Analysis & CAS — ChatMath Wiki

Derivatives — Implemented

Ableitung( <Funktion> ) / Ableitung( <Funktion>, <n> )

Aliases: derivative, Derivative, f'

✓ Done

Symbolic derivative. Optional second argument gives the n-th derivative.

Ableitung(x^3 + 2x^2 - x)   → 3x² + 4x - 1
Ableitung(sin(x))            → cos(x)
Ableitung(x^5, 3)            → 60x²  (3rd derivative)

Partialableitung( <f(x,y)>, <Variable> )

Aliases: partialderivative

✓ Done

Partial derivative with respect to the specified variable.

Partialableitung(x^2 * y + y^3, x)   → 2xy
Partialableitung(x^2 * y + y^3, y)   → x² + 3y²

Integration — Implemented

Integral( <Funktion> ) / Integral( <Funktion>, <a>, )

Aliases: integral, Integral, integrate

✓ Done

Indefinite integral (no bounds) or definite integral from a to b.

Integral(x^2)             → x³/3
Integral(sin(x))          → -cos(x)
Integral(x^2, 0, 3)       → 9
Integral(e^x, 0, 1)       → e - 1 ≈ 1.7183

IntegralZwischen( <f>, <g>, <a>, )

Aliases: IntegralBetween

✓ Done

Area between two functions from a to b: ∫[f(x) - g(x)]dx.

IntegralZwischen(x^2, x, 0, 1)   → 1/6

Limits & Series — Implemented

Grenzwert( <f>, <Variable>, <Wert> )

Aliases: limit, Limit, lim

✓ Done

Computes the limit of f as variable approaches the given value.

Grenzwert(sin(x)/x, x, 0)          → 1
Grenzwert((1 + 1/n)^n, n, ∞)      → e
Grenzwert((x^2-1)/(x-1), x, 1)    → 2

TaylorPolynom( <f>, <a>, <n> )

Aliases: taylorpoly, TaylorPolynomial

✓ Done

Taylor polynomial of degree n around point a.

TaylorPolynom(e^x, 0, 4)
→ 1 + x + x²/2 + x³/6 + x⁴/24
TaylorPolynom(sin(x), 0, 5)
→ x - x³/6 + x⁵/120

Solvers — Implemented

Löse( <Gleichung> ) / Löse( <Gleichung>, <Variable> )

Aliases: solve, Solve

✓ Done

Symbolic equation solver. Returns exact solutions. For systems, pass a list of equations.

Löse(x^2 - 5x + 6 = 0)           → {2, 3}
Löse(x^2 + 1 = 0)                 → {i, -i}  (complex)
Löse({x+y=3, x-y=1}, {x,y})      → {x=2, y=1}

LöseNumerisch( <f>, <start> )

Aliases: NSolve, nsolve

✓ Done

Numerical root-finder using Newton's method. Give a starting point near the expected root.

LöseNumerisch(cos(x) - x, 1)   → 0.7391  (Dottie number)

Nullstelle( <f> ) / Nullstelle( <f>, <a>, )

Aliases: Root, root

✓ Done

Finds zeros of a function. With bounds, uses bisection search in [a, b].

Nullstelle(x^2 - 4)           → {-2, 2}
Nullstelle(sin(x), 3, 4)      → 3.14159

Function Analysis — Implemented

Extremwert( <f>, <a>, )

Aliases: extremum, Extremum

✓ Done

Finds local minima and maxima of a function over an interval.

Extremwert(x^3 - 3x, -3, 3)   → {(-1, 2), (1, -2)}

Wendepunkt( <f> )

Aliases: inflection, InflectionPoint

✓ Done

Inflection points — where the second derivative changes sign.

Wendepunkt(x^3 - 3x)   → (0, 0)

Flächeninhalt( <f>, <a>, )

Aliases: area, Area

✓ Done

Absolute area between f(x) and the x-axis from a to b (handles sign-crossing).

Flächeninhalt(sin(x), 0, 2π)   → 4

Coming Soon

Kurvenintegral( <f>, <Kurve>, <a>, )

⏳ Soon

Line integral along a parametric curve from parameter a to b.

DGl( <dy/dx>, <x0>, <y0>, <endx> )

⏳ Soon

Differential equation solver — numerical integration using RK4 from initial condition.

RiemannSumme( <f>, <a>, , <n>, <Typ> )

⏳ Soon

Riemann sum approximation. Type: "left", "right", "mid", or "trapez".

RiemannSumme(x^2, 0, 1, 100, "mid")   → ≈ 0.3333

Bogenlänge( <f>, <a>, )

⏳ Soon

Arc length of f(x) from a to b: ∫√(1 + f'(x)²) dx.

Bogenlänge(sqrt(1-x^2), -1, 1)   → π  (semicircle)

📈 Analysis & CAS