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The notation of change: the differential operators, the four competing ways of writing a derivative, the higher integrals, and the vocabulary of bounds and limits. What holds the group together is that almost every member is a mark whose meaning lives somewhere other than in its shape — in a superscript that decides whether a limit exists at all, in a strike through an integral sign that reverses what the expression asserts, in the difference between a straight d and a curled one that changes the answer. Several members exist mainly to state the trap: that dy/dx is not a fraction, that a zero Wronskian proves nothing, that the same asterisk means convolution here and conjugation two pages later.
Three integral signs side by side, integrating over a three-dimensional region.
An integral sign whose limits name a curve rather than two numbers.
An integral sign struck through with a short bar, meaning a symmetric limit around a singularity.
Del followed by a dot, measuring outward flow from a point.
Del followed by a cross, measuring rotation about a point.
A subscripted del or a dotted gradient, giving the rate of change along one chosen direction.
A dot above a variable, meaning its derivative with respect to time.
An apostrophe after a function name, meaning its derivative.
A d over a d, naming both the function and the variable differentiated against.
A capital D applied to a function, meaning differentiation as an operation in its own right.
An upright d drawn with a straight stroke, against the curled ∂ of a partial derivative.
A ∂ over a ∂ with parenthesised lists, the determinant of a matrix of partial derivatives.
A capital H of second partial derivatives, testing whether a stationary point is a maximum or a minimum.
A capital W of a set of functions, testing whether they are linearly independent.
A superscript plus or minus on the limit point, approaching from one side only.
lim sup, the largest value a sequence returns to infinitely often.
lim inf, the smallest value a sequence returns to infinitely often.
sup, the least upper bound of a set, which need not belong to the set.
inf, the greatest lower bound of a set, which need not belong to the set.
A small six-pointed star set between two functions, combining them by sliding one across the other.
A small circle between two matrices, multiplying them entry by entry.