Calculus
Lagrange Notation
| Latex | MathJSON |
|---|---|
f'(x) | ["Derive", f, x] |
f''(x) | |
f\prime(x) | |
f\prime\prime(x) | |
f\doubleprime(x) | |
f^{\prime}(x) | |
f^{\prime\prime}(x) | |
f^{\doubleprime}(x) |
@todo: f^{(4)}
Leibniz Notation
| Latex | MathJSON |
|---|---|
\frac{\partial f}{\partial x} | |
\frac{\partial^2 f}{\partial x\partial y} |
Euler Modified Notation
This notation is used by Mathematica. The Euler notation uses D instead of \partial
| Latex | MathJSON |
|---|---|
\partial_{x} f | |
\partial_{x,y} f |
Newton Notation (@todo)
\dot{v} -> first derivative relative to time t \ddot{v} -> second derivative relative to time t
Integral
Indefinite Integral
\int f dx -> [“Integrate”, f, x,] \int\int f dxdy -> [“Integrate”, f, x, y]
Note: ["Integrate", ["Integrate", f , x], y] is equivalent to ["Integrate", f , x, y]
Definite Integral
\int_{a}^{b} f dx -> [“Integrate”, f, [x, a, b]] \int_{c}^{d} \int_{a}^{b} f dxdy -> [“Integrate”, f, [x, a, b], [y, c, d]]
\int_{a}^{b}\frac{dx}{f} -> [“Integrate”, [“Power”, f, -1], [x, a, b]]
\int_{a}^{b}dx f -> [“Integrate”, f, [x, a, b]]
If [a, b] are numeric, numeric methods are used to approximate the integral.
Domain Integral
\int_{x\in D} -> [“Integrate”, f, [“In”, x, D]]
Contour Integral
\oint f dx -> ["ContourIntegral", f, x,]
\varointclockwise f dx -> ["ClockwiseContourIntegral", f, x]
\ointctrclockwise f dx -> ["CounterclockwiseContourIntegral", f, x,]
\oiint f ds -> ["DoubleCountourIntegral", f, s] : integral over closed surfaces
\oiiint f dv -> ["TripleCountourIntegral", f, v] : integral over closed volumes
\intclockwise
\intctrclockwise
\iint
\iiint