Calculus symbols and what they mean
The notation of derivatives, integrals and limits, with the lookalikes separated out — ∂ is not a d, ∇ is not a triangle, and the prime ′ is not an apostrophe. Click any symbol with a link to copy it and see how to type it on Windows, Mac, Word, Google Docs and in LaTeX.
Also known as: calculus symbols, symbols of calculus, calculus notation, symbols for integration.
22 symbols, 15 with a full copy-and-type guide.
Derivatives
| ′ | Prime — f′(x) is the first derivative, f″(x) the second. Read “f prime”. How to type ′ → | |
| ∂ | Partial derivative — ∂f/∂x, the rate of change in one variable holding the others fixed. How to type ∂ → | |
| ∇ | Nabla / del — builds the gradient, divergence and curl. The “upside-down triangle”. How to type ∇ → | |
| Δ | Delta — a finite change in a quantity, as in Δy/Δx before you take the limit. How to type Δ → | |
| d | The differential, as in dy/dx and the dx of an integral. | |
| ẋ | Newton's dot notation — the derivative with respect to time. |
Integrals
| ∫ | Integral — the area under a curve, or the antiderivative. How to type ∫ → | |
| ∬ | Double integral, over a two-dimensional region. | |
| ∮ | Contour integral, around a closed path. | |
| ∞ | Infinity — most often as a limit of integration or of a limit. How to type ∞ → |
Limits and series
| lim | Limit — the value a function approaches. | |
| → | Tends to — x → 0 is read “as x approaches zero”. How to type → → | |
| Σ | Summation — the sum of a series. How to type Σ → | |
| ∏ | Product — the multiplicative counterpart of Σ. How to type ∏ → | |
| ε | Epsilon — the arbitrarily small number in an ε-δ proof. | |
| δ | Lowercase delta — the other half of an ε-δ proof. |
Relations and sets used throughout
| ℝ | The real numbers — the usual domain of a calculus function. How to type ℝ → | |
| ∈ | Is an element of — x ∈ [a, b]. How to type ∈ → | |
| ≈ | Approximately equal to. How to type ≈ → | |
| ≤ | Less than or equal to — the usual form of an interval bound. How to type ≤ → | |
| ≥ | Greater than or equal to. How to type ≥ → | |
| ± | Plus or minus. How to type ± → |