Calculus notation in MV Workstation
Write calculus the way it looks on paper: integrals, derivatives, partial derivatives, limits, sums, products, piecewise functions and aligned working. This is notation only, so it is typeset beautifully and kept exactly as typed; solving will be added step by step.
Type the maths the way you write it and MV Workstation shows the exact answer, the working and, where it helps, a picture you can drag.
Things to try
| What it is | Type this |
|---|---|
| Indefinite integral | integral(x^2, x) |
| Definite integral | integral(x^2, x, 0, 3) |
| Area under a curve | integral(sin(x), x, 0, pi) |
| Double integral | integral2(x y, x, y, 0, 1, 0, 2) |
| Derivative | derivative(x^3, x) |
| Second derivative | derivative(y, x, 2) |
| Partial derivative | partial(f, x) |
| Mixed partial | partial(f, x, y) |
| A limit | limit(sin(x)/x, x, 0) |
| A limit at infinity | limit((1 + 1/n)^n, n, infinity) |
| A one-sided limit | limit(1/x, x, 0, right) |
| A sum | sum(k^2, k, 1, n) |
| A product | product(k, k, 1, n) |
| A piecewise function | f(x) = cases(x^2, x >= 0; -x, x < 0) |
| Lined-up working | align(2x + 3 = 11; 2x = 8; x = 4) |
| Divergence | div(F) = partial(P, x) + partial(Q, y) |
| Prime notation | f'(x) = 2x |
| Typed as written: integral | ∫_0^3 x^2 dx = 9 |
| Typed as written: sum | ∑_{k=1}^n k = {n (n + 1)} / 2 |
| Typed as written: limit | lim_{x→0+} 1/x |
| Typed as written: derivative | dy/dx = 2x |
| Operator on its own | d/dx (x^2 + 1) = 2x |
| Evaluation bar | integral(x^2, x, 0, 3) = evalat(x^3 / 3, 0, 3) |
| Higher derivative | f^(4)(x) = derivative(f, x, 4) |
| Newton dots | dot(x) = v |
| Line integral | \int_C F dr |
| Sum with a condition | sum(k, 0 <= k <= n) |
| Limit superior | limsup(a_n, n, infinity) |
Functions
| Function | What it does | Example |
|---|---|---|
integral(f, x, a, b) | An integral of f with respect to x. Give just f and x for an indefinite integral, or add the lower and upper limits a and b. A single extra argument names a curve or region instead, written under the sign: integral(F, r, C). | integral(x^2, x, 0, 3) |
integral2(f, x, y, x0, x1, y0, y1) | A double integral ∬. Give f and the two variables, and optionally the limits of x then of y, or a single region such as S written under the sign. | integral2(x y, x, y, 0, 1, 0, 2) |
integral3(f, x, y, z, V) | A triple integral ∭ of f over x, y and z. An optional last argument names the region, written under the sign. | integral3(x y z, x, y, z) |
contour(f, x, C) | A closed-curve (contour) integral ∮. The optional third argument names the curve, written under the sign. | contour(f, z, C) |
derivative(f, x, n) | The derivative d/dx of f. A third argument n gives the order: derivative(y, x, 2) is d²y/dx². Leave f as {} to write the operator d/dx on its own. | derivative(y, x, 2) |
partial(f, x, y, z, w, v) | A partial derivative ∂f/∂x. Add more variables for mixed or higher ones: partial(f, x, y) is ∂²f/∂x∂y, partial(f, x, x) is ∂²f/∂x². | partial(f, x, y) |
limit(f, x, a, side) | The limit of f as x approaches a, with x → a written under lim. The optional fourth argument is right or left for a one-sided limit. a can be infinity. | limit(sin(x)/x, x, 0) |
limsup(f, n, a) | The limit superior, written lim sup with the approach underneath. | limsup(a_n, n, infinity) |
liminf(f, n, a) | The limit inferior, written lim inf with the approach underneath. | liminf(a_n, n, infinity) |
evalat(F, a, b) | An evaluation bar: F written in square brackets with the limits a and b at the foot, the step after integrating. Give only a for a single point. | evalat(x^3 / 3, 0, 3) |
dot(x) | A dot over a letter, Newton's notation for the derivative with respect to time. ddot(x) is two dots. | dot(x) |
ddot(x) | Two dots over a letter: the second derivative with respect to time. | ddot(x) |
sum(f, k, from, to) | A sum ∑ with the index and its limits above and below: sum(k^2, k, 1, n). Leave out the limits to show only the index, or give a condition such as sum(k, 0 <= k <= n). | sum(k^2, k, 1, n) |
product(f, k, from, to) | A product ∏ with the index and its limits above and below. prod means the same. | product(k, k, 1, n) |
cases(v1, c1, v2, c2, ...) | A piecewise function: a big brace with one row per value and condition. Separate with commas, or use ; between rows. A condition can be a word such as otherwise. | f(x) = cases(x^2, x >= 0; -x, x < 0) |
align(line1, line2, ...) | Several lines of working lined up on their = signs. Separate lines with ; or commas. | align(x + 1 = 3; x = 3 - 1; x = 2) |
grad(f) | The gradient ∇f. | grad(f) |
div(F) | The divergence ∇·F. | div(F) |
curl(F) | The curl ∇×F. | curl(F) |
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