f′(x₀).
Derivation (KaTeX)
GeoGebra Script
∫ from a to b of f(x) dx
f(x) =
a =
b =
Preset examples
Concepts: Simpson's 1/3 rule composites the parabola approximation. Error O(h⁴).
Derivation (KaTeX)
GeoGebra Script
2nd order linear: y″ + p·y′ + q·y = 0
p
q
y(0)
y′(0)
Preset examples
Concepts: Characteristic roots r = (−p ± √(p²−4q))/2.
Derivation (KaTeX)
GeoGebra Script
Vector field F = (P, Q)
Preset field
Preset textbook examples
Concepts: div F measures source density. In 2D, curl F = ∂Q/∂x − ∂P/∂y measures rotation.
Derivation (KaTeX)
GeoGebra Script
Laplace Transform ℒ{f(t)} = F(s)
f(t) =
Parameter (a, n, or ω)
Preset examples
Concepts: ℒ{f} = ∫₀∞ e−stf(t) dt.
Derivation (KaTeX)
GeoGebra Script